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Investigation for surface resistance of yttrium -barium -copper -oxide thin films on various substrates for microwave applications

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INVESTIGATION FOR SURFACE RESISTANCE OF
YTTRIUM-BARIUM-COPPER-OXIDE THIN FILMS
ON VARIOUS SUBSTRATES FOR
MICROWAVE APPLICATIONS
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INVESTIGATION FOR SURFACE RESISTANCE OF
YTTRIUM-BARIUM-COPPER-OXIDE THIN FILMS ON
VARIOUS SUBSTRATES FOR MICROWAVE APPLICATIONS
A dissertation submitted in partial fulfillment
o f the requirements for the degree o f
Doctor o f Philosophy
By
Hongjun Yao, B.S., M.S.
Fudan University, 1993
Fudan University, 1996
May 2002
University o f Arkansas
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UMI Number: 3055351
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All rights reserved. This microform edition is protected against
unauthorized copying under Title 17, United States Code.
ProQuest Information and Learning Company
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P.O. Box 1346
Ann Arbor, Ml 48106-1346
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This dissertation is approved for
recommendation to the
Graduate Council
Dissertation Directors:
ODr. Fred D. Barlow
Assistant Professor of Electrical Engineering
fry J. Salamo
University Professor of Physics
Dissertation Committee:
Dr. William D. Brown
University Professor of Electrical Engineering
til, fk'm
( J lL & tt
Dr. William F. Oliver III
Associate Professor of Physics
Dr. Paul M. Thibado
Associate Professor of Physics
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Dedication
This work is dedicated to my parents for their long time support. It is also dedicated to
my dearest wife Jiankun and our son Ethan for whose love, patience and
encouragement made it all possible.
iii
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Acknowledgements
I would like to express my sincere appreciation to my major professors Dr. F. D.
Barlow and Dr. G. J. Salamo for their guidance and encouragement throughout this
work.
I would also like to thank Dr. S. S. Ang, Dr. W. D. Brown, Dr. W. F. Oliver III, and
Dr. P. M. Thibado for their insightful discussion and suggestions and for serving on
my dissertation committee.
Special thanks go to Dr. F. T. Chan and Dr. W. A. Luo for their great help to my work.
I would also like to acknowledge S. Afonso, K. Y. Chen, and S. Yan for their previous
work that is still helpful to my research.
iv
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CONTENTS
Chapter 1 Introduction
1
1.1 Background
1
1.2 Purpose o f the Work
4
1.3 Outline o f the Dissertation
5
Chapter 2
Surface Resistance Characterization, HTS
Materials and Substrates
2.1 Surface Resistance o f Superconductor and its Characterization
2.1.1 Superconductivity and Surface Resistance
2.1.2 Surface Resistance Characterization
2.2 Material Selection and YBCO Properties
6
6
6
11
16
2.2.1 HTS Material Selection
16
2.2.2 Substrate selection
17
2.2.3 YBCO Structure and Properties
20
2.2.4 YSZ Structure and Properties
22
Chapter 3 Transmission Line and Loss
23
3.1 Transmission Line Using Lumped-Element Circuit Model
23
3.1.1 General Solutions
23
3.1.2 Lossless Transmission Lines
26
3.1.3 Lossy Transmission Lines
27
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3.2 Loss in Microstrip
30
3.2.1 Formulas for Effective Dielectric Constant
and Characteristic Impedance
31
3.2.2 Microstrip Loss
33
Chapter 4 S Parameter, Network Analyzer and Ring Resonator
4.1 S Parameter
42
43
4.1.1 Impedance and admittance matrices
43
4.1.2 The Scattering Matrix (S Matrix)
46
4.2 The Vector Network Analyzer
47
4.2.1 Basic Principles o f Vector Network Analyzer
47
4.2.2 A Shift in Reference Planes and Calibration
SO
4.2.3 Calibration o f Low Temperature Measurement
S4
4.3 Ring Resonator and Quality Factor
S8
4.3.1 Ring Resonator
58
4.3.2 Coupling Gap o f Ring Resonator
60
4.3.3 Q-factor and Attenuation Constant
61
4.3.4 The Procedure to Calculate Surface Resistance
64
Chapter 5 Thin Film Deposition, Patterning and Characterization Systems
S. 1 Thin Film Deposition System
67
67
S. 1.1 Pulsed Laser Deposition (PLD)
67
5.1.2 Ion Beam Assisted Deposition (IBAD)
70
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5.2 Film Patterning System
72
5.3 Thin Film Characterization System
73
5.3.1 X-ray Diffraction
73
5.3.2 Tc and Jc Measurements
78
Chapter 6 Fabrication
85
6.1 Fabrication of YBCO Ring Resonators
85
6.1.1 Structure o f Ring Resonators
85
6.1.2 Substrate Preparation
90
6.1.3 IB AD YSZ Deposition for Alumina Substrate
91
6.1.4 YBCO Deposition
93
6.1.5 Copper Deposition
97
6.1.6 Patterning: Lithography and Ion Milling
97
6.1.7 Resonator Packaging
99
6.2 Characterization of YBCO Thin Films on Various Substrates
101
6.2.1 Electrical Characterization
101
6.2.2 X-ray Diffraction
101
Chapter 7 Results and Discussion
103
7.1 Alumina Substrate with IB AD YSZ Buffer Layer
103
7.1.1 Surface Resistance o f YBCO thin film
103
7.1.2 XRD Results o f YBCO Thin Film on Alumina
111
7.2 YSZ Single Crystalline Substrate
vii
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115
7.2.1 Surface Resistance o f YBCO Thin Film
115
7.2.2 Mechanism o f YBCO In-Plane Orientation on YSZ
121
7.2.3 Surface Resistance Using Improved Process
129
7.3 LaA103 Single Crystalline Substrate
132
7.4 Tunable Spiral Resonator
141
7.4.1 Basic Principle o f Tunable Spiral Resonator
141
7.4.2 Measurement o f Tunable Spiral Resonator
142
7.4.3 Mechanism o f Frequency Tuning
152
Chapter 8 Conclusions and Future Work
159
8.1 Conclusions
159
8.2 Future Work
162
Reference
165
Appendix I
174
Appendix II
177
Appendix III
181
viii
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CHAPTER1
introduction
1.1 Background
Since the discovery o f high-temperature superconductors (HTSs) with critical
temperatures, T& above the boiling point o f liquid nitrogen (77K) [1-3], enormous
efforts have been made to find practical uses for them by inventing novel devices and
by replacing normal metals in devices with their HTS counterparts. HTS materials
have been used in many devices, such as multi-chip modules (MCMs) [4,5],
microwave devices [6-10], superconductive quantum interference devices (SQUIDs)
[11,12] and Josephson junctions [13,14]. Among them, the most widely used and
promising application involves passive microwave components, such as resonators,
filters, multiplexers and phase shifters. Because HTS materials have 10 to 1,000 times
lower surface resistance than copper at microwave frequencies and can carry current
density up to 107 A/cm2, many passive microwave components and circuits have been
fabricated from HTS materials with unprecedented high performance.
Filters are very important components in microwave circuits and systems [15]. The
function of a filter is to select a designated frequency band either to let the signal pass
through (bandpass) or to stop the signal from passing through (bandstop). The most
common bandpass filter configuration usually consists o f a series o f N resonators to
form a resonant system with IV resonances. The performance o f such a bandpass filter
depends on the number, IV, o f poles. As the number IV increases, the skirt o f the
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frequency response becomes steeper and the offband rejection becomes larger. Both
effects are desirable. However, at the same time, the inband insertion loss increases
with increasing IV because o f the low Q-factor o f the resonator elements made o f
normal metal. The caused high insertion loss sets an upper limit for IV. If N exceeds
this limit, the inband insertion loss becomes unacceptably high. But if the filters are
made o f HTS thin films with low surface resistance, the Q-factor will be orders o f
magnitude higher. The number of poles in the filter can be increased significantly
without sacrificing inband insertion loss. In other words, HTS materials can be used to
make high-performance multipole filters with very steep skirts o f frequency response,
high offband rejection and small inband insertion loss.
In many military and commercial applications, tunable filters with low insertion
loss and high-Q are very desirable because they can greatly enhance performance and
simplify system designs [16]. In the lumped element view o f filter implementation, the
frequency tuning is achieved by either tunable capacitors or tunable inductors. The
majority o f RF tunable filters have used varactor diodes whose depletion region
thickness, and hence the junction capacitance, is varied by changing the reverse bias
voltage [17]. Varactors have the advantage o f simplicity, but they suffer poor Q-factor
and high-frequency nonlinearity. The same problems also happen to so-called “tunable
materials” such as ferroelectries [18]. Using conventional microelectromechanical
systems (MEMS) variable capacitors can mitigate the problems o f nonlinearity
somewhat, but their geometries and implementation with normal metals limit the
attainable Q-factor, and most have serious microphonics problems due to extremely
2
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narrow gap (plate separation) and high-compliance designs necessitated by limitations
o f electrostatic attraction as the driving force.
These problems o f the conventional MEMS variable capacitors driven by
electrostatic force led to the invention o f a structure that is made entirely o f HTS
materials for uncompromised Q-factor. The operating principle behind the actuators is
the use o f magnetic drivers, instead of the weak electrostatic drivers normally used in
MEMS variable capacitors. This is possible due to the unique characteristics o f HTS
materials. A superconducting plate will resist the penetration o f magnetic flux into it,
so that the magnetic field created by passing current through a coil near the HTS plate
will exert a repulsive force between the coil and the plate. The advantage o f the
magnetic drivers is that the force remains nearly constant out to substantial distance
between the coil and the HTS plate, so that the actuator can have displacement ranges
o f a millimeter or more, which directly translates into wide frequency tuning range for
these filters. The simplified structure of the main part o f proposed all-HTS tunable
filter is illustrated in Fig. 1-1. The bottom substrate has all the circuits on it, such as
driving coils, feedback position sense resonator and signal filter, all o f which are made
from HTS thin films. The position of the bottom substrate is fixed during operation
and it has an average thickness of 20 mil or more. The top HTS thin film substrate
(toractor) is suspended above the bottom one with a small gap o f 4 mil using a
tensioned carbon fiber. The toractor may be rotated to different angles in response to
the magnetic force exerted by the driving coil on the bottom substrate, such that the
gap between toractor and the filter circuit is changed, allowing the desired frequency
response for the filter.
3
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Fig. 1-1 Simplified structure of all-HTS tunable filter [16|.
1.2 Purpose of the Work
In order to have a filter with a very quick response time, the toractor has to be
made on a very thin substrate (4 mil or less) to minimize the mass to be moved. These
thinned substrates create some significant challenges for manufacturing, and it is
unclear what range o f thickness is practical. A main objective o f this work was to
investigate the surface resistance o f HTS thin film on several substrate candidates to
optimize toractor design based on these alternatives. Another primary objective was to
demonstrate the concept o f the frequency tuning proposed using this design, as shown
in Fig. 1-1, so that more concrete parameters could be obtained for implementing the
entire filter structure in the future.
4
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1J Outline o f the Dissertation
Justification for the choice o f materials selected and a brief description of the
YBCO properties are given in Chapter 2. The basic theory o f transmission lines and
associated losses are described in Chapter 3. In Chapter 4, the concepts o f microwave
networks and their measurement, as well as die principle o f the ring resonator are
discussed. Descriptions o f various deposition and characterization systems used in this
work are presented in Chapter S. In Chapter 6, detailed descriptions of the processes
used to fabricate the devices are listed step by step. The characterization methods are
also briefly described. Results and discussions are given in Chapter 7. Chapter 8 gives
conclusions and suggestions for future work.
5
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CHAPTER 2
Surface Resistance Characterization, HTS Materials
and Substrates
In this chapter, general knowledge o f superconductivity and surface resistance is
first reviewed in section 2.1. The different techniques for determining the surface
resistance o f superconductors and comparison between them are also included in this
section. Justification for the choice o f HTS materials and substrates selected, and a
brief description o f the YBCO properties, are given in section 2.2.
2.1 Surface Resistance of a Superconductor and its Characterization
2.1.1 Superconductivity and Surface Resistance
Superconductors have zero resistance at DC conditions as long as the DC current
is smaller than the critical current o f the material.
However, at high frequency
conditions, superconductors exhibit a small resistance due to the normal electrons in
the material forming a conduction path in parallel with the superconducting electrons.
In Gorter and Casimir’s two-fluid model [19], it is assumed that the electrons of
superconductors can be divided into two distinct groups: normal electrons and
superconducting electrons at a temperature below the critical temperature. In BardeenCooper-Schreiffer (BCS) theory [19], the normal electrons are known as elementary
excitations, and the superconducting electrons as Cooper pairs that form the BCS
ground state. Two electrons with the same spin angular momentum magnitude but
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inverse direction can be attracted together to form a Cooper pair at temperatures below
Tc. The Cooper pairs can pass through the superconductor without suffering collisions
as the normal electrons do. According to the two-fluid model and classical
electrodynamics [13,14,19], the total current density in superconductors can be written
as:
j=Tn+T,=(*l - j * 2)E=\
[m [l+ o r )
where nn and n,
n ,e 2
n„e2T2o)
m<D
m\l + oj r )
(2.1)
are the number densities o f the normal electrons and
superconducting electrons, respectively, and r is the momentum relaxation time. The
real part of the complex conductivity involves only the normal electrons. For
© V « 1 ( / < 10“ H z), Eq. (2.1) can be reduced to [19]
. n ,e 2
o * a n- - J n
mto
n.
a n— ~ J
n
1
^ 0<ox 2
( 2 -2 )
9t€mX
where a n = ------- is the conductivity in the normal state, n is the total density o f the
m
conduction electrons, and A is the penetration depth. The temperature dependence o f
the London penetration depth [19],
A(f)= . A(QL =
f j\*
1Jc.
(2.3)
was used to derive the last equation.
The formula for the surface impedance o f a good conductor is given by [ 13,14]
7
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The real part o f Zs is the surface resistance, Rs- For a good normal conductor, surface
resistance has the form
V2 a .
=
2
where 8 =.
\a)H Qa
(2-5)
a .S
is the skin depth o f the conductor. The frequency dependence o f
Rs, results from the skin effect o f conductors. Using Eq. (2.2) for the complex
conductivity, the surface impedance o f superconductors can be derived from Eq. (2.4)
as [19]
1
H
* -nl<» 2A3cr„ — + y/<0fi)A.
2
n
(2.6)
The surface resistance o f superconductors is therefore
2
n
< 2 -7 >
It can be shown that the surface resistance o f HTS materials is much smaller than
that o f normal metals such as copper at frequencies lower than 1011 Hz. The low
surface resistance property makes HTS materials superior to normal conductors in
high frequency applications. Eq. (2.7) shows that the surface resistance o f HTS
materials is proportional to the square o f the frequency, whereas the surface resistance
o f a normal metal is proportional to the square root o f frequency as indicated by Eq.
(2.S). Therefore, die increasing rate of the surface resistance for HTS materials with
increasing frequency is much higher than that o f normal conductor. Hence, at
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frequency above 10n Hz, the advantage o f using HTS materials becomes less
significant. Furthermore, when the frequency is high enough, the Cooper pairs can be
destroyed and the superconductivity is lost. This is because the electromagnetic
energy, tu o , can be absorbed by Cooper pairs when hco > 2A , where 2A is the
energy gap o f a superconductor. So the HTS materials do not exhibit low-loss
2A
properties at frequencies co > — (typically above 10" Hz).
h
Although the two-fluid model is a quite simplified model, the results obtained still
give a reasonably accurate picture o f the high frequency behavior o f superconductors
as shown later on. Based on the BCS theory, Mattis and Bardeen developed a
microscopic treatment o f AC electrodynamics [20]. The Mattis-Bardeen theory is
much more complicated than the two-fluid model and contains other parameters such
as the energy, the mean free path and the coherent length. The intrinsic loss o f
superconductors is often compared to the predictions o f the phenomenological twofluid model or microscopic BCS theory.
Many groups have studied the surface resistance o f HTS materials [21-24]. Fig. 21 shows surface resistance versus frequency measured at various laboratories on
YBCO (YiBa2Cu307.x) thin films at 77 K [21]. High quality epitaxial YBCO films can
show a surface resistance as low as 0.3 m fl at 77 K and 10 GHz. In contrast, copper
has a surface resistance of 7-21 mO at 77 K and 10 GHz, depending on the purity and
processing o f the sample. Also shown in the figure is the surface resistance versus
frequency for Niobium at 7.7 K and copper at 77K. Obviously, from the plot, the
surface resistance o f YBCO is almost an order of magnitude or more smaller than that
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Iff4
HbT.7K
0.1
1
10
100
FREQUENCY (GHz)
Fig. 2-1 Surface resistance measurements at 77 K for thin films of YBCO from various
laboratories. The surface resistance of copper at 77 K and superconducting niobium at 7.7 K
are also shown for reference [211.
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o f copper for frequency up to 10 GHz. This difference decreases with increasing
frequency, but up to 100 GHz, YBCO is still better than copper. The plot also verified
the relation between surface resistance and operation frequency as predicted in Eq.
(2.7) based on simple two-fluid model. Other HTS materials also show very low
surface resistance at high frequency. One o f the Tl-based compounds exhibits an
even lower surface resistance than YBCO thin films [25,26]. At 77 K and 10 GHz, the
surface resistance o f high quality Tl2Ba2CaCu20s thin films was found to be - 0.13
m fr [26].
2.1.2 Surface Resistance Characterization
There are many different methods established for HTS thin film surface resistance
measurements. Generally, they can be divided into two categories: a destructive
method or a nondestructive method. Nondestructive methods measure the surface
resistance of unpattemed HTS thin films, while destructive methods measure patterned
transmission lines.
The commonly used nondestructive methods are discussed as follows:
Endwall Replacement Method
Historically, a cylindrical TEon mode cavity was used to measure the surface
resistance of low-temperature superconductors (LTS), such as niobium or lead. A
cylindrical cavity was made entirely o f LTS materials, which gave excellent
sensitivity. But the cylindrical shape o f the cavity limits this method for measuring the
surface resistance of materials that can readily be prepared on curved, as well as flat,
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surfaces. The electrical properties o f HTS materials are extremely anisotropic. Thin
films o f these materials cannot be readily deposited on curved surfaces, and bulk parts
fabricated into curved shapes have surface resistances much higher than those o f the
best thin films.
To make the TEou mode cavity technique suitable for measuring HTS thin films,
one or both o f the flat endwalls o f the cavity is replaced by the HTS thin films, while
the remainder o f the cav ity is made from a good normal conductor (usually copper) or
an LTS (usually niobium). This improved technique is called the endwall replacement
method because o f the new configuration of the cavity [27,28].
In order to determine the surface resistance o f the HTS thin films, the Q-factor of
the cavity needs to be measured twice, once with a copper endwall and once with the
endwall replaced by an HTS plate. By comparing the two Q-factors and solving for the
electromagnetic field inside the cavity, the surface resistance o f HTS materials can be
determined.
The sensitivity o f this method is limited by the fact that more than half o f the inner
walls (sidewall plus one endwall) o f the cavity are made o f copper, which has a much
higher surface resistance than a high-quality HTS thin film. The sensitivity can be
improved by replacing both endwalls with HTS materials. The cavities with higher
resonant frequency will increase the surface resistance o f HTS more than copper, as
stated before. Thus, the use of cavities operating at high frequencies allows for more
sensitive measurement o f the HTS intrinsic surface resistance, when scaled to lower
frequency as f 2. Also, using cavities with higher resonant frequencies can greatly
decrease the size o f the HTS samples.
12
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Parallel Plate Method
Because of the moderate sensitivity o f the endwall replacement method and the
need to measure extremely low surface resistance when temperatures approache 0 K,
the parallel plate method was developed to improve sensitivity [29,30]. A thin
dielectric film is placed as a spacer between a pair o f HTS films to form a parallel
plate resonator, which is a two-dimensional resonator with open circuit boundary
conditions along its edges. By measuring Q-factors of its main modes such as TEio
and TEu and solving for the electromagnetic field insider the dielectric, the surface
resistance of HTS films can be calculated.
The main advantage o f this method is its high sensitivity, which results from the
elimination of nonsuperconducting conductors from the resonant structure. But the
accuracy of this method mainly depends on the accuracy o f the spacer thickness
measurement. The air gap between the HTS films and the spacer can also cause
uncertainty in the measured values.
Dielectric Resonator Method
The dielectric resonator method is a versatile and relatively easy method o f
measuring surface resistance. In a typical configuration, a pair o f HTS films are placed
on opposite sides of a dielectric cylinder fabricated from a materials with a high
dielectric constant and low loss tangent, forming a confined dielectric resonator
[31,32]. The radiation loss is practically eliminated because o f confinement o f most o f
die RF energy inside the dielectric cylinder. The resonator is typically operated at the
TEou mode. The surface resistance o f the HTS films can be calculated by measuring
13
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the Q-factor o f the resonator and analyzing the electromagnetic filed inside the
dielectric cylinder. The dielectric resonator method has excellent accuracy, sensitivity,
repeatability, and dynamic range as demonstrated by many researchers.
The techniques mentioned above all measure the surface resistance of unpattemed
HTS thin films, so that they are all nondestructive. They also share the advantage o f
convenience because there is no need for any special sample preparation. Thus, they
are suitable for routine measurements. They can be used as an in-line quality check o f
HTS thin films prior to additional processing.
Another category o f methods involves the measurement o f the surface resistance
o f patterned transmission line made of HTS thin films. The surface resistance can be
calculated by measuring the Q-factor o f either a line resonator or a ring resonator
composed o f a section of transmission line. The detailed procedure is discussed in
section 4.3. Three commonly used transmission line structures have been investigated
by many researchers to measure the surface resistance o f HTS thin films [33-37],
Among them, the stripline structure was considered to be the best one for such
measurement because it supports a pure TEM wave and it has almost negligible
radiation loss. However, HTS stripline has some practical problems. In order to
fabricate an HTS stripline, three substrates are needed because we cannot deposit HTS
thin films in-situ on both sides of the substrate. Stacking three substrates together is a
complicated process itself and it produces two layers o f air gap that effect the resonant
frequency. The coplanar structure has the advantage o f simplicity because their signal
line and ground are on the same one side o f substrate. But, its field analysis is more
complicated than other types of transmission lines and special consideration needs to
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be taken to press the odd mode when designing the resonator. For a microstrip
transmission line, a quasi-TEM wave propagates along it, which can be easily
analyzed by introducing an effective dielectric constant. The number o f substrates
required reduces to two, so that both fabrication and packaging are much easier than
stripline. Also, because the future tunable resonator is constructed using a covered
microstrip structure, it will be very helpful to try out all the process steps for making a
simple microstrip line beforehand. Therefore the microstrip type resonator was chosen
in this work based on the argument above. The small amount o f radiation loss that is
not negligible due to the microstrip geometry can be determined through the procedure
described in section 4.3, therefore it does not affect the accuracy o f this method.
When the transmission line technique is used to measure surface resistance, it
should be noted that the value measured may be different than that of the original film,
because processing factors related to photolithographic patterning, wet or dry etching,
and edge effects can change the surface resistance. The technique is well suited for
measuring the effect o f such processing steps on surface resistance. From a circuit
designer’s viewpoint, the surface resistance values obtained from this method are
more closely related to the real HTS microwave circuit working conditions than are
surface resistance values measured on unpattemed films. Another advantage o f the
patterned transmission line method is that high current density can be achieved with
low input power because of the narrow line width and high Q-factor. However,
because this method is destructive and requires a great deal o f sample preparation, it is
not attractive as a routine measurement for high volume applications.
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2.2 Material Selection and YBCO Properties
2.2.1 HTS Material Selection
Since the discovery o f HTS materials, many compounds with a Tc higher than
liquid nitrogen temperature have been fabricated and investigated. Among them,
YBCO (YiBa2Cu307.x), BSCCO
(Tl2Ba2Cai CU2O 8,
(BijS^CaiC^Os, Bi2Sr2Ca2Cu30io), TBCCO
Tl 2Ba2Ca2Cu 3 0 io)
and
HBCCO
(Hg 1Ba2Cai CU2O6+X,
HgiBa2Ca2Cu3 0 g+x) are the main HTS materials available in bulk form which are
attractive candidates for thin film based device applications. The availability and ease
o f fabrication o f these HTS materials in bulk form does not necessarily translate into
the same assumption for thin films. BSCCO, with a good Tc in bulk form [38-40], is
difficult to produce in thin film form due to its tendency to form a mixture o f various
unwanted phases [41]. Thallium-based superconducting thin films with Tc -1 1 0 K.
(2212 phase) and TV -125 K (2223 phase) and Jc > 10s A/cm2 have been successfully
fabricated [42-46]. Although these properties are very attractive, the complication of
controlling two volatile elements, T1 and O, during the fabrication o f the thin film is
beyond the capacity o f the existing facilities in HiDEC. The other drawback of
TBCCO compounds is the toxicity o f Tl, which makes handling of the material safely
a major issue. The Hg-based compounds also have attractive properties, but also suffer
from exactly the same drawbacks as the TBCCO compounds [47]. It is then logical to
select YBCO as the best alternative. In comparison to the other HTS materials, YBCO
thin films are relatively easy to fabricate and the yield of good quality films is fairly
high. The former researchers o f HiDEC have successfully developed processes using a
pulsed laser deposition (PLD) method to make YBCO thin films with good critical
16
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temperature and critical current density, which had paved the way for characterizing
the surface resistance of such thin films.
2.2.2 Substrate Selection
In order to grow good quality YBCO thin films, some requirements for the
substrate must be fulfilled. YBCO thin films should be c-axis oriented so that the high
conductivity a-b plane is parallel to the substrate surface, which requires the substrate
also be c-axis oriented and with a good lattice match between the substrate and YBCO
in the a-b plane [48]. A suitable substrate should also have a coefficient o f thermal
expansion (CTE) similar to that o f YBCO, and no chemical interaction with YBCO
[49]. In addition to this, for microwave applications, substrates with moderate
dielectric constant and very low loss tangent, good mechanical strength, and low cost
are desired. The substrate materials commonly used for YBCO preparation, along with
their property parameters, are listed in Table 2-1 [49-52]. The first two columns
indicate the lattice mismatch between substrates and YBCO in the a-b plane, which is
not applicable to alumina polyciystalline substrates.
The best quality YBCO thin films can be readily fabricated on perovskite oxide
(LaA 103 and SrTiCh) substrates because they have the least lattice mismatch with
YBCO in its a-b plane. The extremely high dielectric constant o f SrTi0 3 and its high
loss tangent makes it unattractive for microwave applications, which disqualified its
use for this application.
The original design for the all-HTS tunable filter was based on Thallium-based
compound HTS thin films on MgO substrates, which is a mature process for products
17
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o f STI (Superconducting Technology, Inc). So the low surface resistance o f Thalliumbased compound HTS thin films on MgO has been proven commercially. The leading
concern was that if MgO substrates can be fabricated at very small thicknesses, then
the projected system would not meet the design requirements even assuming high
quality HTS thin film could be deposited. Therefore there was no need to investigate
the surface resistance o f YBCO thin film on MgO, because Thallium-based HTS thin
films would provide a sufficiently small surface resistance. In addition, the surface
resistance o f YBCO thin film on MgO is very likely to be high because o f poor
crystalline structure o f YBCO thin film, due to the large lattice mismatch between
YBCO and MgO, as previously reported [S3].
Table 2-1 Substrate properties [49-52]
YSZ
Aa/a Ab/b
(% )
(% )
+3.6 +6.3
MgO
-9.0
LaAlOa
SrTK>3
Alumina
-0.9
+2.0
-6.7
-2.2
+0.7
Density
CTE
(g/cnr) (ppm/°C)
£r
tan <5
Hardness
6-7X10"4
(77K, 10GHz)
6.2x10-*
(77K, 10GHz)
7.6x10-*
(77K, 10GHz)
6xl0"2
(100K, 300GHz)
0.0001
(300K, 1MHz)
1200(HV)
6.0(Mohs)
5.8
11
27
3.58
13.8
9.65
6.51
10
24
5.12
10.4
277
3.89
8
9.9
6.0(Mohs)
5.6(Mohs)
1800(HV)
9.0(Mohs)
The purpose of this work was to provide more substrate candidates that could
support YBCO thin films with satisfactory low surface resistance as alternatives in
case die Thallium-based compound/MgO system could not satisfy mechanical
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requirements. The alumina polycrystalline substrate was immediately chosen to be the
next candidate because o f its high mechanical strength. Table 2*1 lists one o f the
characteristics of mechanical strength o f materials, hardness, but it does not
necessarily convey the true nature o f each material’s mechanical strength. Although it
is convenient to believe that harder materials have higher mechanical strength, and
thus they have more chance to sustain the very thin thicknesses required, this is not
necessarily the case. Because o f the polycrystalline structure o f alumina substrate, a
buffer layer is needed to provide a textured template for growing YBCO and to
prevent chemical interactions between YBCO and alumina. Using the IBAD (ion
beam aided deposition) method, a biaxially-aligned YSZ (Yttrium Stabilized Zirconia)
buffer layer can be deposited on alumina. YBCO thin film grown on such a buffer
layer has been found to have comparable critical temperature to that grown on YSZ
single crystalline substrates but lower critical current density. Thus it was desirable to
investigate the surface resistance o f YBCO thin film on such buffer layers.
Since the effect of thinning substrates to a very small thickness was unknown, the
surface resistance o f YBCO on YSZ and LaA103 substrates must also be investigated,
although they have a similar hardness to MgO. As seen from Table 2-1, the lattice
mismatch of YSZ with YBCO is fairly high. Therefore, 0°, ±9°, and 45° oriented
YBCO grain boundaries, which tend to degrade the Jc values, are observed [48,54-S9].
The misaligned grains also increase the surface resistance dramatically. However,
using certain techniques to treat the YSZ substrate prior to deposition, the unwanted
orientation o f YBCO can be minimized. The resultant surface resistance can be
comparably small. Because o f its very small lattice mismatch with YBCO, the LaAKZh
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substrate provides an excellent template for growing YBCO thin film. The YBCO thin
films grown on LaAlQ) have perfect crystalline orientation despite the twinning
structure o f the substrate. However, the twinning structure causes very poor
mechanical strength o f LaA103 , which also tends to splinter during removal from the
heater block after the deposition o f YBCO layers with thickness o f 20 mil. Hence,
LaA 103 was the last choice due to the poor confidence in its mechanical strength.
2.2J YBCO Structure and Properties
The exact formula o f YBCO is Y iBa2Cu307 -x- YBCO is usually referred to as a
triple perovskite because the unit cell o f YBCO is made o f three perovskite-like cubes.
Variations in this structure include the orthorhombic and tetragonal structures shown
in Fig. 2-2 [60,61]. The basic structure in both cases consists o f Ba0/Cu02/Y/Cu02
/BaO (1-2-2). The only difference between tetragonal and orthorhombic YBCO is at
the O lA and OIB positions, as shown in Fig. 2-2. In orthorhombic YBCO, oxygen
concentrates along the b axis at OlA positions, and the OIB positions are vacant with
the result that b>a and the Cu02 chains form along the 6-axis. The lattice constants for
the two structures are listed in Table 2-2 [61].
The structure of the YBCO depends on the oxygen deficiency x. If the oxygen
deficiency is such that 0 < x < 0.S, then the structure has the orthorhombic phase.
Furthermore, in the orthorhombic phase, the oxygen concentration governs the Tc. For
0 < x < 0.15, the Tc is around 90 K. This is the structure that is desired for most
practical applications, whereas, for all other values up to x = 0.5, Tc < 90 K. For 0.S <
x < 1, the compound is in the tetragonal phase and not superconducting.
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Tetragonal Phase
Orthorhombic Phase
Fig. 2-2 Crystal structure of tetragonal and Orthorhombic YBCO.
Table 2-2 Lattice Constants for Orthorhombic and Tetragonal Structures [61)
Structure
a (A)
b (A)
c(A )
Orthorhombic
3.8231
3.8864
11.6807
Tetragonal
3.857
3.857
11.814
In the orthorhombic YBCO structure, the CuO layers, or sheets, in the a-b plane
are responsible for the superconductivity. In addition, the CuO chains along the 6-axis
also aid the conduction. Because o f the missing oxygen links to the Cu atoms along
the c-axis, the superconductivity is small. Thus, the anisotropic crystal structure of
YBCO leads to anisotropic electrical properties.
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High quality YBCO thin films are usually made through an in-situ method. The
films are deposited on substrates at a high temperature (670 - 800 °C) using various
evaporation techniques. The YBCO films grown in this condition are o f the tetragonal
phase. During the cooling down procedure after deposition, the chamber is filled with
~ 1 atm oxygen, the temperature is then maintained at about 500 °C for one or two
hours. During this procedure, the tetragonal YBCO absorbs oxygen and transforms
into the superconducting orthorhombic phase [62,63].
2.2.4 YSZ Structure and Properties
Yttrium-stabilized-zirconia (YSZ) was chosen as the buffer layer material on
alumina substrate. The main reason is that the biaxially-aligned YSZ can be grown on
amorphous substrates using the IBAD method at room temperature [64-71]. Other
buffer layer materials have not displayed this property or exhibited unwanted
orientation when deposited using the IBAD technique.
YSZ has a cubic fluorite crystal structure with a lattice constant close to the
diagonal of the YBCO a-b plane ( 'J la YBCO), so YBCO films prefer to grow with their
[100] direction parallel to the YSZ [110] direction. However, since the lattice
mismatch is not very small, other in-plane orientations often occur in YBCO films on
YSZ, resulting in high-angle grain boundaries [49,54-59].
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CHAPTER 3
Transmission Line and Loss
Transmission line theory, which provides a bridge between field analysis and
circuit theory, is the foundation o f microwave network analysis. It has to be well
understood before we proceed with any other microwave concepts. The general
equations o f transmission line theory are introduced in this chapter. The different types
o f transmission line structures, with emphasis on microstrip, and the loss associated
with them are also discussed in detail.
3.1 Transmission Line Using Lumped-Element Circuit Model
3.1.1 General Solutions
The main difference between circuit theory and transmission line theory is the size
o f the network compared to the electrical wavelength [72]. A network with physical
dimensions much smaller than the wavelength can be treated as lumped element, while
transmission lines may be a considerable fraction o f a wavelength, or many
wavelengths, in size. So a transmission line is best defined as a distributed-parameter
network, where voltages and currents can vary in magnitude and phase over its length.
As shown in Fig. 3-1(a), a transmission line is often schematically represented as a
two-wire line, since it always has at least two conductors. A small fraction o f length,
AZ, o f Fig. 3-1(a) can be modeled as a lumped-element circuit, as shown in Fig. 31(b), where R, L, G, C are series resistance, series inductance, shunt conductance,
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shunt capacitance per unit length, respectively. Applying Kirchhoff 's voltage law and
current law to the circuit o f Fig. 3 -1(b), we can get two equations at the condition of
steady sinusoidal wave
^ * l = - ( R + j0,L )l(z),
az
(3.1a)
* & l = -(G + ja )C y (z ).
az
(3.1b)
where (o is the angular frequency o f the wave.
The two equations o f Eq. (3.1) can be mathematically transformed into
0,
az
^ M
az
(3.2a)
- y 2I( z ) = 0 ,
(3.2b)
nz.o
V(z!f)
Az(a)
Hz. t)
Hz +Az. 0
CAz <
=
CAz
v(z + Az. t)
Az-
(b)
Fig. 3-1 Voltage and current definitions and equivalent circuit for an incremental length of
transmission line, (a) Voltage and current definitions, (b) Lumped-element equivalent circuit [72|.
24
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where Y=<*+jP = ij(R + j & L j f j + jcoC)
(3.3)
is the complex propagation constant, which is a function of frequency. In Eq. (3.3), a
is the attenuation constant, and fi is the propagation constant or phase constant.
Traveling wave solutions to Eq. (3.2) can be found as
V(z) = V ;e-» +Vo'e * ,
(3.4a)
/(* )= /> -* + /;* * ,
(3.4b)
where the I'^term represents wave propagation in the ~z direction, and the e* term
represents wave propagation in the - z direction.
The characteristic impedance o f the transmission line can be defined by following
equation relating the voltage and current on the line:
V* - V
Z0 = j r = - j r *o
*o
(3.5)
The current solution can be rewritten in terms o f voltage by plugging Eq. (3.4a)
into Eq. (3.1a)
/ (z) = TR+j(oL
J L T l y°+e~* - K e n -
(3.6)
Comparing Eq. (3.6) to Eq. (3.4b), the characteristic impedance can be found as
R + ja L
Y
=
IR + jtoL
(3.7)
\ G + jgjC
The time domain expression for the voltage waveform is
v(z,t) = \v;\cos(iot-fiz
where
+\v;\cos(at +f}t + 4>~)eca ,
(3.8)
is the phase angle o f the complex voltage V * . The wavelength on the line is
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and the phase velocity is
(3.10)
3.1.2 Lossless Transmission Lines
The above equations are general solutions for the transmission line including loss
effects due to finite conductivity and lossy dielectric. The loss o f the transmission line
is usually very small, so it can be neglected in many cases for the purpose o f
simplification. If the transmission line is said to be lossless, then R = 0 and G = 0 in
Eq. (3.3), which gives the propagation constant as
Y = a + jf} = y W Z c ,
or 0 = coylLC,
(3.11a)
a= 0.
(3.11b)
As expected for the lossless case, the attenuation constant a
is zero. The
characteristic impedance of Eq. (3.7) reduces to
(3.12)
which is now a real number. The general solutions for voltage and current on a
lossless transmission line can be written as
v{z)=v;e-J*+v;e*,
(3.13a)
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l { z ) =^ - e - J*
*0
,
(3.13b)
Zo
with wavelength
A = ^ =- ^ = ,
P <ojLC
(3.14)
and the phase velocity
vp
'
^ = - t =P J lc
<3 1 5 >
3.13 Lossy Transmission Lines
The goal o f this work was to find the surface resistance o f superconducting YBCO
thin film by measuring the quality factor of the ring resonator. In the situations similar
to this, the effect o f loss itself is o f interest, so that it has to be taken into account.
Based on Eq. (3.3), the complex propagation can be rearranged as
= ,W Z c jl-y
( R
G'
■+
ioL coC
RG
a 2LC
If both the conductor loss and dielectric loss are small in the low-loss case, the
RG
conditions o f R « coL and G « aC should hold. The higher order term —:------can
<
o 2LC
thus be ignored, and Eq. (3.16) reduces to
r =
j ^
f W
¥
) -
( 3 i7 >
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By using the first two terms o f the Taylor series expansion for -Jl+x « l+ x/2 h— ,
we can reduce Eq. (3.17) further to
(3.18)
Y*jo>
so that
(3.19a)
P * c o jL C ,
(3.19b)
where Z0 = y — is the characteristic impedance o f the lossless transmission line. Note
from Eq. (3.19b) that the propagation constant P is the same as die lossless case o f
Eq. (3.1 la). By the same order o f approximation, the characteristic impedance Z 0 can
be approximated as a real number:
(3.20)
The above equations (3.19) - (3.20) are only valid for iow-loss and high frequency
conditions. According to the equations, the propagation constant and characteristic
impedance for a low-loss transmission line can be closely approximated by
considering the line as lossless.
Although the general solutions seem to solve everything for given transmission
lines, they cannot be utilized in most practical cases. Only for transmission lines with
certain shapes, such as coaxial, two wire or parallel plate, the distributed parameters R,
L, G, C can be computed by closed-form formulas, thus the exact solutions o f
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characteristic impedance, attenuation constant and propagation constant can be
calculated from above equations. But for planar transmission lines, which are used in
most practical cases, no simple closed-form formulas for the distributed parameters
can be found. Therefore, the exact solutions can only be solved through numerical
computation. But for practical purposes, simple empirical formulas have been
developed by curve fitting to the exact solution. Also many researchers have done a
great deal o f experimentation to determine the loss of the planar transmission lines,
which will be discussed in next section.
Early microwave systems used waveguide and coaxial lines for transmission line
m edia Waveguides have the advantage o f low loss and high power-handling
capability but are bulky and expensive. Coaxial lines have very high bandwidth and
are convenient for test applications and interconnects, but are not suitable for the
fabrication o f complex microwave components. After 1950, planar transmission lines,
in the form o f stripline, microstrip, slotline, coplanar waveguide, and many other types
o f related geometries, were developed [73,74]. Such transmission lines are compact,
low cost, easy to fabricate, and are capable o f being easily integrated with active
devices to form microwave integrated circuits. But they all suffer higher loss than
waveguide and coaxial lines, which makes it especially attractive to replace normal
conductors (such as copper) in those planar transmission lines by superconductors. In
this work, the microstrip type transmission line was chosen to determine the surface
resistance o f YBCO thin film on different substrates because o f the ease o f fabrication.
Thus we will only discuss the microstrip transmission line in detail while omitting a
discussion o f other types.
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3.2 Loss in Microstrip
O f the many types of planar transmission lines, microstrip lines appear to be the
most convenient and inexpensive topology for batch processing of microwave
integrated circuits. The geometry o f a microstrip line is illustrated in Fig 3*2. A
narrow “ strip” conductor o f width w and thickness t is printed on a thin, grounded
dielectric substrate o f thickness h and relative permittivity e r.
In order to determine the surface resistance o f the conductor, it is necessary to
know how the characteristic impedance, phase velocity, and attenuation constant of
the dominant microstrip mode depend on: (1) geometrical factors, (2) the electronic
properties of the substrate and conductors, and (3) the frequency. In microstrip
structure, most electromagnetic fields concentrate between the strip conductor and the
ground plane, and some small fraction exists in the air above the substrate. Thus the
pure TEM mode cannot be supported by the microstrip structure, since the phase
velocity o f TEM fields in the dielectric would be
, but the phase velocity of
conductor
Dielectric
Ground plane
Fig. 3*2 Structure of microstrip transmission line.
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TEM fields in the air would be c . To solve the exact fields o f a microstrip structure
composed o f a hybid TM-TE wave needs extremely complicated analysis techniques.
However, the thickness o f dielectric substrate is usually much smaller than the
wavelength for most practical cases, so the fields are almost the same as those o f static
cases. The fields in microstrip are called quasi-TEM. By introducing the effective
dielectric constant etff, the mixed dielectric sytem of microstrip can be treated as a
homogeneous dieletric system with an dielectric constant o f e tff. Thus the phase
velocity and propagation constant can be expressed in the same way as a pure TEM
wave in homogeneous dielectric:
vp
c
(3.20a)
(3.20b)
where k0 is the propagation constant in vacuum.
In the following section, the design formulas for the effective dielectric constant
and characteristic impedance o f microstrip transmission line are listed. The
approximate formulas are obtained by curve-fiting rigorous quasi-static solutions.
3.2.1 Formulas for Effective Dielectric Constant and Characteristic Impedance
The effective dielectric constant is given approximately by [72]:
(3.21)
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Since some of the field lines are in the dielectric region and some are in air, the
effective dielectric constant should have the value within the following range:
\< e t < er.
The more field lines exist in the dielctric, the closer the effective dielectric constant e t
is to the dielectric constant e r . Obviously e t is also dependent on the substrate
thickness h and conductor width w , because they affect the field distribution o f the
microstrip structure. Note when h « w , et approaches e r, while £, approaches
e. +1
when h » w .
For a given dimension o f a microstrip transmission line, the characteristic
impedance can be calculated as [72]
60
In
w
for
4h
^<1
h
120it
*0 =
(3.22)
fo r
-+ 1 .3 9 3 + 0.667 In —+1.444
h
^>1
h
For design purposes, the characteristic impedance Z Qand dielectric constant e r o f
w
the substrate are often given. Then the — ratio can be found as [72]
h
Se'
w
n
fo r
r A- 2
-1 - ln(2B - 1 ) + ^ — jln (fi - 1)+0.39 - — ]
2e„
e.
fo r
—
h
—
h
<2
(3.23)
>2
where
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(3.23a)
(3.23b)
For the purpose o f simplicity, the transmission lines are usually designed to have
SO Q characteristic impedance in order to match the connections o f most microwave
instruments. To design a SO ohm microstrip transmission line, a useful rule o f thumb
W
says that the — ratio should approximately equal to one when the substrate has a
h
dielectric constant o f 10.
The higher the dielectric constant o f the substrate, the
smaller the line width, and verse versa. In practical terms, the impedance o f devices
used in a microwave circuit are often found not to be 50 Q, so transmission lines with
different impedances are also needed to form matching networks.
3.2.2 Microstrip Loss
There are mainly three types of loss in a microstrip transmission line, namely
radiation loss to the environment, dielectric loss in the substrate and conductor loss in
the strip conductor and the ground plane [75-78].
Supposing all these losses per unit length to be small, we can represent them in
terms of an attenuation constant a in the expression for transmitted power P{z) at
point z
(3.24)
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where z denotes a point along the direction o f propogation parallel to the strip
conductor and P0 the transmitted power at a point z = 0. Letting a = a r + a d + a c,
the sum o f the radiation attenuation constant a r, the dielectric attenuation constant
a d and conductor attenuation constant a c, we get
d P /d z
a = ~ 2 P (z)=
A Pr + A Pd + A Pc
(3.25)
2P(z)
or
(3.25a)
(3.25b)
(3.25c)
where APr, APd and APc are the average radiation power loss, dielectric power loss
and the conductor power loss per unit length.
Radiation Loss
A microstrip transmission line is an asymmetric structure and is often used in
unshield or poorly shielded circuits. By design, there is always a certain amount o f
power lost due to radiation leakage. In particular, discontinuities such as abruptly
open-circuit microstrips, as well as steps and bends in the signal trace will all radiate
to a certain extent. Such discontinuities form essential features o f a microwave
integrated circuit, therefore radiation cannot be avoided totally. Efforts must be made
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to reduce such radiation and its underdesirable effects. However, for circuits such as
filters and resonators, this radiation is very small. The ring resonator used in this work
has even less radiation loss because the ring geometry does not suffer from the openended effect and the circuit is well shielded by the copper packaging housing.
Although the radiation is extremely small in this work, it still can not be simply
neglected. Keep in mind the surface resistance o f YBCO superconducting thin film is
also extremely low at 77K, so any small error incurred by including losses other than
conductor loss will affect the accuracy o f the measured surface resistance a great deal.
But there is almost no way to directly measure the small radiation loss for this kind o f
resonator in this work. Therefore, we developed a procedure to extract the conductor
loss from the total loss without directly measuring the radiation loss. The procedure
will be discussed in Chapter 4.
Dielectric Loss
Dielectric loss is caused by the heat dissipation in the dielectric medium. There are
three primary loss mechanisms depending on frequency and temperature: ion
migration loss due to the DC conduction o f the ion jump relaxation, ion vibrationdeformation loss, and electron polarization loss. The actual dielectric loss is the sum o f
each contribution at a given frequency.
It is convenience to define complex dielectric constant, e r , and loss tangent,
tan <5,
e r =e'r - y e ' = e '( l- y tan<5),
(3.26)
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in order to characterize the dielectric loss. The imaginary part o f e r accounts for
dielectric loss in the medium. The complex propagation constant o f the transmission
line can be derived assuming a lossless dielectric medium (real dielectric constant),
then the loss can easily be introduced by replacing the real dielectric constant with a
complex dielectric constant.
For a transmission line or wave guide completely filled with a homogeneous
dielectric, the complex propagation constant can be written as
y —a d + jfi = <Jk; - k 2 = J k 2 - t o 2fx0e 0e r{ l - j t m 8 )
(3.27)
where kc is the cutoff wavenumber.
In practice, most dielectric materials have a very small loss ( tan £ « 1), so the
above expression can be simplified by using the first two terms o f the Taylor
expansion,
*
sIa 2 + x 2 = a + —
— j, f o r x « a .
(3.28)
Then Eq.(3.27) reduces to
Y = J k 2 - k 2 + j k 2 tan<5
(3.29)
2^kc - k
£ 2 tan <5
jB
2 /}
H
= --------------- +
where k 2 =<u2/i0e 0£r is the real wavenumber in the absence o f loss and
P - V*2 ~^e
*s the propagation constant. Eq. (3.29) shows that the propagation
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constant
is unchanged when the loss is small, while the attenuation constant due to
dielectric loss is given by
a d = — ****** Np/m (TE or TM waves).
2p
(3.30)
These results apply to any TE or TM wave, as long as the guide is completely filled
with a homogeneous dielectric medium. It is also valid for TEM wave, such as in
stripline transmission line, where kc - 0, so /) = k,
k \m 8
a d = — - — Np/m (TEM waves).
(3.31)
For a mixed dielectric system such as microstrip transmission line which supports
quasi-TEM waves, the above result cannot apply directly. However, by multiplying a
“filling factor”,
& (e —l)
. c
whi ch accounts for the factor that the fields around the
* e (« r-U
microstrip line are partly in air and partly in the dielectric, the dielectric attenuation o f
a microstrip transmission line can be determined as
a
2V M er - l )
If the loss tangent is known for a specific substrate, then the dielectric attenuation
can be easily calcaulated using Eq. (3.32). However, the loss tangent values obtained
from the data sheets provided by vendors are usually measured at frequency range o f
MHz and room temperature. Since the loss tangent of a dielectric strongly depends on
operating frequency and temperature, we cannot simply use those values at frequency
range of GHz and 77 K. But to measure the loss tangent o f a dielectric at a certain
frequency and temperature is not a trivial job in itself it will complicate this work to
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find the surface resistance of the superconducting YBCO thin film. Fortunately, the
procedure mentioned before will also bypass this difficulty, which will be discussed in
detail in Chapter 4.
Conductor Loss
In a microstrip transmission line over a low-loss dielectric substrate, the
predominant loss is the conductor loss caused by the nonperfect conductors. If the
current distribution inside conductors were known, theoretically, the conductor
attenuation constant can be computed directly using the formula [79]:
(3.33)
where Z0 is the characteristic impedance o f the microstrip, Rsl and Rs2 the surface
resistance for the strip conductor and ground plane, respectively, J t(x) and J 2(x ) the
corresponding surface current densities, and |/| the magnitude o f the total current.
AP
This expression is based on Eq. (3.23c), a c = — f-r , using the fact that
(3.34)
and
(3.35)
where APc is the power loss per unit length. The integral
J
implies integration o f the
surface current density around all surface o f the strip conductor.
38
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As shown in Fig 3-3, a sketch o f the current distribution for a strip o f nonzero
thickness, the current density in the strip conductor and in the ground conductor is not
uniform in the transverse plane because of the finite strip width.
Note in some books and references, many researchers have used a very simple
formula
a c = -§ * - Np/m,
Z 0w
(3.36)
without recognizing the oversimplified assumption behind it. The current distribution
is thought to be uniform and equal to — in both conductors o f same materials, and
w
i i w
confined to the region Jjc| < — . This condition is only valid for large strip width
w
►oo . According to Robert A. Pucel et al. ’s experiments [79], the above expression
h
w
w
overestimates the conductor loss by 80% for — < 2. Even for — as large as three, the
h
h
Bottom of strip
■Top of strip
J*(«>
:•
\
—
> •* *
k1
Fig. 3-3 Sketch of the current distribution on microstrip conductors [79|.
39
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
discrepancy is still very large. They believed that the good agreement with experiment
claimed by some for this simple expression was caused by extraneous sources o f loss.
Pucel used another technique to calculate the conductor loss, which achieved much
higher accuracy. The technique is based on the so-called “ incremental inductance
rule”, which was developed by Wheeler [80]. This method utilizes the similarity o f the
equations for the inductance per unit length and resistance per unit length o f a
transmission line, as given by the following equations:
(3.37)
Kl
(3.38)
In other words, the conductor loss o f a line is due to current flow inside the conductor
which is related to the tangential magnetic field at the surface o f the conductor, and
thus to the inductance o f the line.
The complete procedure to derive the conductor loss using this technique for
microstrip transmission line is veiy complicated and lengthy, and is not the emphasis
of this work. Therefore only the results are given below, and they are utilized in the
following chapters to find the surface resistance o f YBCO thin films.
First let us introduce the Wheeler’s correction terms to take the thickness o f the
strip conductor into account:
(3.39)
40
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thus,
w '= w + Aw
(3.40)
Assuming Rsl = Rj2 = Rs , which is true in most practical cases, we can get the
derived formulas as below:
w
1
— < —7T :
h
2
<*cZoh
R.
_1_
2n
14h j
. h
1+ —
1
h
l r ( ^ +
+ —
W
7TW'
-
-
w_
r
(3.41a)
t
1+-
Ajcw
1
w
—n < — < 2:
2
h
a cZ 0h
R.
1
2n
1-
KAhJ
11 + —h
w'
h
. (2 h
7 tw '
H
t
.
+i
i+i
___ h
(3.41b)
1+ —
2 h.
W_
a cZBh
h
'
I f M
K
— +0.94
2h
r H
i+i
h
, h
h
1+— + —
7M/
1+--2h .
(3.41c)
where a c is in Np/m. The joint error in the above expressions at
w
1
*s
than
w
w
6 percent, at — = 2, less than 8 percent. Note that in the limit o f wide strips — » 1 ,
h
h
Eq. (3.41c) approaches the form same as Eq. (3.36) as it should.
41
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CHAPTER 4
S Parameter, Network Analyzer and Ring
Resonator
The dimensions for circuits operating at low frequency are small compared to their
wavelength, so that there is negligible phase change from one point in the circuit to
another. Therefore, they can be treated as an interconnection o f lumped components
with unique voltages and currents defined at any point in the circuits. In this situation,
die well-known KirchhofF voltage and current laws and impedance concepts o f circuit
theory are capable to solve the problems. But for high frequency circuits, their
dimensions are significant fraction o f a wavelength or many wavelengths, such that
the voltages and currents may change in magnitude and phase over their length. The
techniques used at low frequency are generally not directly applicable at high
frequency, however, the circuit and networks concepts can be extended to deal with
many microwave problems.
In this chapter, the concepts o f network, impedance and admittance matrices are
first introduced, then the more commonly used scattering matrix (S parameter) is
discussed in section 4.1. The basic principles o f network analyzer are described in
section 4.2, and the procedure o f calibration and testing, especially for devices under
low temperature is also discussed in detail. Finally, the theory and application o f the
microstrip ring resonator, the concept o f quality factor (Q-factor), and its measurement
are included in section 4.3. The methodology to find surface resistance of
42
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
superconducting YBCO thin films using the microstrip ring resonator is also described
step by step in this section.
4.1 S Parameter
4.1.1 Impedance and admittance matrices
The term impedance was first introduced in the nineteenth century to describe the
complex ratio of voltage to current in AC circuits consisting o f resistors, inductors,
and capacitors, therefore an AC circuit could be analyzed in a similar way to that o f an
DC circuit. It was then applied to transmission lines, using iumped-element equivalent
circuits and the distributed series impedance and shunt admittance o f the line. In the
1930s, the impedance concept was extended to electromagnetic fields in a systematic
way, and was regarded as characteristics o f the type o f field, as well as the medium
[81]. The concept o f impedance forms an important link between field theory and
transmission line or circuit theory.
For a microwave network, we can use the impedance or admittance matrices to
relate the voltages and currents o f different ports to each other, which gives a matrix
description of the network. This kind o f representation also leads to the development
o f an equivalent circuit o f arbitrary networks, which is very useful when discussing
the design of passive components such as resonators and filters.
Let us consider an arbitrary N -port microwave network, as shown in Fig. 4-1. The
ports in the figure may be any type o f transmission line or transmission line equivalent
o f a single propagating waveguide mode. At a specific point on the nth port,
a terminal plane,
is defined along with equivalent voltages and currents for the
43
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Vt it
vi i:
Fig. 4-1 An arbitrary N-port microwave network [72|.
incident ( V *, I * ) and reflected ( V~, / * ) waves. It is very important that the terminal
planes provide a phase reference for the voltage and current phasors. Now at the nth
terminal plane, the total voltage and current is given by [82]
V .= v : + v ; ,
(4.1a)
w : - / ; .
<4 | b >
as observed from 2 = 0.
These voltages and currents can be related by the impedance matrix
[z]of the
• ••
2
t -XN
i----
Zx2
L
1
»
II
*2
"1
microwave networks:
z *
I
____ 1
N
1
• ^ 1
____
...
or in matrix form as
44
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[ V M Z \1 \.
(4.2)
1
rw'
v2
:
I
•
.
t
i
}
_ i
1--------*■«
-
...........
h
I
X ra
r2l
I
i
-------- 1
I f we define an admittance matrix [f] in a similar way, the relationship should be:
or in matrix form as
M -M r].
(4.3)
The [Z] and [T] matrices are the inverses of each other according to their definition:
M =W -
(4.4)
Note that both [Z ] and [f] matrices relate the total port voltages and currents.
From Eq. (4.2), we see that Z can be found as
(4.5)
=0 fo r k » j ’
which means that Z,y can be found by driving port j with the current Ir opencircuiting all other ports (so Ik = 0 for k * j ) , and measuring the open-circuit voltage
at port i . Thus, Z„ is the input impedance seen looking into port / when all other
ports are open-circuited, and Z :J is the transfer impedance between ports i and j
when all other ports are open-circuited.
Similarly, from Eq. (4.3), Yu can be found as
(4.6)
45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
which states that Yy can be found by driving port j with the voltage
short-
circuiting all other ports (so F* = 0 for k * j ) , and measuring the short-circuit current
at port j .
4.1.2 The Scattering Matrix (S Matrix)
The concepts o f impedance and admittance matrices are straightforward, but for a
real microwave network it is very difficult to directly measure the voltages and
currents which involve the magnitude and phase at the same time. So in practice, a
representation associated more with direct measurements, and with the ideas of
incident, reflected and transmitted waves, is given by the more often used scattering
matrix.
Similar to the impedance or admittance matrix for a N -port network, the
scattering matrix also provides a complete description o f the network as seen from
each of its N ports. While the impedance and admittance matrices are defined based
on the total voltages and currents seen at each port, the scattering matrix is based on
the voltage waves incident on the ports as well as those reflected from the ports.
Now consider the IV -port network shown in Fig. 4-1, where V* is the amplitude
of the voltage wave incident on port n , and V~ is the amplitude o f the voltage wave
reflected from port n . The scattering matrix is defined in relation to these incident and
reflected voltage waves as [82]
46
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
•
1
r
^
...
Sm_
•
^
•
=
*
v;
Sw K '
K
1------------
•••
's „
> ." ■
M = [ s lr ) .
or
(4.7)
From Eq. (4.7), the specific S -parameter S 0 can be found as
S9
y *
(4.8)
Vt'= 0 fo r I tr j ’
which says that S:J is found by driving port j with an incident wave o f voltage V *,
and measuring the reflected wave amplitude, V ~, coming out of port /. Except for the
j th port, the incident waves on all other ports are set to zero, which means that all
ports should be terminated in matched loads to avoid reflections. Thus, S„ is the
reflection coefficient seen looking into port i when all other ports are terminated in
matched loads, and Sv is the transmission coefficient from port j to port / when all
other ports are terminated in matched loads.
4.2 The Vector Network Analyzer
4.2.1 Basic Principles of Vector Network Analyzer
The scattering parameters either can be calculated using network analysis
techniques, or can be measured directly with a vector network analyzer [83]. Vector
network analyzers such as HP8310 measure the magnitude and phase characteristics o f
networks and components such as filters, amplifiers, attenuators, and antennas. There
are two kinds of measurements:
reflection measurements and transmission
47
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measurements. An incident signal generated by an RF source controlled by HP8510 is
applied to the test device and compared with the signal reflected from the device input
or transmitted through it.
Reflection measurements are made by comparing the reflected signal to the
incident signal. This results in measurement data on reflection characteristics o f the
device such as: Return Loss, Standing Wave Ratio (SWR), Reflection Coefficient, and
Impedance.
Transmission measurements are made by comparing the transmitted signal to the
incident signal. This results in measurement data on transmission characteristic of the
network such as: Insertion Loss or Gain, Transmission Coefficient, Electrical Delay
from which Electrical length can be obtained, Deviation from Linear Phase, and
Group Delay.
A simplified block diagram o f the general-purpose HP8510 network analyzer
system is shown in Fig. 4-2. It is composed o f a high performance vector receiver with
four inputs, two independent measurement channels, and an internal microcomputer to
automate measurement, data processing, display, and data input/output operations. A
special system bus provides fast digital communication between the instruments that
make up the system, allowing the network analyzer to make full use o f the source and
test set capabilities. This interface also provides direct data transfer to the hardcopy
device for permanent records of the measurement display.
To test, the device under test is connected to analyzer with one port or two ports.
In operation, the RF source is usually set to sweep over a specified bandwidth, which
can be defined anywhere in the range from 540 MHz up to 26.5 GHz. A four-port
48
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r r
TOT « T
Fig. 4-2 Simplified system block diagram (83|.
reflectometer samples the incident, reflected, and transmitted RF waves; a switch
allows the network to be driven from either port 1 or port 2. Four dual-conversion
channels convert these signals to second 100 kHz IF frequencies, which are then
detected and converted to digital form. A powerful internal computer is used to
calculate and display the magnitude and phase of the S parameters, or other quantities
that can be derived from the S parameters, such as SWR, return loss, group delay,
impedance, etc. These values all can be read from the CRT display. However, for S
parameters, we can get them more conveniently through computer controlled
49
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measurement procedure using a software called Wincal. The data then can be saved
into computer and post-processed easily. Wincal also has other useful functions that
greatly enhance the capability o f the analyzer.
An important feature of this network analyzer is the substantial improvement in
accuracy made possible with error correcting software. Errors caused by directional
coupler mismatch, imperfect directivity, loss, and variations in the frequency response
o f the analyzer system are accounted for by using a twelve-term error model and a
calibration procedure [83]. Another very useful feature is the capability to determine
the time domain response of the network by calculating the inverse Fourier transform
o f the frequency domain data, although we did not use this function in this work.
4.2.2 A Shift in Reference Planes and Calibration
Because S parameters contain information o f both magnitude and phase o f
traveling waves incident on and reflected from a microwave network, phase reference
planes must be defined for each port o f the network. We will first show the
transformation of S parameters when the reference planes are moved from their
original locations.
Considering the N-port microwave network shown in Fig. 4-3, where the original
terminal planes are assumed to be located at z n = 0 for the nth port, and where z n is
an arbitrary coordinate measured along the transmission line feeding the nth. The
scattering matrix for the network with this set o f terminal planes is denoted by
[s].
Now consider a new set of reference planes defined at z n =/„, for the nth port, and
50
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
v
Tw k
Vi
r — <jlT
Port I
2, = 0
2, = / ,
network
151. [5'1
I
I
v F W
v: 'I f t j w
r
v; ^ Q P
Port n
yn- — w
T
I
Zn = Ifl
z« =0
Fig. 4-3 Shifting reference planes for an N-port network [72|.
let the new scattering matrix be denoted as [£']. Then in terms o f incident and reflected
port voltages we have that
[ r - ] = [S ][r+],
[ r - ]
(4.9a)
= [ S '] [ r +],
(4.9b)
where the unprimed quantities are referenced to the original terminal planes at
z„ = 0 ,
and the primed quantities are refemced to the new terminal planes at z„ =/„.
If we consider the simple case o f lossless transmission line, the relation between
the new wave amplitudes to the original ones is
v ny
=
vn;ej6' ,7
(4.i0a)
vy
= v ; e - je-,
(4.10b)
51
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where 0 n = /)„/„ is the electrical length o f the outward shift o f the reference plane o f
port n . Writing Eq. (4.10) in matrix form and substituting into Eq. (4.9a) gives
V®1
V'®1
o '
e*
o
IH = [s ]
0
M .
0
e J°-
(4.11)
e~J°M
Multiplying by the inverse o f the first matrix on the left side gives
V ;®'
y*
o
0
e-,®
:
[5]
M =
0
M -
(4.12)
0
e~,0s
Comparing with Eq. (4.9b) shows that
> e,
y*.
0
0
cp - a
C
(4.13)
[S
M 0
g-l°s
0
g-JBs
which is the desired result.
Because the above equations are based on lossless transmission line assumption,
they only show phase change at different reference planes. In the real world, the cable
extensions, sometimes more than one section, are often used to make connection
between device under test and analyzer. Those cables are usually low loss cable with
very good quality, but they still have a certain measurable loss. Also all the
connections are not perfectly matched, which can cause power reflction. Therefore not
only the phase, but also the magnitude o f the traveling wave will be change at
different reference planes. To get “ real” S parameters o f a device, the reference plane
52
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
should be set precisely at the place where the device makes connection with cable
extensions. This can be accomplished through a calibration procedure, which tells the
analyzer to set the reference planes at die right positions.
A measurement calibration procedure transfers the accuracy of the calibration
standards to the measurement o f the device. Since the response of the standards is
known to a high degree o f accuracy, the analyzer can measure one or more standards,
then use the results o f these measurements to develop coefficients for a model o f die
measurement system. Finally, accurate S parameters can be computed by measuring a
device under test and using the model and the coefficients to remove the error
contributions.
The HP8510 network analyzer has several different types o f calibration for various
applications [83]. In this work, the FULL 2-PORT calibration using 3.5 mm standards
is applied. Selecting FULL 2-PORT at the Calibration menu will bring the menus o f
the FULL 2-PORT calibration onto the CRT display, which includes REFLECTION,
TRANSMISSION and ISOLATION. They may be selected in any sequence to bring
their submenus onto the CRT. Then, connect proper standards (such as OPEN,
SHORT, and LOAD) to port 1 or port 2 cable extensions, and select the corresponding
menu to measure the standards. For REFLECTION, it measures the OPEN, SHORT
and LOAD for port 1 and port2. For TRANSMISSION, it measures the THROUGH
(including forward transmission through, forward match through, reverse transmission
through and reverse match through). The perfect THROUGH should be formed by
connecting two cables together directly, which means the two cables have connectors
with opposite sex. Unfortunetely, our device is so-called “ noninsertable”, since it has
53
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
two connectors with the same sex (female in our case). So, the connectors o f two cable
extensions o f analyzer must be male. Then a male-to-male adapter is used to make
THROUGH, which is not exactly THROUGH. Considering the very small electrical
length o f the adapter comparing to the wavelength, we assume the error caused by that
can be neglected. For ISOLATION, keeping the two cables far away forms the
standard. After the measurement is completed, the analyzer will calculate the
coefficients and save them. When the device is measured, the errors will be
automatically corrected according to the saved coefficients.
4.23 Calibration of Low Temperature Measurements
In order to test the superconducting ring resonator, the device has to be cooled to
boiling point o f liquid nitrogen (77K) by a cryo-chamber. As shown in Fig. 4-4, the
device is positioned at the bottom o f the cryo-chamber, and electrically connected to
two SMA RF connectors on the top of the cryo-chamber through two low loss RF
cables. There is also a T-type thermo-couple (Omega) placed right above the device so
that it can monitor the temperature. Before testing, the whole chamber is vacuumed
and back filled with helium for several cycles to remove the moisture inside the
chamber. Then the chamber is filled with helium and sealed so that no moisture will
condense on the surface of the superconducting thin film when the device is cooled
down to 77 K. The reason to choose helium is that it has fairly good thermal
conductivity among all kinds of gases (Hydrogen has better thermal conductivity but
is flammable). Finally, the cryo-chamber is placed into a liquid nitrogen dewar with
liquid level o f approximately one foot, and the device is cooled slowly to 77 K.
54
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
S .1
Ufa
Fig. 4-4 The structure of the cryo-camber.
The calibration is usually done at room temperature, while it is assumed to still be
valid at 77 K by most researchers according to published reports. This assumption is
not correct generally because the characteristics of the two cables connecting the cold
device and analyzer will change when cooled down from room temperature to 77 K.
However the error caused by the temperature difference can be neglected in many
cases as some researchers pointed out. Possibly, it is because the cables used in many
cryostats are very short. Some ciyostats cool the device only by conducting the heat
through the bottom surface o f the device, so that the cables are not as cold as device,
because they only can transfer heat through small areas contacting with the wall of
55
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
device. All o f these factors cause the change o f characteristics of cables small enough
to be neglected.
For the cryo-chamber used in this work, the two cables are more than three feet
long and are also cooled by the helium inside the chamber during measurement. So at
least the bottom part of the cables which are below the level of liquid will be as cold
as device. With such large temperature difference and long cables, the change o f
characteristic (such as loss and impedance) is too large to be neglected. Fig. 4-5 shows
the S parameters o f a THROUGH after calibrated at room temperature. It is a good
THROUGH according to the S parameters. The magnitude o f -60 dB o f Sn and S 22
denotes almost no power was reflected, while 0 dB magnitude o f S 2l and S l2
indicates total transmission. Fig. 4-6 shows the S parameters of the same THROUGH
while measured at 77 K. It is very clear that the S parameters changed dramatically.
All the power levels seemed to increase to some extent. Note that S2l and S l2 became
positive value, which is not true for passive device. The resistance o f the conductor
inside the cables decreased very much when temperature change from room
temperature to 77 K, so that the conductor loss o f the cables decreased. While the
analyzer still thought the cable had the original loss, the measured power
level
increased. In order to acquire more accurate measurement, low temperature
calibration is required. The proper standards need to be connected to the cables
according to the prompt of calibration menu, then the corresponding function key is
pressed after the cryo-chamber being cooled down to 77 K. The cryo-chamber then
needs to be warmed up to allow changing o f the standards, then cooled down again
56
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
n r jo
P» E* tf—
200. «H
511
S21
C A Y A O ^ C A ifH R O . M D P
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24
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Fig. 4-5 S parameters of a THROUGH at room temperature.
Elt Ed tfow Mo-0* tido
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20
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i
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Fig.4-6 S parameters of a THROUGH at 77K.
57
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
S21 Maffatude
S l l Magnitude
e^v«oc«wi_*>Mw
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J_
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, j.l
522 MagwHKle
c ^Y*ocAki
mor
S12 Magnitude
CAYAOCALI„•> MOT
an
,
kdi.ui. iii-i am
i i iuj i i t i
i i u niiii i n i i u i J i i i n i B i
IMHI
i l i .i k i i y
IVHJVPH
aa
on
am
an
an
Fig.4-7 S parameters of LOAD to port 1 and SHORT to port 2 after low temperature
calibration.
for calibrating. To complete a FULL 2-PORT calibration needs S cycles o f cooling
down and wanning up, which takes almost a whole day. As shown in Fig. 4-7, the S
parameters o f LOAD connected to port 1 and SHORT to port 2 show correct response
at 77 K after the low temperature calibration.
4J Ring Resonator and Quality Factor
43.1 Ring Resonator
The microstrip ring resonator was first proposed by P. Trough ton in 1969 for the
measurements o f the phase velocity and dispersive characteristics o f a microstrip line.
Along with the development of sophisticated field analyses, which gave accurate
modeling and prediction o f the ring resonator, many other applications such as
antennas, filters, oscillators, mixers, baluns, and couplers were also reported. In this
58
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work, the ring resonator is utilized, through the measurement of its Q-factor, by which
the surface resistance of superconducting thin films may be calculated based on these
results (84-90].
The ring resonator is a simple circuit and easily fabricated. It is merely a
transmission line formed in a closed loop. The basic circuit consists o f the feed lines,
coupling gaps, and the resonator as shown in Fig. 4-8. Power is coupled into and out
o f the resonator through feed lines and coupling gaps. When the mean circumference
o f the ring resonator is equal to an integral multiple o f a guided wavelength, resonance
is established. This may be expressed as
27 tr - n k g,
for n = 1,2,3,...
(4.14)
where r is the mean radius o f the ring that equals the average o f the outer and inner
radii, k %is the guide wavelength, and n is the mode number.
Coupling Gap
Feed Lines
Fig.4-8 Simple structure of microstrip ring resonator.
59
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I f we consider the two coupling gap locations as two fixed points, and the half ring
as the string tied in between the two points with certain tension, the resonance
condition is similar to the condition o f standing wave on a string. The guide
wavelength Ag can be expressed as
where A0 is the wavelength in vacuum, e rff is the effective dielectric constant.
One o f the drawbacks o f using ring resonator is the effect o f curvature. According
to W olff and Knoppik’s experiments, the influence o f curvature becomes large only if
substrate materials with small relative permittivities and lines with small impedance
are used. Under these conditions the widths o f the lines become large and a mean
radius is not well-defined. Fortunately, the dielectric constants o f materials used in this
work are 10 (alumina), 27 (YSZ) and 24 (LaAlOa) respectively, and the line
impedance is the typical value o f SO Q , so the line widths are very narrow compared
to the ring radius, hence the curvature effects are small enough to be neglected.
4.3.2 Coupling Gap of Ring Resonator
The coupling gap is an important part o f the ring resonator. It is the separation of
the feed lines from the ring that allows the substrates to only support selective
frequencies. The size of the coupling gap will affect the performance o f the resonator.
I f a very small gap is used, the fields in the ring structure will be disturbed by the feed
lines, thus the resonant frequency will deviate from the intrinsic frequencies of the
ring and the Q-factor will be lowered greatly. If the gap is too large, the energy
60
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coupled into the resonator will be too small to be measured. In the application such as
this work, the so-called “ loose coupling” is desired, which means the coupling is large
enough for resonance response to be measured, but also small enough not to seriously
disturb the resonance o f the ring structure [91].
There is no definite criterion for “ loose coupling” o f a ring resonator. Usually the
peak value of the resonator’s insertion loss should around -30 dB for a loosely
coupled resonator. In the past, the conditions of “loose coupling” were realized by
“try-and-correct” procedure, which is a tedious and time-consuming process.
However, using an RF-capable simulation tool (such as An soft HFFS), we can
simulate the resonator response to determine the right coupling gap without building
and testing the real resonators. The results are usually close to the desired value.
4J J Q-factor and Attenuation Constant
For a resonator composed by transmission line, the dissipative loss can also be
interpreted in terms o f a Q-factor (quality factor) as defined by the following
expressions:
Q =^ ~ ,
W
(4.16)
where <a0 is the angular resonant frequency, U is the stored energy per cycle, and W
is the average power lost per cycle. This figure of merit indicates the quality o f a
resonator, which is the reason it is referred to as “ quality factor” . From Eq. (4.16), it is
easy to see that the higher the Q-factor, the lower the loss.
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Using the general solutions o f transmission line, the relationship between Q-factor
and attenuation constant can be derived. Supposing Vp and I p, the peak voltage and
current at some plane along the line, we can rewrite Eq. (4.16) as following, for unit
length,
ju l/2 + C V ;/l)/2
„
"
(R ii+ a y ;)/2
'
where L, C, R, G are the same as defined previously.
The above equation can be further reduced to
Q = (°° R V l / Z \ +GV; = R/Z0 +GZ0 ’
(418)
by substituting I p = Vp/ Z 0 and Z0 = yjL/C for low loss transmission line.
Comparing with Eq. (3.19a) and (3.19b), we get a simple formula to relate the Qfactor to the attenuation constant
Q =—
2a
(4.19)
The total attenuation constant can be written into the sum of radiation loss,
dielectric loss and conductor loss, as described in chapter 3. So the Eq. (4.19) can be
rearranged into
1
Q
V
2 (a r + a d + ac)
J
P
,
1____1_
(4.20)
~ Q , + Q < + Qe
where the individual Q-factors associated with radiation loss, dielectric loss and
conductor loss are defined as following:
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(4.21b)
(4.21c)
To measure the total Q-factor of the ring resonator, a network analyzer is used to
measure the S parameters. Fig. 4-9 shows a typical resonator frequency response. The
loaded Q-factor o f the resonator is
where at0 is the angular resonant frequency and <u, -co2 is the 3-dB bandwidth. The
reason o f the measured Q-factor being called loaded Q-factor is that it includes the
effect o f feed lines and measurement loading effects.
S 21
▲
p
I
f
Fig.4-9 Resonator frequency reiponie.
63
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The Q-factor o f ring structure itself is called unloaded Q-factor (Q 0), which can be
derived from loaded Q-factor using following equation:
<4 -23'
where L is the insertion loss in dB o f the ring at resonance [92]. It is obvious that the
higher the Q-factor is, the sharper the resonant peak.
4.3.4 The Procedure to Calculate Surface Resistance
Eq. (3.41) in chapter 3 give us the relation between the surface resistance R, and
the conductor attenuation constant a c. Once we find a c, R, can be easily calculated
because all other things such as impedance, width o f the line, and thickness o f the
substrate can be either calculated or measured. The Eq. (4.21c) tells that we need to
find Q-factor associated with conductor loss Qc in order to know a c. The propagation
constant P can be computed as following:
P =T~
where the guide wavelength
(4-24)
is actually the mean circumference o f the ring
according to the resonance condition, thus it can be measured. Now, the only problem
that remains is how to separate Qc from the total unloaded Q-factor Q0. As stated in
Chapter 3, the measurement o f the radiation loss and dielectric loss is not trivial, so the
researcher developed a method to overcome this difficulty.
64
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Because die radiation loss and dielectric loss only depend on the dimension o f the
ring and the feed lines, the structure o f the packaging house and the substrate
materials, and they have nothing to do with the materials o f the conductor. So, if we
built a resonator using another conductor such as copper while keeping the dimension,
the packaging and the substrate the same, it should have the same radiation loss and
dielectric loss as the superconducting resonator.
For copper, its surface resistance can be calculated using following formula:
(4.25)
where a is the conductivity o f copper, and <5, is the skin depth that can be calculated
as:
(4.26)
Since Rs is known, we can get the Qc from Eq. (4.21c). We still can measure the
loaded Q-factor of copper ring resonator at 77 K, so that we can calculate the total
unloaded Q-factor Q0. Then according the Eq. (4.20), the term — + — o f copper
r
Md
ring resonator can be computed as
J 1_____11_ = J ___ 1_
Q r +Qd~Qo
(4.27)
Qc'
which should be exact same as that o f superconducting ring resonator. Then using the
same equation, Qc o f superconducting resonator can be computed, and therefore, R,
o f superconducting thin film can be solved for.
65
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Note that the conductivity o f copper will be different depending on different
process conditions, also, it will increase as temperature decreases. So, we measured
the actual conductivity o f copper thin film deposited at the HiDEC facility using a
meander line resistor instead o f the value from a handbook. The standard four-probe
method was employed. The curve o f conductivity versus temperature is shown in Fig.
4-10 [93]. The measured conductivity o f copper thin film is 4 .5 x l0 7 ( Q m ) ' 1 at 300 K
and 1.38x10s
at 78 K.
1.40E+08
1.30E+08
C
v
|
1.20E+08
I.10E+08
£
1.00E+08
■§ 9.00E+07
S
8.00E+07
|
7.00E+07
6.00E+07
5.00E+07
4.00E+07
70
120
170
220
270
Temperature (K)
Fig. 4*10 The conductivity of copper thin film versus temperature.
Courtesy of Shi Yan.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
320
CHAPTER 5
Thin
Film
Deposition,
Patterning
and
Characterization Systems
For depositing YBCO or dielectric thin films, many deposition techniques are
available, such as pulsed laser deposition (PLD), DC or RF sputtering, molecular
beam epitaxy (MBE), thermal and electron beam evaporation/co-evaporation, and
metal-organic chemical vapor deposition (MOCVD) [94].
In this work, we used the PLD technique that will be described briefly in the
section S.l. Since the YBCO thin films have to be patterned into lines to make ring
and feed lines, brief descriptions o f the photolithography process and ion milling
techniques for dry etching are included in section 5.2. In order to optimize and
monitor the process used in fabrication of YBCO or dielectric thin films, it is
necessary to be able to characterize them. Section 5.3 discusses methods and systems
used in characterization o f the films.
5.1 Thin Film Deposition System
5.1.1 Pulsed Laser Deposition (PLD)
Among many different techniques that have been used to deposit YBCO thin
films, pulsed laser deposition (PLD) was the first technique used to produce in situ
YBCO films with high critical temperatures, and it is still one o f a few techniques
which can produce high quality YBCO films. It uses the high energy density o f the
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pulsed laser beam to vaporize the target. The vaporized particles then condense on the
substrate parallel to the target to form thin films. An intrinsic advantage o f PLD is its
ability to transfer the target stoichiometry to the film. This is accurate, not only for
YBCO, but also for many oxides such as Ce02 and YSZ, making PLD suitable for
fabrication o f multilayer structures. Another advantage is that it functions well in
relatively high oxygen pressures, which is desirable in YBCO film deposition. One o f
the disadvantages o f PLD is that its uniform deposition area is relatively small because
of the limited size o f the plume and the angular distribution of ablated material.
Another major drawback of PLD is the presence o f particulates in deposited films.
Although several approaches can be used to reduce particulates, the complete
elimination of particulates in PLD is still a difficult task [95].
In this work, the PLD system was used to deposit both YBCO films and YSZ
buffer layers. The system consists o f an ArF excimer laser (Model: LPX305iH,
Lambda Physik, Inc.), an aperture, a double convex lens, and a deposition chamber, as
shown in Fig. 5*1. The excimer laser can generate pulses with energy up to 650
mJ/pulse at 193 nm wavelength. The dimension o f the aperture is 0.5 inch by 2 inch.
The lens is made o f MgF2 with a focal length o f about 49 cm. The deposition chamber
(Kurt J Lesker) is cylindrical with a diameter o f 16 inches and a height o f 18 inches.
The windows are made of UV grade silica (Suprasil) which need to be cleaned quite
often by gently wiping with a Simple Green soap solution and fine mesh CeC>2 powder
because o f deposition of the target materials during process. The vacuum system
consists of a mechanical roughing pump, a turbo-pump (Model: TMP151C, Leybold
Vacuum Product, Inc.), isolation valves, a gate valve, and pressure gauge. The base
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Laser Beam
Aperture
Target
Motor
Ion Source
Fig. 5-1 Schematic of PLD system.
69
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pressure obtained is SxiO*6 Torr. The chamber contains a target carousel assembly
which can hold up to six targets (Neocera, Inc.), enabling the deposition o f multilayer
structures without breaking the vacuum, and a three-axis sample manipulator on which
the substrate heater is mounted. The heater and substrate can move ±2.5 cm in X and
Y directions (parallel to the substrate surface) using two computer-controlled stepper
motors, making large area film deposition possible. The heater also can be manually
moved 10 cm in the Z direction (perpendicular to the substrate surface), which allows
variation o f the substrate to target distance. A mechanical feedthrough is used to
operate a shutter between the target and substrate. The angle between the target
normal and laser beam is 45°. An ion gun is also installed in this chamber for ionbeam assisted deposition, which will be discussed in the next section.
5.1.2 Ion Beam Assisted Deposition (IBAD)
The biaxially-aligned YSZ buffer layer is essential for growing YBCO on low cost
substrates or as part o f a multilayer structure. It provides an ordered structure for
texturing the top YBCO layer.
Thin films deposited on an amorphous or polycrystalline substrate often exhibit a
preferred orientation because the film has a lower surface energy when the film
surface is parallel to that particular set o f planes rather than other planes (out-ofplane). These films typically have a random distribution o f orientations in the
azimuthal direction (in-plane). Such a structure is called fiber texture or the film is
said to be uniaxially aligned. For example, YSZ films deposited on polycrystalline Nibased alloys can exhibit (111) orientation or (100) orientation, but they are not in70
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plane aligned [68,%]. On such a YSZ buffer, YBCO can be grown with its c-axis
oriented perpendicular to the substrate, whereas, the a and b axes are randomly
distributed in the substrate plane, resulting in a maximum attainable Jc o f 104 A/cm2 at
77K [68,97-99].
Yu et al. [100,101] found that the in-plane alignment was enhanced using the
IBAD method due to off-normal incidence ion bombardment during deposition o f
Niobium film on amorphous silica. Currently, no comprehensive theory exists to
explain the enhancement o f the in-plane alignment using IBAD. However, it was
proposed that the main mechanism for grain orientation is the difference in sputtering
yield between oriented grains and non-oriented ones [100-102]. Grains oriented to
allow channeling will grow faster than non-oriented grains which have higher
sputtering rate. So the oriented grains gradually dominate the surface. This mechanism
is based on the sputtering and channeling phenomena observed in the bombardment o f
single crystals [103,104]. The atom density is lower along some small index direction.
The sputtering yield is reduced for incidence o f the ion beam along these directions o f
the target and the channeling takes place in these directions.
Ion beam assisted deposition was successfully used to prepare biaxially-aligned
(in-plane aligned) YSZ buffer layers on a Ni-based alloy substrate by Iijima et al.
[68,105] in a dual ion source system. The best in-plane alignment was obtained when
the incident angle o f the ion beam was 55° from the substrate normal, indicating that
the channeling direction is along the YSZ <111> axis (54.7° from <100> axis).
Subsequent deposition o f YBCO produced biaxially-aligned films with critical current
densities of 2.5x10s A/cm2 at 77 K, which is one order of magnitude higher than the
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values obtained on uniaxially aligned YSZ buffer layers. Since then, biaxially-aligned
YSZ thin films have been fabricated on many different substrates using a variety of
evaporation sources [69-70, 106-108] with fairly good results, demonstrating that
good quality YBCO films can be fabricated on non-single-crystalline substrates.
In this work, a PLD system was used to deposit biaxially-aligned YSZ buffers. The
pulsed laser was the evaporation source, while an additional intemal-mount RF ion
source with a beam diameter o f 3 cm (3RF-1200-100, Ion Tech, Inc.) was installed in
the system to provide the off-axis ion beam during deposition, as shown in Fig. 3-1.
Argon is used as the ion source gas, and two mass flow controllers (UFC-1100A, Unit
Instruments, Inc.) are used to control argon gas flow to the ion source and neutralizer.
A third mass flow controller is used to control the O 2 gas flowing into the chamber.
The incident angle of the ion beam is fixed at 35° with respect to the substrate normal.
The ion source should be as far as possible away from the substrate in order to achieve
uniform ion beam bombarding onto the substrate. Limited by the size of deposition
chamber, the distance between the ion source and the substrate is 11 cm in our system.
5.2 Film Patterning System
In order to form ring and feed lines, YBCO thin films have to be patterned into
lines. In this work, the ion milling method was used to etch YBCO films. Patterns
were generated using a positive photoresist (AZ P4330-RS, Shipley) spun at 4300 rpm
for 30 seconds, followed by a three minutes soft bake at 80 °C. After exposure to UV
light for 100 seconds (light integration set to 9) in a Canon mask aligner, the samples
were developed in a 1:3 developer (AZ400K, Shipley) versus water solution for 1
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minute, then rinsed in DI water and blown dry with ty . The sample was inspected
under a microscope. If there were any defects present, rework should be done by
rinsing off the photoresist using acetone and starting over again.
The patterned sample was mounted on a holder inside the chamber of the ion
milling equipment. After pumping down to the desired vacuum (lxlO*5 Torr), Ar gas
was introduced into the chamber. A 3-cm diameter Ar ion source was used to produce
an ion beam which bombarded the sample vertically and etched everything in its path.
The part o f the thin film not covered by photoresist was etched away, while the part
underneath the photoresist remained because the resist prevented it from being
bombarded by Ar ions. After etching, the remaining photoresist was removed in a bath
of acetone. The end point o f the ion milling process was determined by observing the
sample through the window. A certain amount o f over etch was used in order to avoid
shorts between lines. A detailed ion milling system setup can be found in [109].
5J Thin Film Characterization System
5.3.1 X-ray Diffraction
X-ray diffraction (XRD) is a useful tool for investigating the fine structure o f
matter. It can be used in many different ways. In this work, we mainly used XRD to
exam the phase purity and orientation o f YBCO films and YSZ buffer layers.
A. 6 - 2 0 scan
Suppose that a beam o f monochromatic x-rays with wavelength X is incident on a
crystal at angle 6 , where 0 is measured between the incident beam and the particular
73
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Fig.5-2 Schematic of Bragg condition.
lattice plane as shown in Fig. 5*2. A diffracted beam may be defined as a beam
composed o f a large number o f scattered rays that are in phase and mutually reinforce
each other (constructive interference) [110]. The diffracted beam can only be formed
in the direction that makes an angle 6 o f reflection equal to the angle 6 o f incidence.
As shown in Fig. 5-2, from basic theory of optics, we know that the scattered rays 1’
and 2’ will be completely in phase if the path difference is equal to an integral number,
n, of wavelengths, that is
2dsin0= nX
(5.1)
where d is the plane spacing and n is called the order o f reflection. Eq. (5.1) is known
as the Bragg condition. When this condition is satisfied, the intensity o f the reflected
X-rays is enhanced significantly due to the sum o f their coherent amplitudes. When
the Bragg condition is not satisfied, the intensity o f reflected X-ray is reduced because
74
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o f the sum of non-coherent amplitudes. The angle between the diffracted beam and the
incident beam is always 2 0 . It is this angle, 2 0 , rather than 0 , that is usually
measured experimentally. In all other directions o f space, the scattered beams are out
o f phase and cancel each other (destructive interference).
The basic features of an x-ray diffractometer are shown in Fig. 5-3. A sample
being examined, C, is placed on a sample holder which can be rotated about an axis O
perpendicular to the plane of the drawing. The x-ray source, S, generates a
monochromatic x-ray beam that irradiates the sample. The intensity o f a diffracted
beam is measured by a detector (counter), D, which can also be rotated about the axis
O. Some diffractometers are equipped with a three-circle goniometer as a sample
holder, enabling one to determine the orientation o f a single crystal or to measure the
in-plane alignment o f an oriented thin film. The three-circle goniometer provides the
three possible axes: one coincides with the diffractometer axis O, the second (AA *) lies
in the plane of incident beam / and diffracted beam R and tangent to the sample
surface, while the third (BB *) is normal to the sample surface. The diffractometers that
have a three-circle goniometer are commonly referred to as four-circle diffractometers.
In a 0 - 2 0 scan, the sample is rotated about O and the detector is also rotated
about O. The detector is always rotated twice as much as the sample is rotated. Thus,
the 0 - 2 0 condition is always sustained. The intensity o f the diffracted beam and the
20 angle is recorded. Sharp peaks occur at certain 20 angles where the Bragg
condition is met.
From the 0 - 2 0
scan, information about phase purity and
orientation of the sample thin films can be obtained. The 0 - 2 0 scan only can tell
which o f the lattice planes are parallel to the substrate surface. In other words, it gives
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20
\C
Fig. 5-3 Schematic of an X-ray diffractometer.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the degree o f out-of-plane orientation. If we want to leant the degree o f in-plane
orientation, the Pole figure or 0 scan is needed.
B. Pole Figure and 0 Scans
A pole figure is a stereographic projection that shows the variation of pole (peak)
density with pole orientation for a selected set o f crystal planes. It can describe
textures or in-plane alignments o f thin films. If a thin film has a (001) preferred
orientation as determined by a 0 - 26 scan, we then may want to know whether or not
there is a preferred orientation in the (100) plane parallel to some reference direction
and how much o f the preferred orientation (in-plane alignment) is present. Such
information can be obtained by making a pole figure o f a 0 scan.
To determine an (hkl) pole figure, the detector is fixed at the proper 26 angle and
the sample is at an angle o f 9 to receive the reflection from a set o f (hkl) planes. For
example, one often measures the (111) reflection for a (100) orientated sample, and
therefore, the detector is set to the corresponding 26 position. A three-circle
goniometer is used to rotate the sample. The sample is first rotated about the axis AA ’
to a certain angle y/, then it is rotated 360° about axis B B This procedure is a repeated
at different angle yf. If there are four poles detected in the range 0 = 0-3 6 0 ° and
yf = 0 - 90°, then we know that the film has a preferred in-plane orientation. The poles
corresponding to the four sets o f (111} planes should lie in yr = 34.7°, because it is
the angle between the <111> and <100> axes. After obtaining the pole positions, the
orientation of grains relative to a specific sample direction can be determined.
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Since (111) poles should appear at y/ = 54.7° if a ( 100) orientated film is in-plane
aligned, we can set y to 54.7° and only rotate B B ' from 0 to 360° . The resulting
curve o f intensity versus <f> is called the <f> scan. A <j> scan actually corresponds to a
special set o f data from a pole figure. It provides the main information about in-plane
alignment of films and it takes less time to record a <f> scan than a pole figure. Four
peaks should appear on a (111) ^ scan for an in-plane aligned sample. The full width
at half maximum (FWHM) o f the peaks o f 0 scans can be used to examine the degree
o f in-plane alignment. The smaller the width, the better is the in-plane alignment.
In this work, XRD measurements were performed on an X’PERT system (Philips)
using Cu-Ka radiation. The X’PERT system consists o f two diffractometers, one of
which has a three-circle goniometer, enabling us to make pole figures and <f> scans.
The wavelengths of the Ka doublet for a Cu target are Kai= 1.5406 A and
K<i2= 1.5444 A. Kcii is about twice as strong as K a 2, so the weighted wavelength for
K a is 1.5418 A.
5J.2 Tc and Jc Measurements
A. Inductive Measurements (non-contact method)
The inductive method uses instrumentation techniques suggested by Claassen et al.
[ I l l ] to measure the induced shielding currents using a single coil. When an audio
frequency sine wave current drives a flat multitum coil which is placed close to a
superconducting film surface, it induces shielding currents that flow on the film
surface. Critical currents can be measured in this way by detecting the development of
78
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die odd harmonic components across the coil as die drive currents through the coil are
increased. Classen et al. showed that at currents above the critical current, the
amplitude of the odd harmonic increases rapidly from a steady value. Hence, by
monitoring the amplitude o f the third harmonic signal, one can determine the critical
current.
As shown in Fig. 5-4, a sine wave oscillator produces a sine wave ( f = lKHz). The
signal is then amplified using a power amplifier which produces the required sine
wave drive current. The drive current is monitored through a 100 f i resistor and a
multimeter. The drive coil also acts as a pick-up coil. The voltage across the coil is
then filtered through a twin-tee notch filter with a center frequency o f 1 KHz and
analyzed by the lock-in amplifier which measures the amplitude (voltage) o f the third
harmonic signal. The drive current is incremented and the corresponding amplitude o f
the third harmonic is measured. A plot o f the drive current versus amplitude o f the
third harmonic usually shows a steady value, -10 pV or lower, until the critical drive
current is approached and the third harmonic voltage rises rapidly. We usually take the
current corresponding to a third harmonic voltage 10 pV as the critical current. The
critical current density is then determined using the following empirical relation,
J c(MA/cm2) * 120I c(m A )/t
(A)
(5.2)
where Ic is the critical current in mA and t is the thickness o f thin film in
A.
All Jc
measurements are performed at liquid nitrogen temperature (77K).
The same set up is also used for the measurement o f the critical temperature, Tc,
with minor change in the connections as shown in Fig. 5-4. In this case, the inductive
signal, or reactive component o f the coil voltage at the fundamental drive frequency
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HP 6825A
Power Supply/Amp
*4
>82
IN My1 4 *
-w e
O
O
Keithley Multimeter
Connect for
TcMeanranent
Connect for
JcMeanranent
OUT
••
[Function Generator
lH *i«
- [-tF M ln i
Lock-in Amplifier
too
o0 -1
f - lkHs
Connect
to
V Coil
Connect
Fig. 5-4 Block diagram of inductive measurement of Tc and J e (112].
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(10 KHz), is measured as a function o f temperature. The inductance, and hence, the
reactive component o f the voltage from the coil, drops substantially at the critical
temperature due to the shielding supercurrent induced in the superconducting film that
tends to cancel out the fields penetrating into the film. By cooling down the sample
from room temperature and measuring the reactive component o f the coil voltage at
regular intervals, the Tc can be obtained from a plot of the reactive component o f the
coil voltage versus the temperature.
B. Transport Measurements (contact method)
Transport Tc and Jc measurements were employed to characterize superconducting
YBCO films. This measurement system consists of a cryoprobe which fits into a
stainless steel tube, a liquid nitrogen dewar, and the instrumentation equipment. At
one end o f the probe is the sample holder made o f copper. The connections to the four
probe wires are also provided on the same block. The sample is usually pasted on the
sample holder block with GE 700 varnish and the four probes are connected to the
sample using silver paste. After the sample is mounted, it is covered by screwing on a
shroud which helps to maintain a uniform temperature within the shroud volume and
also prevents moisture condensation on the sample. Heating o f the sample is provided
by sending a small current through a couple o f turns of Cu wire wound at the bottom
o f the sample holder block. The temperature o f the block is sensed via a diode
temperature sensor right below the sample. The other end o f the probe consists o f gas
inlet and external electrical connectors for carrying signals from the holder end to die
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outside and vice versa. The whole probe can be encased in a stainless steel tube, which
can be filled with helium gas to provide a steady rate for cooling.
The block diagram o f the transport measurement system is shown in Fig. 5-5
[113]. For Tc measurements, the resistance o f a bridge is measured for different
temperatures down to 77 K (from room temperature). The bridge resistance is
measured by passing a constant current through the outer two probes and monitoring
the corresponding floating voltage between die inner two probes. In order to nullify
the effects of thermal voltages, a current I is first passed through the bridge in the +V
direction and the floating voltage V~ is noted. The current direction is then reversed to
the - V direction and the corresponding floating voltage V is noted. From these two
values, the resistance is obtained as R = (V*-V) 2I. The thermal voltages cancel out
since they have the same polarity. The temperature at which (V*-V) < lp V is
determined as the critical temperature or zero resistance temperature, Tc.
In the Jc measurement, the probe is directly immersed in liquid nitrogen. Two
holes on the top o f the holder block allow liquid nitrogen to flow into the volume
between the sample holder and shroud, thus maintaining the sample temperature at a
constant value o f 77 K. The sample current 7Cis increased gradually and the voltage
across the bridge is monitored using the multimeter. The critical current is determined
as die current at which the voltage across the bridge o f the sample increase to lpV.
The critical current density is simply calculated by
where w is the width o f bridge and d is the thickness o f the thin film.
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Temperature Sensor
Computer
Sample Holder
Multimeter
Fig. 5*5 Block diagram of tranaport measurement system [113|.
In this work, the non-contact method is used to check the critical temperature o f
every deposited YBCO thin film because o f its non-destructiveness and convenience.
The surface o f YBCO thin films may even be protected by a layer o f photoresist to
reduce the possibility o f scratches during measurement without interfering with the
sensing o f the inductive signal. Then the good quality YBCO can be fabricated or
incorporated into devices after cleaning. Some researchers used the contact method by
applying silver paste or wire bond to gold pads to make a good ohmic contact, but it is
destructive. The YBCO thin films tested using the contact method for measurement
can not be used for devices. One o f the advantages o f the contact method is that it
provides information on the real resistance o f thin films rather than the less
meaningful inductive voltage for non-contact method. For critical current density
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measurement, the contact method gives more accurate results. The contact method can
also be utilized to measure the resistance versus temperature o f other conductors such
as copper in this work.
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CHAPTER 6
Fabrication
A detailed description o f the process used to fabricate the YBCO ring resonators is
discussed in section 6.1. The characterization methods are described in section 6.2.
6.1 Fabrication o f YBCO Ring Resonators
6.1.1 Structure o f Ring Resonators
The pattern o f the ring resonator was very simple as shown in Fig. 4-8. It consisted
o f a ring and two feed lines. In order to make the characteristic impedance o f the feed
lines SO fi, two different patterns were designed. For an alumina substrate whose
dielectric constant is 9.9 and thickness is 25 mils (Accumet Engineering Corp.), the
line width was designed to be 24 mils, which made the impedance S0.1 Q based on
Eq. (3.23). The radius o f the ring was 148 mils so that the guide wavelength was 2.362
cm. The coupling gap was decided to be 22 mils after some simulation work. For YSZ
single crystalline substrate with a dielectric constant o f 27 and a thickness o f 20 mil, a
line width o f 5.6 gave 50.3 Q as the characteristic impedance. The radius of the ring
was set to be 200 mils, which gave guide wavelength as 3.19 cm. The coupling gap
was 35 mils. The LaAlC>3 single crystalline substrate had the same thickness as YSZ
but a smaller dielectric constant o f 24. Since the pattern for YSZ only brings the
impedance on LaAlC>3 to 53.3 ft, which still matches 50 f l adequately, we used the
same design for YSZ substrate, for convenience. The guide wavelength was still 3.19
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cm. Both two single crystalline substrates were from Coating and Crystal Technology,
Inc. All the patterns were confined in a square o f 600 mils by 600 mils, which was the
size of the substrate, with the ring in the center and feed lines reaching the edges o f the
square.
In the final stage o f this work, a tunable spiral resonator was built on a LaAlC>3
substrate to demonstrate the feasibility o f frequency tuning. The pattern is shown in
Fig. 6-1. The dimension of the outer square is the same as simple ring resonator. The
inner dashed square indicates the size o f toractor, which is another superconducting
plane floating about 4 mils above the signal plane. The spiral is 6.5 turns with 5 mil
line width and 5 mil gap in between adjacent turns. The coupling gap is 35 mils also.
Because the presence o f toractor will change the impedance of the feed line, the feed
lines underneath the toractor have different width from the rest o f them to make 50 f t
lines.
j
j
ii
i
i
I
j
i
[
Fig. 6-1 The pattern of tunable apiral resonator.
Courtesy of Humayun Kabir.
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The process flow is shown in Fig. 6-2 step by step, using an alumina substrate as
die example. The YSZ buffer layer was first deposited on the alumina substrate to
provide a template for YBCO deposition. After YBCO deposition, a layer o f gold was
immediately deposited using PLD without breaking the vacuum, so that the gold layer
had extremely small contact resistance with YBCO layer. Because the microstrip feed
line o f the resonator needs to be connected with a coaxial-to-microstrip transition
terminal by mechanical contacting its metal tip, the contact resistance will be very
high if the tip directly contacts YBCO surface. But contact resistance o f metal to gold
is relatively small. Using gold layer as an interface, YBCO thin film can have very
small contact resistance with the metal tip.
Exposure
Photo m is t
Gold
Mask 2
YBCO
Alumina substrate
I
,
Exposure
|
|
YSZ
|
Process end ion milling
Procass and ion milling
Clean up
Clean and put photo resist
Fig. 6-2 Process (low of fabricating resonators.
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Since the gold layer is only needed on top of the feed lines, it is etched away by
ion milling from other areas after first photolithography because its presence on top of
the ring will
complicate the data analysis afterwards.
Then
the second
photolithography, followed by ion milling, is conducted to define the ring and feeding
lines. Note that the edges o f the substrate are always not clear during the lithography
because the photoresist is thicker at the edges than other areas, after spin coating. The
thicker resist areas will not get the equivalent amount o f UV light exposure that is
designed for normal thickness. Hence, there is some resist remaining along the edges
o f the substrate after developing, which protects the YBCO underneath during ion
milling process. Therefore there will be a rim o f YBCO along the edges of the
substrate, which m ay cause short circuit. In order to achieve clean substrate edges, the
substrate starts with size slightly larger, such as 650 mils by 650 mils, then is diced
into designed size after finishing all the above steps. Hence, the YBCO residues along
the edges are cut o ff and the new edges are clean.
Fig. 6*2 actually only illustrates the fabrication o f the signal plane. Because we use
in-situ method to deposit YBCO, which is impossible to deposit on both sides of the
substrate so far, another substrate with YBCO thin film is needed to provide a ground
plane. The ground plane has the same width o f 600 mils as signal plane but larger
length of 800 mils. The center square area of 600 mils by 600 mils that is not covered
by gold layer will contact with the bottom surface o f signal plane closely to form
microstrip structure. While the two stripes o f 600 mils by 100 mils covered by gold
layer extend out o f the two ends o f signal plane, they will contact the wall of the
packaging housing, which is the ground of the device.
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For resonators built on single crystalline substrates, the steps are essentially the
same, except that we skip the deposition o f a YSZ buffer layer. The packaging
housing is made of copper as shown in Fig. 6-3. The ground plane is inserted into a
slot and pressed against copper wall by the screws coming up from the bottom. Thus
the YBCO thin film on die ground plane is electrically connected with the ground o f
the device. The signal plane is placed on top o f ground plane. The dps o f two
connectors mechanically press the feed line to form contact and fix the position o f
signal plane. Finally a lid is covered on top o f housing to shield and protect the device.
Notice that another lid with an extension in the center is for tunable spiral resonator.
The toractor is mounted on the extension o f the lid so that it will be a few mils away
from the signal plane when the lid is closed. The variation o f gap between toractor and
signal plane is achieved by inserting spacers between the lid and the wall of packaging
housing.
Signal plans
C oppsr hom ing
G round p la n s
T o n jd o r
•>
o
-
CoaiiaMo-microstnp
transition tarmmal
\ /
Lid
Sidewsw
Top «rsw
Fig. 6-3 Packaging Housing of resonators.
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6.1.2 Substrate Preparation
The substrates we used for the YBCO ring resonators were individual square
pieces o f alumina, single crystalline (001) oriented YSZ and single crystalline (001)
oriented LaA103 substrates. All the substrates are chosen to be two-side-polished not
only because it is easier to remove the silver paste on the back side after high
temperature deposition, but also two substrates can form more complete contact when
being stacked together as described earlier. Before depositions, the substrates were
ultrasonically scrubbed in isopropanol (IPA), followed by acetone, then IPA again for
one or two minutes each. The cleaned substrate was then blown dried with nitrogen.
To attach the substrate to the heater block, silver paste was spread uniformly with a
brush over an area slightly larger than the substrate. After being placed on the paste,
the substrate was gently pressed with tweezers, so that the substrate contacted well
with the paste and entrapped air was minimized. All excessive paste was removed
with a razor blade to avoid contamination o f silver paste to the substrate top surface.
Once the substrate was sufficiently well mounted, the heater block was heated to ~
ISO °C for 5 minutes, followed by 250 °C for 3 minutes, and finally 350 °C for 5
minutes to dry the paste solvents while it was still outside the deposition chamber. The
heater block with substrate was then transferred into the chamber for the YBCO
deposition.
The good attachment of the substrate to the heater block is critical to ensuring the
good temperature uniformity across the substrate. Since the YBCO deposition is
performed under very high temperature (730 °C), any air bubbles underneath the
substrate will incur a lower temperature on the surface o f substrate at that spot than
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other areas, which will degrade the quality o f YBCO deposited on that spot. For
alumina substrate, the deposition o f YSZ buffer is conducted under room temperature.
So substrate attachment is not that critical, as long as the substrate is securely fixed.
6.13 IBAD YSZ Deposition for Alumina Substrate
The IBAD YSZ layer serves as a template for growing YBCO thin film because o f
its good c-axis and in-plane orientation. After the substrate was mounted on the
holder, it was then transferred into the deposition chamber. The chamber was first
evacuated to a pressure o f 10 mTorr with a mechanical pump, then a turbo-pump was
activated to further lower the pressure to 10'5 Torr. Argon and Oxygen were
introduced into the chamber with proper gas flow set by mass flow controllers. The
YSZ target was ablated by laser beam for one or two minutes before actual deposition
while the shutter was in the “ close” position, so that clean and fresh YSZ material was
exposed at the surface. The ion source was then turned on to bombard the substrate for
about one minute to further clean the substrate surface. After pre-ablating the YSZ
target and pre-bombarding the substrate, the shutter was opened to start the deposition.
The conditions used for the IBAD YSZ deposition are listed in Table 6-1. The
thickness o f the YSZ film is usually 3000 A, which is achieved by about one hour
deposition.
Because the laser beam evaporates the material out o f the target, it will leave a
circular groove on the surface o f target very soon. When starting deposition with flat
target surface, the uniform area o f the thin film is large enough to accommodate the
full size of the substrate. When the groove gets deeper and deeper, if the laser beam
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Table 6-1 Parameters for IBAD YSZ Deposition
Chamber base pressure
5x10'* Torr
Target to substrate distance
85 mm
Laser energy density
3 J/cm2, 350 mJ on external power meter
Laser repetition rate
6 Hz
At flow for ion source
10 seem
At flow for neutralizer
9 seem
O 2 flow
5 seem
Forward RF power
45 W
Ion beam current/voltage
16 mA/250 V
Acceleration current/voltage
3 mA/200 V
Neutralizer current/voltage
20 mA/lOV
Deposition temperature
Room temperature
keeps hitting at the same position, the uniform area will become smaller and smaller,
because the side walls of the groove narrows the angle in which the evaporated
material comes out from the bottom o f the groove. So the position of laser beam needs
to be moved to a flat surface after certain time deposition to ensure good thin film
uniformity. By moving the focus lens up or down, the position of laser beam on the
target can be moved up or down. Starting from the edge o f target, the laser beam is
moved towards to the center about 2 mm after four depositions, then 2 mm
successively after another three depositions, two depositions and one, because more
material is consumed for the same time o f deposition when the laser beam
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approaching to the center. After all four positions have been utilized, the target is
taken off and polished using sand paper to create a new flat surface. The polished
target is put back, and a new cycle starts again.
The advantage o f above the procedure is that the position o f uniform area will not
change significantly over time. Therefore, there is no need to check the position o f
uniform area using a dummy wafer prior to every deposition, as we did when we
initially moved the laser beam randomly. The other condition that needs to be noted is
that the substrate should be kept as far away as possible from the ion source. The YSZ
thin film will crack if too much stress was built up because o f receiving excessive ion
bombarding.
6.1.4 YBCO Deposition
Once the heater block was transferred into the deposition chamber, its temperature
was maintained at 2S0 °C while pumping down the chamber. The turbo pump was
turned on when die vacuum achieved 10'2 Torr. A base vacuum o f 10's Torr was
attained within 1 0 - 1 5 minutes. The temperature was gradually ramped up at a rate o f
-100 °C/2-3 minutes (5 Volts/2-3 minutes for the variac). When the temperature
reached about 500 °C (30 Volts for the variac), all the valves were closed, and
approximately 200 Torr o f oxygen was introduced into the chamber. After a 5 minute
soak, which helps to dry the silver paste completely and oxidize the possible
contamination on the surface o f substrate, the valve to the mechanical pump was
opened fully so that the chamber was evacuated to about 10*2 Torr. Then the turbo
pump was connected to bring down the vacuum to 10"* Torr for 5 minutes to clean out
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possible byproducts o f the oxidation. Then the turbo pump was isolated and switched
off. By adjusting valve to the oxygen tank and the valve to the pump, the oxygen
partial pressure was m aintained at ISO ~ 175 mTorr for deposition on LaAlC>3
substrate. The substrate was then heated to the deposition temperature o f 730 °C in
about IS minutes. For deposition on YSZ substrate, the oxygen pressure was regulated
at 200 Torr again, and the substrate was heated to deposition temperature and annealed
at that temperature for 20 minutes. The reasoning for that will be explained in the next
chapter. For a well attached substrate, the substrate looks uniformly as red as the
heater block due to the high temperature.
During the entire heating process, the laser should be running at the desired high
voltage to stabilize the output power. A power checkup using an external power meter
is recommended. After the substrate reached the deposition temperature, the target was
ablated for 2-3 minutes with a 6-Hz laser beam with the shutter in the closed position.
Next, the shuttle was opened and the deposition was started. The typical deposition
parameters are shown in Table 6-2.
Right after deposition, the film was soaked in 640 Torr oxygen. The variac stayed
on 54 Volts (-700 °C) for 5 minutes, then 50 Volts (-660 °C) for 10 minutes, 45 Volts
(-600 °C) for 10 minutes, and 40 Volts (-560 °C) for 10 minutes. Finally, the film was
annealed at 34 Volts (-500 °C) in about 500 Torr oxygen for 1-2 hours. When the
annealing process was over, the temperature was decreased at the rate o f 60 °C/4-5
minutes (5 Volts/4-5 minutes for variac). The thin film must be cooled inside the
chamber after turning off the power to the heater for at least 30 minutes before taking
out for further processing.
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Table 6-2 YBCO film depMltloa parameters
Chamber base pressure
10° Ton-
O 2 pressure
150 m Torr-175 mTorr
Target to substrate distance
65 mm
Laser energy density
3-4 J/cm2, 470 mJ on external power meter
Laser repetition rate
6 Hz
Heater voltage
54 V
Deposition temperature
730 °C
Deposition time
18 min
Annealing condition
500 -550 Torr O 2, 500°C, 1-2 hours
Film thickness deposited normally
-3000 A
For most samples used for building resonators, a layer o f gold was deposited
immediately after YBCO deposition. After substrate was cooled, the chamber was
evacuated again to 10's Torr with mechanical and turbo pump and without opening it.
The gold target was brought into position by rotating the target carousel. The
condition of gold deposition is listed in Table 6-3.
A good quality YBCO thin film has a dark color and reflective surface. When a
gold layer is deposited over it, the surface is gold in color and still highly reflective. If
any area appears cloudy, then the quality o f the YBCO may be assumed to not be very
good. Next, the silver paste on the back o f the substrate needs to be removed before
any further processing. After undergoing high temperature, the dried silver paste stuck
with the substrate very firmly, and we had to use a razor blade to peel it off initially,
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Tabic 6*3 Gold film deposition parameters
Deposition pressure
10° Torr
Target to substrate distance
65 mm
Laser energy density
3-4 J/cm2, 470 mJ on external power meter
Laser repetition rate
6 Hz
Heater voltage
5V
Deposition temperature
100 °C
Deposition time
20 min
Film thickness deposited normally
-3000 A
which took great patience to do. But quite often, the substrates will splinter under the
blade because o f the uneven force added. For LaA103 substrate, situation is even
worse because o f its twining structure and poor mechanical strength. Later on, a new
approach finally solved the problem. An etchant bath composed o f H2O2 and NH4OH
with 1:1 ratio in volume can etch the silver so effectively that the silver disappears
within seconds. Note the YBCO layer needs to be protected by coating a layer of
photoresist before the substrate was dipped into chemical. After etching, the substrate
was rinsed by Di-water and blown dry with nitrogen. The Tc o f the YBCO film was
then tested using the inductive method before patterning. At last, the photoresist was
stripped in acetone. Thus, the resist also protected YBCO from possible scratches
during the measurement of Tc.
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6.1.5 Copper Deposition
In order to extract the Q-factor associated with conductor loss from the total Qfactor, parallel copper ring resonators with exacting geometry were fabricated. The
copper thin films were sputtered by XM-8 which is manufactured by Van an Corp.Thin Film Division. The process parameters are shown in Table 6-4. An RF etch was
used to clean the surface o f the substrate prior to deposition. A thin titanium layer is
needed to provide better adhesion between copper and substrates. An 11-second
titanium sputtering at 1 KW gave a very thin layer o f 200
sputtering followed at 3KW and produced 3000
layer was chosen to be 3000
A thin
A.
A 15-second copper
film. The thickness o f copper
A for the signal plane and 2 tun for the ground plane. The
2 pm copper film was sputtered in seven steps with four minutes in-between to avoid
overheating o f the substrate.
Table 6-4 Copper thin film deposition parameters
RF etch time
30 seconds
Titanium sputtering
11 seconds at 1 KW
Copper sputtering
15 seconds at 3 KW, 7 runs with 4 minutes interval
6.1.6 Patterning: Lithography and Ion Milling
In this process, the ring and feed lines were defined through lithography and ion
milling techniques. Firstly, the clean and dried sample was placed on a spinner chuck.
Then, 4-5 drops o f positive photoresist were injected slowly onto the central part of
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the sample surface and the spinner was turned on at a speed of 4500 rpm for 30
seconds. The thickness o f the photoresist was 3*4 pm. After spinning, the sample was
placed on a hot plate at 80 °C for two and a half minutes to remove the residual
solvent in the resist. The resist coated sample was then transferred to a mask aligner.
A glass mask was aligned above the sample, and the sample was exposed to UV light
for 100 seconds with the light integration set to 9. After exposure, the sample was
immersed in developer for 1 minute, then rinsed in DI water and blown dry with
nitrogen. Therefore, the exposed parts o f the resist dissolved away and the pattern was
formed. Inspection under a microscope was required to insure there were no defects in
the pattern. In fact, defects occurred very often due to particles and resist that
remained on the mask from the previous exposure. An additional step was adopted to
prevent the formation of defects. We cleaned the mask using acetone before every
exposure. The chances of defects were greatly decreased. However, if defects still
happened sometimes, we used acetone to strip the resist, cleaned the sample and
repeated the entire lithographic process again.
Since we used ion milling to etch the sample, the sample with the resist pattern
was placed directly into the chamber without a hard bake. The sample was mounted on
a holder whose surface was perpendicular to the 3 cm Ar ion source. After a base
vacuum of 10's Torr was attained, Argon gas at a 15 seem flow rate was introduced
into the chamber and the ion source was turned on. The parameters used for ion
milling are listed in Table 6-5.
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Table 6-5 Parameters used in ion milling
Base vacuum
10* Ton-
Ion source to substrate distance
14 cm
Ar flow rate
15 seem
Discharge current/voltage
0.55 A/55 V
Beam current/voltage
30-32 mA/500 V
Accelerator current/voltage
2-4 mA/250 V
Neutralizer current
38-40 mA
The Ar ions etched everything in their path, but the patterned parts o f the YBCO
film covered by resist were protected, while the exposed part was sputtered away. The
ion milling proceeded until the transparent substrate was clearly seen through the
quartz window of the chamber. The typical etch time was about 20*25 minutes and
included an over etch time in order to ensure complete etching o f the sample. The etch
rate o f gold is much faster than YBCO, so that it only took about one minute to etch
the gold layer.
After ion milling, the resist on the substrate was stripped in acetone. The substrate
was then ultrasonically scrubbed in acetone, followed by IPA, and blown dry.
6.1.7 Resonator Packaging
Because the signal plane started with the size larger than the final size for die
reason described before, it needs to be diced into right size after done all the
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patterning. A layer o f photoresist is also needed to protect the YBCO circuit because
die cooling water will keep washing the substrate during the dicing process.
The package o f the resonator provides a housing for the resonator circuit, a
mechanical carrier for the substrate and a means of electrical connection to the
resonator. The completed signal plane and ground plane together with the packaging
housing prior to being packaged are shown in Fig. 6-4, taking the tunable spiral
resonator as example. Notice the YBCO toractor on the extension o f the lid, which
will sit right above the signal plane when lid is closed. For a simple ring resonator, just
replace the special lid in the figure with a flat copper lid. Fig.6-5 illustrates the
packaged ring resonator without lid on. The two coaxial-to-microstrip transition
terminals have been connected to the feed lines and are ready for cable connection.
Fig. 6-4 The signal plane, ground plane and packaging housing prior to being packaged.
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Fig. 6-5 A packaged ring resonator.
6.2 Characterization of YBCO Thin Films on Various Substrates
6.2.1 Electrical Characterization
The TcS of the YBCO layers were determined using the inductive method since it
is efficient and non destructive to the thin film. The samples with good critical
temperatures then went on for further fabrication. To find the conductivity o f copper at
77 K, a meander line resistor w as built and tested using transportation method.
6.2.2 X-ray Diffraction
X-ray diffraction 0-20 and <f> scan were performed on the YBCO thin film on
various substrates. The 0-20 scan was used to determine the phase purity o f the
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YBCO thin film and its c-axis orientation. The 0 scan was used to check the in-plane
orientation o f both the IBAD YSZ layer and YBCO layer on it.
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CHAPTER 7
Results and Discussion
In this chapter, the results for the measured surface resistance o f YBCO thin films
on various substrates are presented and discussed. Section 7.1, 7.2 and 7.3 are for
alumina, YSZ and LaAHZ>3 substrates, respectively. Different substrates were utilized
in order to achieve a low surface resistance. The concept and performance o f a tunable
spiral resonator, a fundamental element for an all-HTS tunable filter, is described in
section 7.4.
7.1 Alumina Substrate with IBAD YSZ Buffer Layer
7.1.1 Surface Resistance of YBCO thin film
The alumina substrate was initially chosen because o f its strong mechanical
strength and low cost. Since alumina is polycrystalline, an YBCO thin film cannot be
grown directly on its surface. However, using IBAD and PLD to deposit a bi-axially
aligned YSZ layer, a superconducting YBCO thin film may be grown on an alumina
substrate.
The critical temperature of YBCO on an alumina substrate with an YSZ buffer
layer is usually comparable to that o f YBCO on an YSZ single crystalline substrate,
while the critical current density o f YBCO on alumina is at least an order lower than
that on single crystalline YSZ substrate, according to K.Y. Chen’s work [113]. At an
early stage of this work, only the critical temperature o f all samples was measured
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using an inductive method. A sample with a good critical temperature (high switching
temperature and narrow transition width) was taken for fabricating devices. However,
as we will discuss later, measuring the critical temperature is not enough to ensure the
good quality of YBCO thin films.
Fig. 7-1 shows the critical temperature o f an YBCO thin film on an alumina
substrate prior to being patterned into ring resonator. The switching temperature is
close to 88 K and the transition width is less than 1 K, which represents a good critical
temperature. Another sample with larger size was built to serve as ground plane. Its
critical temperature is shown in Fig. 7-2, which is close to the previous one. The two
samples were patterned into a ring resonator, then packaged and tested under 77 K
using network analyzer.
The S parameters o f the ring resonator made o f YBCO thin film on alumina is
shown in Fig 7-3. From the measurement, the resonant frequency reads as 4.87 GHz,
the insertion loss at resonance is -26.63 dB, and the loaded Q-factor QL is 220.
As described in chapter 4, a resonator using copper thin film on alumina with exact
geometry was built and tested under 77 K. The copper resonator has a resonant
frequency o f4.9445 GHz, insertion loss o f -30.9 dB and loaded Q-factor o f 207. The
fact that the copper resonator has a Q-factor close to that o f the YBCO resonator
already indicated a much higher surface resistance o f the YBCO thin film on the
alumina substrate than expected. These results were discouraging since it made no
sense to make a superconducting device which has almost the same performance as
that made of copper.
104
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1.60E-05
1.50E-05
Inductive Voltage (V)
1.40E-05 1.30E-05 1.20E-05 1.10E-05 1.00E-05 9.00E-06 8.00E-06 7.00E-06
80
82
84
86 88
90
92
Temperature(K)
94
96
98
Fig. 7-1 Critical temperature of YBCO thin film on alumina substrate as signal plane.
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100
1.60E-05
1.50E-05
Inductive Voltage (V)
1.40E-05
1.30E-05
1.20E-05
1.10E-05
1.00E-05
9.00E-06
8.00E-06
7.00E-06
6.00E-06
80
82
84
86
88 90 92 94
Temperature(K)
96
98
100
Fig. 7-2 Critical Temperature of YBCO thin film on alumina substrate as ground plane.
106
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S ll M agnitude
S21 M agnitude
M aM R A \V K O « C T IJ I.lJ « *
D ttJU IU U Y B C O W IS.f.I A C T
00-01-3000 15« 4 ;«
-0.08 « j-
w *m
•0.10 • j- —
—
—
--------—
—
ssd
—
0*01.2000 150440
------------
**—
w**
•30
fc
•0.16
•020
•46
-90
M
«l
41
« ;
4J
45
44
(OMiJ
41
41
47
41
1<3HU
S12 M agnitude
S22 M a g itu d e
D tt_M *A \Y »C O W TS_f_l A C T
Dtt.M IUUYBCCXHTS.f_l A CT
0*01.2000 1 5 0 M
0*01*3000 150*40
•0.1
•0.2
•39
C
-40
-04
•OS
•46
- 0.0
44
44
44
47
44
47
45
44
40
4.1
43
Fig. 7-3 S parameters of YBCO resonators on alumina substrate.
107
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43
14
The surface resistance of the YBCO thin film on the alumina substrate can be
found using Eq. (4.23) to Eq. (4.27) in chapter 4 and Eq. (3.39) to Eq. (3.41) in chapter
3. The detailed calculation is given in appendix I.
The resulting surface resistance o f the YBCO thin film on the alumina substrate is
22.2 mO, while the surface resistance o f copper is 24.2 mO based on its conductivity
at 77 K and the thickness of the thin film. Apparently something was wrong regarding
the quality o f the YBCO thin film on alumina, since the best reported surface
resistance o f YBCO thin film is 0.3 mH at 77 K and 10 GHz [21]. Considering the fact
that most reported low surface resistance YBCO thin films were grown on single
crystalline substrates, we immediately suspected that the high surface resistance o f the
YBCO thin film was due to the YSZ buffer and polyciystalline alumina substrate. As a
result o f the poor performance, the YSZ single crystalline substrate became our next
candidate.
Before we investigated YSZ single crystalline substrates, another YBCO resonator
on alumina was built and tested. This one had an even smaller Q-factor o f 160 than the
previous one, as calculated from Fig. 7-4. The power dependence o f Q-factor was
observed by adjusting the power level o f network analyzer from the default value o f
10 dBm to 1 dBm. The Q-factor increased about 25% to 202, as computed from Fig.
7-5.
The observation that the Q-factor increases with a decrease in incident microwave
power is a typical characteristic o f poor quality superconducting thin films [114-117]
due to the presence of many weak links such as high angle grain boundaries and grain
boundary impurities in such thin films. When microwave energy propagates along a
108
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-2 0
-25
Magnitude (dE
-30
-35
-40
-45
-50
-55
-60
4.5
4.7
4.9
5.1
5.3
Frequency (GHz)
Fig. 7*4 S2 1 of the resonator with Q-factor of 160 measured at 10 dBm power level.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5.5
-2 0
-25
Magnitude (dB)
-30
-35
-40
-45
-50
-55
-60
-65
-70
4.5
4.7
4.9
5.1
5.3
Frequency (GHz)
Fig. 7-5 Sji of the resonator with Q-factor of 202 measured at 1 dBm power level.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5.5
superconducting transmission line, the microwave current flowing inside the
superconductor is proportional to the square root o f total incident power. Once the
microwave current is high enough to exceed the critical weak link current, a weak link
can be switched to the normal state. If this weak link is situated in the path o f
microwave current, there will be local heating, which in turn may create a normal state
region around the junction. Therefore, the surface resistance o f such thin films
increases appreciably when incident microwave power increases. As stated in a
previous paragraph, the critical current density o f YBCO thin films on alumina is at
least an order lower than that on a single crystalline substrate. It is understandable that
the Q-factor o f the above resonator strongly depends on the incident power level. A
good quality superconductor has a very high critical current density, thus within the
low power level o f a network analyzer (maximum 20 dBm), the Q-factor o f a
resonator made o f good quality superconductor should show no dependence on the
incident power level. If the power level is much higher in practical applications, there
certainly will be an upper limit of operating power above which the Q-factor of the
resonator will become dependent on power.
7.1.2 XRD Results of YBCO Thin Film on Alumina
XRD was employed to determine the phase purity and crystalline orientation o f
YBCO thin films on an alumina substrate with YSZ buffer layer. The standard 6 - 2 0
scan was conducted. As shown in Fig. 7-6, the YBCO thin film showed only c-axis
orientation, which indicates perfect out-of-plane orientation o f the YBCO thin film. A
Phi scan o f the YBCO (103) plane was also conducted to investigate the in-plane billl
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axially alignment o f the YBCO thin film. As shown in Fig. 7-7, there exist two in­
plane orientations that are 45° to each other. The FWHM (full-width at the half­
maximum) o f the larger peak is about 25°. The mechanism o f the formation o f mixed
in-plane orientation and its effect to surface resistance will be discussed in the next
section.
112
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1.00E+05
«r>
©
0)
C
3
O
O
o
O.
C
41
O.OOBOO
0
10
20
30
40
50
2 theta (degree)
Fig. 7-6 9
—
26 Man of YBCO thin film on alumina substrate with YSZ buffer layer.
The peaks marked by thick arrow are coming from alumina substrate.
113
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60
20000
Intensity (cps)
15000
10000
5000
120
180
240
300
360
<|>(degree)
Fig. 7-7 Phi scan of (103) planes for the YBCO thin film on alumina with YSZ buffer layer.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
7.2 YSZ Single Crystalline Substrate
72.1 Surface Resistance o f YRCO Thin Film
We suspected that the alumina substrate and YSZ buffer layer caused the high
surface resistance o f the YBCO thin film deposited on them. The YSZ single crystal
was used to verify the assumption. The YSZ has the dielectric constant o f 27, which is
much higher than 9.9 o f alumina Therefore, a new ring resonator was designed to
make the characteristic impedance o f the transmission line SO Cl. The critical
temperatures o f two samples are shown in Fig. 7-8 and Fig. 7-9, respectively. These
two samples served as the signal plane and ground plane after being patterned.
The new resonator’s RF response was tested and shown in Fig. 7-10. Surprisingly,
the unloaded Q-factor o f the new resonator was only 39, much smaller than expected.
Part of the reason for such a low Q-factor is due to the new geometry o f the ring. The
width o f the new ring is only one fifth o f the previous one for alumina substrate, which
greatly decreases the Q-factor even with the same surface resistance. Using the same
procedure, the surface resistance is calculated to be 30 m ft, which is even higher than
that on an alumina substrate. Refer to appendix II for a detailed calculation.
Since the substrate is a perfect single crystal YSZ, it is clear that a problem exists
with the YBCO thin film. XRD was utilized to investigate the structure o f the thin
film. The 9 - 2 6 scan still shows good c-axis out o f plane orientation, as illustrated in
Fig. 7-11. But the in-plane orientation is much poorer as shown in Fig.7-12. There are
two major orientations that are 45° to each other, also a small amount o f two
orientations that are ±9° away from one of the major orientations. Such a poor in-plane
orientation was determined to likely be the cause of the high surface resistance.
1is
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Inductive Voltage (V)
1.60E-05
1.50E-05
1.40E-05
1.30E-05
1.20E-05
1.10E-05
1.00E-05
9.00E-06
8.00E-06
7.00E-06
80
85
90
95
100
Ternperative(K)
Fig. 7-8 Critical Temperature measurement of YBCO on YSZ single crystalline substrate
as signal plane.
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Inductive Voltage (V)
1.60E-05
1.50E-05
1.40E-05
1.30E-05
1.20E-05
1.10E-05
1.00E-05
9.00E-06
8.00E-06
7.00E-06
80
85
90
95
100
Temperature (K)
Fig. 7*9 Critical Temperature measurement of YBCO on YSZ single crystalline substrate
as ground plane.
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magnitude (dB)
-10
-15
-20
-25
-30
-35
-40
-45
2
2.5
3
3.5
Frequency (GHz)
Fig. 7*10 YBCO resonator on YSZ single crystalline substrate with Q-factor of 39.
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4
1.00E+06
9.00E+05
Intensity (co u n ts)
8.00E+05
7.00E+05
6.00E+05
5.00E+05
4.00E+05
3.00E+05
2.00E+05
1.00E+05
I
O.OOE+OO
0
10
20
30
40
50
2theta (degree)
Fig. 7-11 8
—
20
Kan of YBCO thin film on YSZ single crystalline substrate.
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60
1.00E+05
9.00E+04
8.00E+04
*
e
a
o
o
7.00E+04
6.00E+04
^
5.00E+04
«
e
4.00E+04
ae
2.00E+04
0
SO
100
150
200
250
300
350
Phi (degree)
Fig. 7-12 Phi scan of (103) planes of YBCO thin film on YSZ single crystalline substrate (the
substrate was heated in Iff4 Torr oxygen).
120
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7.2.2 Mechanism of YBCO In-Plane Orientation on YSZ
Since discovering the poor in-plane orientation of YBCO on an YSZ single crystal
substrate, a literature research was conducted. Several researchers [48, 54-59] have
reported such phenomenon and have proposed models to explain the mechanism. For
YBCO
on
the
YSZ
substrate,
the
most
common
orientations
are
YBCO[ lOOJIIYSZ[ 100] and YBCO[l 10]|[YSZ[100], which are referred to as 0°
orientation and 45° orientation, respectively. Besides these two orientations, in-plane
rotations in the vicinity o f 9° from the 0° and 45° orientations, respectively, were also
often observed, which are referred to as ±9° orientations. The mixed in-plane
orientation will form high-angle grain boundaries, which always act as weak links.
The superconducting current will attenuate when it passes through a weak link, which
will decrease the critical current density and increase the surface resistance. So even a
small amount of mixed orientation will greatly increase the surface resistance [53].
Based on the phi scan shown in Fig.7-12, it is not surprising that the surface resistance
is as high as 30 mft.
The creation of mixed in-plane orientation also occurs when depositing YBCO on
an MgO substrates [118]. Most researchers have attributed mixed orientations to a
lattice constant mismatch. Here, when the lattice constant mismatch between substrate
and YBCO is large, the YBCO will have more than one direction with which to match
the lattice o f the substrate. By comparing the unit cells, the smallest mismatch between
YSZ (001) and YBCO (001) is obtained when the YBCO lattice is rotated around the
surface normal by 45° with respect to the substrate lattice, i.e., YBCO[ 110]||YSZ[ 100].
Considering overlap o f the oxygen sublattices of the materials, the lattice parameter o f
121
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YSZ
is
smaller
and
the
mismatch
is
about
6%.
However,
with
an
YBCO[100]||YSZ[100] orientation (0° rotation), 3 unit cells o f YSZ have a very small
mismatch to 4 unit cells o f YBCO, and the interfacial energy should be relative low.
These are the two main competing orientation relations for YBCO. A third orientation,
with the YBCO rotated approximately ±9° with respect to the substrate has been
argued to also represent a low energy in a NCSL (near coincidence site lattice) model
[119].
The competing in-plane orientations make the film growth sensitive to the
deposition conditions. Some researchers claimed that they could control the in-plane
orientation simply by adjusting the deposition temperature [120]. The higher
deposition temperature and hence larger surface mobility lead to thin films dominated
by 0° orientations while lower deposition temperature lead to films dominated by 43°
orientations. But after several trials, we could not find a correlation between in-plane
orientation and deposition temperature using our PLD system. Other researchers [48]
believed that a perfect smooth single crystal YSZ surface tended to introduce mixed
orientation, because such a surface will promote the surface mobility o f atoms so that
the long-range order orientation, such as 0° and ±9° orientations are easier to form. If
an YSZ substrate was pretreated prior to deposition by either mechanical means or
thermal annealing, which created some micro-steps on the surface, the YBCO grown
on such a surface will only have one in-plane orientation. In general, these
crystallographic steps act as nucleation sites for a growing film and can impose a
certain in-plane orientation on the nuclei. The thermal annealing method interested us
very much because o f its simplicity. It is usually performed by annealing YSZ
122
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substrates at 1400 °C in atmosphere for 1 or 2 hours. The micro-steps created by
annealing could actually be observed by AFM (atomic force microscope). Since our
heater does not have the capacity to such a high temperature, we tried heating YSZ
substrates to deposition temperature (730 °C) in stead.
Recall the deposition process o f bad orientated YBCO sample, the substrate was
heated up in a vacuum of 10*4 Torr. Therefore, we first tried to heat the substrate in
ISO mTorr oxygen, which is the deposition pressure, from 500 °C to deposition
temperature (730-7S0 °C). According to the phi scan, the intensity o f the unwanted
orientation decreased significantly, while the intensity o f the desired orientation
increased, as shown in Fig. 7-13.
Encouraged by the preliminary results, we increased the oxygen pressure to 200
Torr and annealed the YSZ substrate at a deposition temperature (730 °C) from 20
minutes. The phi scan indicated an almost perfect single in-plane orientation, as shown
in Fig. 7-14. It seemed that we have found a new approach to control the in-plane
orientation, which is more convenient than others. Before we built a new ring
resonator, many runs of YBCO deposition had been performed to test the
reproducibility o f the new process. The process was found to be repeatable, because
we could routinely obtain good orientation as shown in Fig. 7-15. But it is still
difficult to repeat the perfect orientation such as shown in Fig. 7-14. Occasionally,
very bad orientations are produced. Apparently, the mechanism behind this annealing
procedure was not as simple as it first appeared.
After going through the details o f many deposition procedures, we noticed a very
interesting fact. For poorly oriented YBCO samples, some delay always happened
123
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2.0GE+04
O.OOE+OO
0
50
100
150
200
250
300
350
Phi (degree)
Fig. 7-13 Phi scan of (103) planes of YBCO thin film on YSZ single crystalline substrate (the
substrate was heated in 150 mTorr Oiygen).
124
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3.50E+05
Intensity (counts)
3.00E+05
2.50E+05
2.00E+05
1.50E+05
1.00E+05
5.00E+04
mmm
0.00E+00
0
50
100
150
200
250
300
350
Phi (degree)
Fig. 7-14 Phi scan of (103) planes of YBCO thin film on YSZ single crystalline substrate (the
substrate was annealed in 200 Torr oxygen).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1.40E+05
Intensity (counts)
1.20E+05
1
a
o
1.006+05
£
£
8.00E+04
g
e.ooe+04
•
— 4.006+04
2.00E+04
O.OOE+OO
0
50
100
150
200
250
300
350
Phi (degree)
Fig. 7-15 Phi ican of (103) planes of YBCO thin film on YSZ single crystalline substrate using
improved deposition process.
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prior to the deposition. After substrate was annealed in 200 Torr oxygen, the pressure
of the chamber was decreased to ISO mTorr for deposition and the target was ablated
for one minute with shutter off to expose the fresh surface. This process usually took
about 3-4 minutes if everything went smoothly. The orientation o f the YBCO thin film
deposited afterwards was usually good. But sometimes adjusting the pressure took
longer time and preablating target was also delayed by some unexpected situation. The
orientation of YBCO thin film was usually bad under this circumstance. It seemed that
the annealing in 200 Torr oxygen and at 730 °C for 20 minutes did not leave
permanent changes on the substrate surface as other researchers’ methods did. The
effect o f our annealing process somehow can be reversed if the substrate was in 130
mTorr oxygen and at high temperature for a certain period. This assumption was
partially verified by measuring the roughness o f the YSZ surface after being annealed
but without depositing YBCO. The AFM picture showed perfectly smooth surfaces o f
YSZ single crystal substrate.
The only thing that could happen during the annealing process is the exchange of
oxygen atoms between the substrate and the environment. Note that YSZ and other
metal oxide such as TiC>2 and SnC>2, are widely used as oxygen sensors operating at
high temperature [121-123]. Thus, their ability to exchange oxygen atoms with
environment according to the different oxygen pressure is not doubtful. Although
porous ceramic materials or thin films are usually used for application o f gas sensor in
order to facilitate the exchange o f oxygen, we believe that for YSZ single crystalline
substrate, the exchange o f oxygen will still happen at least from the surface to a short
depth into the substrate. When oxygen pressure o f the environment is high, oxygen
127
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atoms will diffuse into YSZ and occupy the vacant oxygen positions, which leaves the
YSZ surface with fewer vacant oxygen positions. While oxygen pressure remains low,
the oxygen atoms inside YSZ escape into the environment, which leaves more vacant
oxygen positions on the YSZ surface. The epitaxial growth o f YBCO thin films on
YSZ substrate is realized by overlapping the oxygen sublattices o f both materials. So
the oxygen atoms on the surface o f YSZ substrate also act as nucleation sites for a
growing thin film. If all the oxygen positions on the surface are occupied, more
nucleation sites are provide to attract the oxygen atoms o f YBCO. Therefore the
mobilities o f the deposited oxygen atoms are small, and the short-range order 45°
orientation tends to form. If more vacant oxygen positions exist on the surface, the
surface mobilities o f the deposited oxygen atoms become larger due to the lacking o f
nucleation sites. Thus, the long-range order 0° or ±9° orientations are easier to form.
The theoretical mechanism o f different surface states affecting the in-plane orientation
of YBCO grown on the YSZ substrate is consistent with observations that annealing
YSZ substrate at high oxygen pressure leads to 45° dominant thin films. Obviously the
progress o f the oxygen exchange can not be instantaneous. Otherwise we would not
have had the ability to use this method to control the orientation o f YBCO thin films
because they are deposited at the same oxygen pressure o f ISO mTorr.
The different surface states, i.e. different percentage o f vacant oxygen positions
could possibly be frozen by cooling down the substrates from high temperature to
room temperature in either high oxygen pressure or vacuum after annealing. Then
using XPS, shifts o f some specific element peaks could probably be observed.
Unfortunately, because o f the need to continue exploring alternative substrates for
128
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small surface resistance YBCO deposition, the investigation on this specific area did
not go any further.
For the YBCO thin film deposited on an alumina substrate with an YSZ buffer
layer, the mixed orientation is much better than the bad case o f YSZ single crystal
substrate. The reason is probably that the surface o f the YSZ buffer layer is not
perfectly smooth as single crystal substrate. The unevenness o f the YSZ buffer layer
plays a similar role to that o f microsteps for the pretreated YSZ single crystal substrate
as mentioned previously. If we use the improved deposition process, the orientation
possibly could be improved even further. But even for single in-plane orientation, the
25 0 FWHM has already contains enough high angle grain boundaries to limit the
surface resistance to a certain value. Unless we can greatly decrease the FWHM o f phi
scan figure by improving the IBAD process, the alumina will not be a good substrate
candidate for the desired low surface resistance YBCO thin film deposition. Some
researchers [124-130] have reported that they have achieved FWHM o f YSZ buffer
layer less than 10 0 using dual ion gun IBAD technique. The surface resistances o f
YBCO thin films grown on this kind o f buffer layer is very close to those o f thin films
grown on single crystal substrates.
7.2.3 Surface Resistance Using Improved Process
Using the improved process, a new resonator was built. There is only small
fraction o f unwanted orientation as shown in Fig. 7-15. We suspect that would be
difficult to totally eliminate the unwanted orientation using the current technique.
Even a small amount of mixed orientation still increases the surface resistance a great
129
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deal. As shown in Fig. 7-16, the unloaded Q-factor o f new resonator is 504, which is
more than 10 times better than the previous one. The calculated surface resistance is
about 1.4 m£2, while the reported best value is 0.3 m fl at 10GHz. If we scale down the
surface resistance to the resonant frequency of 2.9 GHz as shown in Fig. 7-16 using
f z relation, the best value should be 0.026 mft. It is very clear that the surface
resistance o f YBCO thin films on the YSZ single crystal substrate is too high even
using the improved deposition process. As a result, LaAHZ>3 single crystalline
substrates are explored as a possible substrate candidate.
130
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-10
-15
Magnitude (dB)
-20
-25
-30
-35
-40
-45
2.5
2.6
2.7
2.8
2.9
3
3.1
3.2
3.3
3.4
Frequency (GHz)
Fig. 7-16 YBCO resonator on YSZ single crystalline substrate with Q-factor of 504.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3.5
7 J LaAK>3 Single Crystalline Substrate
LaA103 is one of the best substrates for YBCO thin films because o f its very small
lattice mismatch with YBCO, so that the epitaxial thin film growth is straightforward.
The critical temperature of YBCO grown on LaAIOs is usually one or two degrees
higher than that o f grown on YSZ. Fig. 7-17 shows a critical temperature measurement
o f YBCO on LaAIOs. It has a switching temperature about 90 K and very sharp
transition. The crystalline structure o f YBCO on the LaAK>3 substrate is also very
good: only the single in-plane orientation is formed. Fig. 7-18 shows 0 - 2 6 scan of
an YBCO thin film, which indicates perfect c-axis orientation. Fig. 7-19 shows phi
scan o f an YBCO thin film with very sharp peaks.
One o f the main drawbacks o f LaAIOs is its twinning structure that makes it
fragile and easy to break. The twinning also causes its dielectric property to be
unpredictable. As a result, LaA103 is not used for complicated RF devices. However
in the proposed all-HTS tunable filter, the substrate o f the toractor only serves as a
template for the superconducting thin film and will not interfere with the performance
o f the RF circuit. The large density is another potential drawback for the proposed
application, because the reaction time will become slower as the toractor becomes
heavier.
A resonator using YBCO on a LaA103 substrate was built. Since the dielectric
constant of LaA103 is 24, we used the same mask that was used for YSZ single crystal
substrate. The only concern is that it will cause a slight impedance mismatch, which
we believe could be neglected.
132
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The S 2l o f the resonator measured under 77 K is shown in Fig 7-20 with incident
power level o f lOdBm. The unloaded Q-factor is as high as 11015, which translates
into 0.032 m£2 surface resistance. The detailed calculation is given in appendix III.
The best result o f surface resistance is 0.019 mft if we scale down from the value o f
0.3 m fl at 10 GHz. Our result is still slightly larger than the best value. But if we
consider the processing factors related to photolithographic patterning, ion milling,
and edge effects, the surface resistance value o f the original film should be even closer
to the best value. The measurements were also performed at power level o f 0 dBm and
-10 dBm, with unloaded Q-factor o f 12614 and 11508, respectively. No significant
power dependence was observed, as shown in Fig. 7-21, which means a very good
quality YBCO thin film was observed under test. This surface resistance value is
adequate for use in the proposed filter. Hence, LaAIOs single crystalline substrate was
selected as working substrate for constructing the filter.
When we tried to retest the resonator, an interesting resonance splitting was
observed as shown in Fig. 7-22. The split resonant frequencies are very close to the
original resonant frequency, and only 15 MHz apart. The Q-factors decreased to 7525
and 5847 respectively. After taking apart the resonator, a small crack on the back o f
the substrate was found. The crack situated right underneath one o f the two coupling
gaps.
The ring resonator design has an inherent mode degeneration problem (i.e., two
orthogonal modes share the same resonant frequency). For instance, at the lowest
fundamental resonance, there are two degenerated modes: one has a voltage peak at
the coupling gap, the other has a current peak at the same location. Any slight
133
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asymmetry, such as a defect on the line or nonuniformity o f the substrate, will cause
coupling between these two modes and a split o f the degenerated resonant frequencies,
which results in a lower Q-factor. The frequency splitting phenomenon was observed
several times in HTS ring resonators [89], including ours. The degeneration problem
can be solved by introducing a cutoff gap on the ring at the location o f coupling gap.
The gap does not affect the mode with a voltage peak there, but it suppresses the other
mode with a current peak there. As a result, the degeneration is eliminated.
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Inductive Voltage (V)
1.60E-05
1.50E-05
1.40E-05
1.30E-05
1.20E-05
1.10E-05
1.00E-05
9.00E-06
8.00E-06
7.00E-06
80
85
90
95
Temperature (K)
Fig. 7*17 Critical Temperature of YBCO thin film on LaALOj substrate.
135
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100
8.00E+05
Intensity (counts)
7.00E+05
6.00E+05
5.00E+05
4.00E+05
3.00E+05
2.00E+05
1.00E+05
0.00E+00
0
10
20
30
40
SO
2 theta (degree)
Fig. 7*18 6 —26 scan of YBCO thin film on LaAIOj substrate.
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60
1.20E+05
Intensity (counts)
1.00E+05
8.00E+04
6.00E+04
4.00E+04
2.00E+04
O.OOE+OO
0
SO
100
150
200
250
300
Phi (degree)
Fig. 7-19 Phi scan of (103) planes of YBCO thin film on LsAIOj substrate.
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350
-10
Magnitude (dB)
-20
-3 0
-4 0
-5 0
-6 0
-7 0
-8 0
-9 0
2 545
2 547
2 549
2 551
2 553
2 555
2 557
2 559
F r e q u e n c y (QHs)
Fig. 7-20 S 2l of YBCO resonator on LaAI03 substrate with unloaded Q-factor of 11015.
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Unloaded Q Facot
14000
12000
-
10000
-
8000 -
6000 -
4000 ■
2000
-
-10
•8
6
■
A
2
0
2
4
6
8
Paw ar l e v e l (dBm )
Fig. 7-21 The unloaded Q-factor versus incident power level.
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10
Magni t ude ( 4 1 )
-35
-40
-
45
•
-50
.
•
-55
-6 0 -
-85
255
2 555
2 585
2 56
257
2 .5 7 5
F r e q u a n ey (GH z)
Fig. 7*22 Resonance splitting.
140
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2.58
7.4 Tunable Spiral Resonator
7.4.1 Bask Principle of Tunable Spiral Resonator
The proposed tunable spiral resonator is a critical element for realizing an all-HTS
tunable filter. It detects the frequency that is fed back to the control system to
determine the rotation of the toractor. Since a very narrow band tunable filter is
desired, a resonator with an extremely high Q-factor is needed.
The tunable spiral resonator has a structure similar to the ring resonator we used
previously to measure surface resistance. Instead o f a simple microstrip transmission
line, it uses the covered microstrip transmission line, which means a metal (YBCO
toractor in our case) plate covering a microstrip. In a conventional covered
transmission line, the cover plate is used for electrical shielding and physical
protection, and is usually situated several substrate thicknesses away from the
microstrip. For our spiral resonator, the purpose o f the toractor is to tune the
frequency, so it is placed very close to the microstrip and its presence greatly disturbs
the electromagnetic fields o f the resonator. Thus the resonant frequency can be
changed by adjusting the gap between the toractor and microstrip. The thickness o f
substrate we used is 20 mil, while the gap is around 4 mil. The spiral geometry is
utilized because it takes much less space compared to the ring or straight line o f same
length. The length, meanwhile, is related to the resonant frequency. The longer the
line, the lower the frequency.
In the proposed HTS tunable filter, the tuning is realized by tilting the very thin,
suspended toractor using the HTS driving coil. In this preliminary work to investigate
141
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the characteristics o f such a spiral resonator, the tuning is done by manually changing
the gap between the top plate and the microstrip.
The packaging method applied to the tunable spiral resonator is similar to the ring
resonator. Instead o f using a flat copper lid to cover the housing, it uses a copper lid
with a square (0.4” x0.4” ) extension at the center into the housing. An identically-sized
LaAlCb substrate coated with YBCO was mounted on the top o f extension. The height
of the extension was designed so that the surface o f the YBCO thin film is about 4 mil
above die microstrip. Different gap sizes were investigated by inserting different
thickness spacers (tapes) in between the lid and the wall o f the housing. The resonator
was cooled and measured using the same methods as stated before.
7.4.2 Measurement of Tunable Spiral Resonator
Fig. 7-23 shows the S 2l parameters of the resonator at different resonant
frequencies, in other words, measured at different gap distances. Because o f the very
high Q-factors, the peaks are very sharp as shown in the figure. The maximum data
points is 801 for HP8S10 network analyzer, so we have to shrink the frequency range
o f measurement in order to get higher frequency resolution so that the Q-factor can be
calculated precisely. In fact, the frequency range for Q-factor measurement is just 10
MHz, so the resonant peaks seem so narrow when put into the Fig. 7-23 with range o f
500 MHz.
The relationship between resonant frequency and gap is summarized in Fig. 7-24.
The frequency corresponding to the dashed line is measured when using a normal flat
lid that is about 250 mil above the microstrip. Thus, the gap at this situation can be
142
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considered to be infinitely large, and this frequency is the low limit that can be
obtained for the resonator. It is clear that as the gap decreases, the resonant frequency
increases. The tunable frequency range for the spiral resonator is approximately 500
MHz.
Fig. 7-25 shows the simulated curve o f resonant frequency versus gap using high
frequency simulator (Microwave Office) by Humayun Kabir. The curve based on real
testing results agrees with the simulated results nicely. They show similar relationship
o f the change o f resonant frequency with the change of the gap. But for a certain gap,
the resonant frequency from testing is a slightly higher than that from simulation. The
small difference is possibly caused by the different boundary condition definitions.
For the fabricated resonator, the YBCO plate above the microstrip was not electrically
connected with any other part o f the device because that is the real boundary condition
in die proposed HTS tunable filter. But in the simulation, if the boundary condition is
defined according to the real situation, the computing process will require an
unacceptable period o f time. In order to facilitate the simulation process, a
simplification was made by electrically connecting the floating plate to the ground
plane o f the resonator.
143
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-20
-25
-30
-35
-40
4 -45
2e
a -50
i
-55
-60
-65
-70
0.9
1
1.1
12
1.3
1.4
Frequency (GHz)
Fig. 7-23 S2I parameters of the resonator at different resonant frequencies (different gap
distances).
144
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Resonant frequency (GHz;
15
1.4
- • — frequency at
smal gap
15
—
frequency at
irfn ie gap
12
OS
OB
3
4
5
7
6
8
Toractor gap (mil)
g
10
Fig. 7*24 Resonant frequency versus gap of spiral resonator.
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11
GHz)
1.8
1.7
Resonant frequency
1.6
1.5
1.4
1.3
1.2
1.1
1
2
3
4
T o r a c to r g a p (m il)
Fig. 7-25 Resonant frequency versus toractor gap by simulation.
Courtesy of Humayun Kabir.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5
Fig. 7-26 illustrates the Q-factors at different resonant frequency. It actually
consists o f two curves. The resonator was measured at a small gap at the beginning,
then it was measured four more times with increased gaps. As a result, the resonant
frequency was gradually decreased to the lower limit. The Q-factor was increasing
with the decrease of the frequency for the first two measurements. Then unfortunately,
the LaAlC>3 substrate (toractor) detached from the copper extension, possibly because
o f the large thermal shock caused by die temperature change between 77 K and room
temperature. The substrate was reattached to the extension and tested again. But the Qfactor had a big drop at the third measurement, although the resonant frequency was
lower. Then the Q-factor increased again with the decrease o f frequency for the forth
and fifth measurements (see the circular data points in Fig. 7-26).
For a simple ring or line resonator made o f superconductor, the Q-factor should
increase as the resonant frequency increases. Rewrite Eq. (4.19) as following:
2a
while f3 = — =
. According to the Eq. (3.41), the conductor attenuation constant
a c is proportion to the surface resistance Rz o f the conductor. If we neglect the
radiation and dielectric loss, the Eq. (4.19) can be rearranged as:
(7.1)
where R, <x f 1 according to Eq. (2.7) in superconductor theory. So we finally have
Q * f~ \
(7.2)
147
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20000
18000
first tun teat
16000
■ Ratoat at small gap
Q-factor
14000
12000
10000
8000
6000
4000
o.g
1
1.2
Frequancy(GHz)
1. 1
1.3
Fig. 7-26 Q-factor versus frequency.
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14
which means the Q-factor is inversely proportional to the resonant frequency.
However, for a spiral resonator, the situation is more complicated than for a simple
ring or line resonator because o f the mutual coupling effect between adjacent turns.
Irregardless, the Q-factor still should increase with a decrease in frequency.
Therefore, the big drop in Q-factor for the third measurement is abnormal. It was
immediately assumed to be caused by the remounting process. To prevent the
substrate from falling o ff again in the future, a simple tool was used to add more
pressure to the substrate surface, which caused some scratches on the YBCO surface.
As we observed, the scratches greatly increased the surface resistance o f the YBCO
thin film, and therefore decreased the Q-factor. The resonator was measured again at a
small gap, similar to the first measurement. The Q-factor was much lower than those
o f the first two measurements as expected, which strongly supported the above
assumption (see the square data point at the comer of the curve). If we use a line to
connect this point with the other three points on the left, the curve will show a
monotonous change as predicted by Eq. (7.2). This phenomenon clearly demonstrates
that the quality of the toractor YBCO thin film plays a major role in the value o f the
Q-factor. Since the electromagnetic wave propagates on the surface o f a toractor, the
signal line and ground plane, the total conductor loss of the resonator comes from the
toractor, signal plane and ground plane.
To better clarify the above explanation, another high quality toractor was made
and mounted without any damage. The resonant frequency versus gap shows similar
curve as illustrated in Fig.7-27. The Q-factor increases monotonously with a decrease
in frequency as shown in Fig.7-28.
149
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Resonant frequency (GHz)
1.5
1.4
“•— frequency at
small gap
1.3
- - frequency at
infinite gap
1.2
1.1
1
0.9
0.8
3
8
13
18
23
Toractor gap (n i)
Fig. 7-27 Resonant frequency versus gap of spiral resonator.
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19000
1900017000* 16000-
I
O 15000 •
1400013000-
12000
0.9
1
1.1
1.2
1.3
Frequency (GH3
Fig. 7-28 Q-factor versus frequency.
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1.4
7.43 Mechanism of Frequency Tuning
In the ring resonator on LaAlOa substrate, the coupling gap between the feed line
and ring is 35 mil, while in the spiral resonator, the gap between adjacent turns is only
5 mil. The coupling in the ring resonator is limited to the small area between the end
o f feed line and ring, while the coupling happens around the whole circumference o f
each turn. Obviously, there exists a significant amount o f mutual coupling among
different turns in a spiral resonator, which greatly complicates the situation. Thus, the
resonant frequency can’t be predicted using the same simple standing wave condition
as for the ring resonator. To thoroughly understand the mechanism o f spiral resonator,
a great deal of theoretical research is still needed. However, two simple models are
rendered in the following in an attempt to give a conceptual picture.
One way to picture the spiral resonator is to define a new effective dielectric
constant £tflpiral, which not only takes into account the inhomogeneous dielectric, but
also the mutual coupling effect. As stated in Chapter 3, the effective dielectric constant
is actually an indicator o f how much the electromagnetic fields exist inside the
dielectric or air. The more fields that contained in the dielectric, the closer the
effective dielectric constant is to the actual constant of the dielectric. Since there is
strong coupling between different turns o f a spiral resonator, more field lines
concentrate in the dielectric in between lines than for a ring resonator. So £ ^ pira/
should be higher than
o f a ring resonator, or in other words, much closer to the
actual dielectric constant £ r , given the same line width and substrate thickness.
152
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After defining
, we can write the standing wave condition for spiral
resonator as follow:
Ag = /
(7.3)
where I is the total physical length o f the spiral, and Agis the guide wavelength
defined as
A„
3 - ____1*°
Ag
(74)
c
f y j e effspxral
where A0 is vacuum wavelength, c is the speed o f light and /
is the frequency.
Rearrange the Eq. (7.4), we get resonant condition o f the spiral resonator
f = ~r~r=-----If t C
.*
0ejfspiral
(7.5)
Since the physical length o f the spiral can’t be changed once the lithography and
etching were completed, the resonant frequency only can be altered by changing
^eflspiral'
The effect o f toractor is to change the distribution o f the fields. When it is placed
very close to the microstrip, it attracts some o f the field lines to extend into air and end
up onto its surface. The closer the toractor is to the microstrip, the more field lines are
contained in air. Therefore, as shown in Fig. 7-29, fewer field lines exist in the
dielectric, which means the effective dielectric constant becomes smaller. According
to the Eq. (7.5), the resonant frequency increases when the effective dielectric constant
153
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Large Gap
Snail Gap
Fig. 7-29 The exaggerated illuitration of the field change with the gap of toractor.
decreases. The tested resonant frequency indeed increases when the gap decreases as
we observed.
The above mechanism can also be verified from another aspect, the coupling o f the
feed lines. As described in Chapter 4, the coupling gap is designed to form so-called
“loose coupling” , which can be judged by measuring the peak value o f insertion loss.
If the gap is very small, more energy is transmitted to the other port o f the resonator.
Thus, the peak value of insertion loss will be close to 0 dB, which means an “ over
couplingi” . If the gap is very large, then the peak value will approach negatively
infinity, because much less energy is transmitted. The amount of coupling is mainly
determined by the coupling gap as shown previously. However, the existence o f the
toractor also has a modest effect on it. As shown in Fig. 7-30, the measured values of
our spiral resonator are in the range from -35.3 dB to -31 dB, which all indicate
perfect “ loose coupling”. Still, we can say that the higher the insertion loss, the larger
the coupling. Obviously, the coupling is larger when the gap between the toractor and
the spiral is larger. The reason can be easily visualized from Fig. 7-29. When the
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toractor is far away from the microstrip, there are many field lines in between two
lines. The interaction between two lines through the field lines forms die coupling.
When the toractor is placed very close to the microstrip, not only does the density o f
the field lines decrease, but also some of the field lines that should have interacted
above the microstrip are intercepted by the toractor, which results in no effective
interaction. All these effects decreased the amount o f coupling, which results in
decreased insertion loss as demonstrated by Fig. 7-30. The good agreement between
the predicted response for this proposed mechanism and the actual measured results
strongly supports the validity o f this assumption.
Another approach to explain the mechanism o f frequency tuning for the spiral
resonator is to use the inductance-capacitance resonator model. The resonant
frequency o f a LC resonator can be found as:
/ =*^£C
<?'6)
where L is the inductance, and C is the capacitance.
The inductance o f the spiral without toractor above it can be calculated by
summing up the loop self-inductance and mutual inductance between loops. For
example, considering a spiral with 4 turns, its inductance can written as [16]:
L = L,, + A /|j + A/ l3 + A /u
m
21+ l 22+ m 23+ m 24
m
31+ m 32+ l » + m » '
m
41 + m 42 + m 43 + l u
where the Lti are the loop self-inductance and the M v are mutual inductance between
loops. Since M tJ = M Jt, Eq. (7.7) can be reduced to
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Maximum Insertion Loss (dB)
-31
-
31.5
-32
-
32.5
-33
-
33.5
-34
-
34.5
-35
-
35.5
0
10
20
T o r a c t o r Gap (mil)
Fig. 7-30 Insertion loss versus toractor gap.
156
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30
When the toractor is placed above the spiral, the field distribution is equivalent to a
“mirror spiral” with opposite current on above the spiral with twice the distance
between toractor and spiral. Thus, all o f the mutual inductances
r between spiral
and its image are negative. Hence, the total inductance o f the spiral with toractor
above it can be written as:
L = Lu +2Ml2+ 2M l3+ 2 M lA
+
L2 2
+ 2 A /- J J +
2M U
+ £33 + 2 M U
+ Lu
- M n. - 2M n. - 2A/13. - 2 M XV
(7.9)
- M 22. - 2 M ly - 2 M 2a.
Obviously, the presence o f the toractor decreases the total inductance o f the spiral.
The closer the toractor is to the spiral, the larger the negative terms in Eq. (7.9), and
thus, the smaller the inductance. According to Eq. (7.6), the decrease o f the inductance
has the effect o f increasing the resonant frequency if the capacitance remains
unchanged.
The effect o f the presence o f the toractor is to increase the capacitance, which has
the effect of decreasing the resonant frequency if the inductance is constant. But the
capacitance of the spiral is very small considering the geometry o f the spiral, so its
effect is effectively offset by the effect o f inductance change. Therefore, the overall
157
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trend is that the resonant frequency increases with the decrease o f the toractor gap,
which was demonstrated by the experiments.
158
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CHAPTER 8
Conclusions and Future work
8.1 Conclusions
One of the major challenges inherent in the design o f the proposed all-HTS tunable
filter is to build a toractor, which is composed o f a layer o f HTS thin film on a very
thin (~ 4 mil) substrate. Among all the substrates suitable for HTS thin film
deposition, it was necessary to determine which ones could remain mechanically
robust at critically thin thicknesses. This was totally unknown before they were
actually tried out. Although it is natural to think that substrates with higher mechanical
strength were more likely to survive the very thin thicknesses required, there was no
guarantee about it. The main goal o f this work was to investigate the surface resistance
o f YBCO thin films on various substrates deposited using PLD method, so that more
candidates that meet the electrical requirements would be available when
implementing the toractor. The other primary objective was to develop a procedure for
fabricating and testing the spiral tunable resonator, so that the feasibility o f the allHTS tunable filter could be demonstrated from the view o f actual fabrication.
We started with alumina polycrystalline substrate because o f its obvious higher
mechanical strength than others. Since there is a very poor lattice match between
alumina and YBCO due to the polycrystalline structure, an YSZ buffer layer was
needed to provide a crystalline ordered template for YBCO deposition. The YSZ layer
was deposited by IBAD method using pulsed laser as evaporating source.
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Unfortunately, the measured surface resistance o f YBCO on alumina substrate at 77 K
is similar to that o f copper at the same temperature, which makes this substrate
material a poor candidate for the HTS filter. The high surface resistance can be
attributed to existence o f a great number o f high angle grain boundaries in YBCO thin
film, which act as weak links. For YBCO thin films, the transition from strong
coupling for low angle grain boundaries to weak link behavior occurs over an angular
range o f 5 °-10 °, while the phi scan o f YBCO (103) plane reveals that there exist two
in-plane orientations with 45 0 to each other and the FWHM o f the (103) peak is about
25°. Both o f them form a large amount o f in-plane misorientation, with an angle more
than 10°, hence the surface resistance increases drastically.
The two mixed in-plane orientations, referred to as 0° and 45° orientations, are
caused by the fairly large lattice mismatch between YSZ and YBCO. The amount of
unwanted orientation can be minimized, or even eliminated by an improved deposition
process as we have shown. But the FWHM o f the YBCO phi scan peak can not be
narrowed more because it is limited by the FWHM o f the YSZ buffer layer
underneath. Since the former researcher [113] had done extensive work optimizing the
process o f IBAD YSZ deposition, the current FWHM o f YSZ layer is very unlikely to
have more room to be improved further using the existing method. Unless some future
discovery allow us to decrease the FWHM of YSZ buffer layer greatly, alumina
substrates are not the right candidates in spite o f its very attractive mechanical
properties and low cost.
The YSZ single crystalline substrates were then studied because they have perfect
in-plane orientation with FWHM less than 1°. The measured surface resistance was
160
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much higher than expected at beginning due to the large amount o f mixed orientations.
By annealing YSZ substrate in 200 Toir oxygen prior to deposition, we have
successfully minimized the unwanted orientation as shown by phi scan examination.
But this process cannot guarantee the elimination o f unwanted orientations, therefore a
small amount o f these often remains, which increases the surface resistance a great
deal. The resultant surface resistance decreased to an order lower than that o f copper at
77 K, which is still a little higher than best results reported in literature. Therefore,
unless a new process can be developed, which eliminates the unwanted orientation, the
YSZ single crystalline substrate is a potential, but not reliable, candidate for our
application.
The LaAlC>3 single crystalline substrates were finally investigated. T he YBCO thin
films deposited on it have perfect in-plane and c-axis crystalline orientation because o f
their good lattice match with YBCO. The measured surface resistance is comparable
to the reported best results, which meet the electrical requirement o f o u r application.
Therefore, LaA103 was the preferred candidate material for all-HTS tunable filter
based on the requirement of very low surface resistance.
The concluding study of spiral tunable resonators turned out to be quite successful.
The resonator built on LaAK)3 single crystalline substrate exhibits frequency tuning
phenomenon almost exactly the same as predicted by simulation. The Q -factor o f the
resonator was well above 10,000, which is sufficiently large for the required high
performance o f the proposed all-HTS tunable filter. The fact that the resonant
frequency changed with the variation o f toractor gap can be explained by the change
161
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o f the inductor from the lumped element view or change o f the effective dielectric
constant from the phenomenological view.
8.2 Future Work
Only LaA103 single crystalline substrates were formed to meet performance
criteria from the consideration o f the low surface resistance requirement. However,
some more work can be done in the future, possibly to discover new candidate
substrates or modify the performance o f existing candidates to meet requirement.
Recently, some researchers [124-130] have reported that they had fabricated YSZ
buffer layer by IBAD method using a dual ion gun deposition system. The FWHM of
deposited YSZ phi scan is less than 10 °. The YBCO thin film deposited on such YSZ
buffer layer has vety low surface resistance comparable to that o f YBCO on single
crystalline substrates. Comparing to the current results we have, this huge
improvement is not only the decreasing o f the value o f FWHM o f YSZ, but also
converted most of the grain boundaries o f YBCO from high angle, weak link into
small angle, strong coupling. Therefore, the YBCO deposited on such good quality
YSZ buffer layer has acceptable surface resistance for microwave application.
The major differences between the reported dual ion gun setup and our PLD IBAD
deposition system is deposition pressure and the evaporating sources. The dual ion gun
system uses a much lower working pressure than the PLD system. In the PLD system,
target materials are evaporated away by the heat o f laser beam, while they are
sputtered away by ion beam in die dual ion gun system. Therefore, the target materials
depositing onto substrate in dual ion gun system are particulate free and traveling in
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parallel direction. That is possibly the reason that the dual ion gun system can achieve
FWHM much better than PLD system. Since not much improvement can be done with
PLD system, it may be worth investigating the dual ion gun setup in the future. If the
reported in-plane orientation can be achieved, then alumina or other less expensive
substrates with better mechanical properties can be reconsidered as candidates for our
application.
For YBCO deposition on YSZ single crystalline substrate, some researchers
[54,55] reported they could routinely obtain the single in-plane orientation by
depositing a CeC>2 buffer layer before YBCO deposition. The lattice constant o f Ce02
is between YSZ and YBCO, so that it improves the original large lattice mismatch.
Other researchers [56,58] claimed that they could even get single in-plane orientation
by depositing a YSZ layer on YSZ single crystalline substrate. Although the same
material, the surface o f deposited YSZ layer is less perfect than the single crystal
substrate, so the YBCO grown on it exhibits different orientation from YBCO on
substrate directly. These methods all introduce an additional buffer layer, hence
complicate the process and increase the expense. But if they can ensure the good in­
plane orientation o f YBCO on YSZ substrate, and therefore very low surface
resistance, it is worthwhile to try these methods in future. Then YSZ single crystal
substrate is also a very promising substrate for our application.
After fabricating and testing the spiral tunable resonator, whose frequency is tuned
manually, more work need to be done towards the proposed all-HTS tunable filter.
The next step is to build a spiral tunable resonator whose frequency is tuned by a
rotating a real toractor. In order to determine the maximum magnetic field produced
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by the driving coil and finalize the design o f driving coil, the critical current density o f
YBCO thin film and the smallest feature (line width, gap between lines) that can be
made using die equipment available at the HiDEC facility need to systematically
investigated. The processes necessary to thin the different substrates down to 4 mil
thick using polishing equipment also needs to be developed at the same time.
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Reference:
[1]
M. K. Wu, J. R. Ashbum, C. J. Tom g, P. H. Hor, R. L. Meng, L. Gao, Z. J.
Huang, Y.Q. Wang, and C.W. Chu, Phys. Rev. Lett. 58,908 (1987).
[2]
H. Maeda, Y. Tanaka, M. Fukutomi, and T. Asano, Jpn. J. Appl. Phys. 27,
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APPENDIX I
Calculations for th e Surface Resistance of YBCO
Thin Films on Alumina Substrate
For copper resonator:
Thickness of the copper thin film: t = 3xl0~7 m = 0.00118
mil
Thickness of the substrate: h = 6.35 x 10-4 m = 25 mil
Width o f the transmission line: w = 24 mil
Guide wavelength: k =0.02362 m
So, Aw = i l n ^ ^ + l j = 0.03821 mil
w '= w +Aw = 24.03812 mil
< * c_coppefZ oh
s _ copper
1
2n
.
h
1+ —
W
1-
h
-
w
t
+ —
TZW'
1 +-
>=0.76012
Amv
Characteristic impedance: Z0 = 50 Q
Conductivity o f copper at 77 K: or = 1.38x10s (ft-m )r
Surface resistance of the copper thin film: Rs
Conductor attenuation constant: a c ^copper
l
= — = 0.0242 G
ta
0.76012R s _ copper
Z0h
= 0.57937 N pl m
174
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Q-factor for conductor loss o f copper: Qe
r
------
= 229.57
<*c_co p p e rK
-
Measured loaded Q-factor and insertion loss o f copper resonator:
207
S 2l coppi, = -30.9 dB
Unloaded Q-factor o f copper resonator: Q0 copptr =
= 213.07
1-10
20
1
1
1
1
B ecause----------- =-—-------- + —---------+
Q o ^copper
So
Q c _ copptr
Q d _ copper
Q r ^ copptr
1
1
-------+
+ ----- ■-----=—--------------------l------= 3.3723x10“'
Q d _ copptr
Q r _ copper
Q o ^copptr
Q c co p p er
For YBCO resonator:
Thickness o f the YBCO thin film: t = 3xl0~7 m = 0 .0 0 118
mil
Thickness o f the substrate: h = 6.35 xlO-4 m = 25 m il
Width o f the transmission line: w = 24 mil
Guide wavelength: Ag =0.02362 m
So, Aw = i - l n p ^ + l j = 0.03821 mil
w' = w + Aw = 24.03812 mil
175
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Measured loaded Q-factor and insertion loss o f the YBCO resonator:
Q l _ hts
=220
S 2l f f TS= -
26.2346 dB
Unloaded Q-factor of copper resonator:
Q
0 ffTS =
- 230.756
1-10“
SinC$
Qd
copptr = Q d Q r _ c o p p e r
-l
— l-— + — l-—
'-d _ HTS
hence,
Q r _H TS
Q c HTS
+ -----1----- = 3.3723x 10-4
Q d _ copper
*
^
»
fflS
~Qr_HTS
r
Q r _ copptr
i
--------- h-
\\£ d _ H T s
Q-factor for conductor loss o f YBCO:
i
'
= 0.0039%
y£r_irrs
Qr
Q c
^
=250.228
Conductor attenuation constant o f YBCO: a c ^
---= 0.53154 Np! m
Qc_ms^g
O-r rm;Zah
Surface resistance o f YBCO: R. ^ = — =----------= 0.0222 Q
' - ms
0.76012
176
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDIX II
Calculations for the Surface Resistances of YBCO
Thin Films on YSZ Single Crystal Substrate
For copper resonator:
Thickness o f the copper thin film: t = 3 x l0 ~7 m - 0.00118
mil
Thickness of the substrate: /» = 5.08xl0~‘ m = 20 mil
Width of the transmission line: w = 5.6 mil
Guide wavelength: A =0.0319 m
j
So, Aw = — l n ^ “ +1 = 0.03265 mil
w'=w+Aw = 5.63265 mil
a c_coPptrZ0h
^scopper
1
2?T > - f - T
47tw
, h
h
1 + — + — In
+1
W itw'
1
-
-
w
-
1+
2.098
4nw .
Characteristic impedance: Z0 = 50 f t
Conductivity of copper at 77 K: a = 1.38x10* ( f t m )-1
Surface resistance of the copper thin film: Rs
Conductor attenuation constant: a c
= — = 0.0242 f t
ta
2 098/?
. = ------ ^ ' r eopptr _ j 9 9 9 ft p / m
Z 0h
177
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Q-factor for conductor loss o f copper: Qc copptr = ----- -—— = 49.265
^ c _ c o p p tr ^ g
Measured loaded Q-factor and insertion loss o f copper resonator :
Q l _c€pp€t =44-8
5 21copprr= -25.324 dB
Unloaded Q-factor o f copper resonator: Q0 copptr =
= 47.366
1-10
20
1
1
1
1
B ecause----------- ------------- + ----------- + ---------Q o _ copptr
So
Q c_copptr
Q r copptr
= --l-------------
-----+ -------Q d _copptr
Qd_copper
Q r _ copper
Q o_copper
= 8.137x10'*
Q c _ copper
For YBCO resonator:
Thickness o f the YBCO thin film: t = 3xl0~7 m = 0.00118
mil
Thickness o f the substrate: h = 5.08 x lO-* m - 20 mil
Width o f the transmission line: w = 5.6 mil
Guide wavelength: k g =0.0319 m
So, Aw = 1 -l n p y ^ + 1j = 0.03265 mil
w’= w + Aw = 5.63265 mil
a c_m sZ0h _ 1
hts
W
4h
\2
. h
h
1+— + —
W 7iw'
1-
1+-
-
w
2.098
4 tiw_
178
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Sample 1:
Measured loaded Q-factor and insertion loss o f die YBCO resonator:
Ql _hts =34.1
Su ms
17.957 dB
Unloaded Q-factor o f YBCO resonator: Q0 ^
=39.039
1- 10 “
SineG Qd co/iptr ~Q d _HTS
1+ —
Qd
Q r_ H T S
hence,
*
Qc
*
H
TS
ffTS
-l
+
l= 8.137xl0-4
Q d_ copptr Q r _ copptr
-— =
_HV5
Qrcopptr —Qr
Qo
H
TS
-+ — l-—
1
<Q d _ H T S
=0.0248
Q r _H TS
Q-factor for conductor loss o f YBCO: Qc im = 40.32
Conductor attenuation constant o f YBCO: a c ^
-----
= 2.443 N p /m
Q c _H T S^g
Surface resistance o f YBCO: Rs
-
= _ c- w7y 0 = 0 .0 3 q
2.098
Sample 2:
Measured loaded Q-factor and insertion loss o f the YBCO resonator:
Ql
hts
= 467
S2I
ms
= -22.6727 dB
179
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Unloaded Q-factor of copper resonator: Q0 ^
Sinet
Qd
1
c o p p e r -Q d h t s
1
+-
d _ HTS
Q r _HTS
1
Qc
HTS
—Qr_Hrs
Q r eopptr
+ -----
\ £ d _ copper
1
hence,
and
Qr
=504.055
= 8 .137xl0"4
copper
1
Qo
HTS
= 0.0017
\Q d
_H TS
Q r _H TS
,
Q-factor for conductor loss o f YBCO: Qc fiTS - 854.565
Conductor attenuation constant o f YBCO: a c
= 0.115 N p/m
HTS
Qc
Of
H T S ^s
trr^Zt nh
Surface resistance o f YBCO: R, ™. = — ---------- = 0.0014 f2
2.098
180
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APPENDIX III
Calculations for the Surface Resistance of YBCO
Thin Films on LaAIO, Single Crystal Substrate
For copper resonator:
Thickness o f the copper thin film: / = 3*10 ~7 m - 0.00118
mil
Thickness o f the substrate: h = 5.08 xlO"* m - 2 0 mil
Width o f the transmission line: w = 5.6 mil
Guide wavelength: A =0.0319 m
t . ( 4mv ,
So, Aw = —In ------+1 = 0.03265 mil
x V t
w '= w +Aw = 5.63265 mil
a
_
c copper^o^
^ ■ ic o p p tr
1
,
1{4 h
h
1
h
1+ — + —
W 7M?
-
-
w
t
1+
2.098
4tew.
Characteristic impedance: Z 0 =53.3 Q
Conductivity o f copper at 77 K: <y = l.38xl0*
Surface resistance o f the copper thin film: R s
Conductor attenuation constant: a e afftr =
(flw )" ’
r = — = 0.0242 Q
ta
2.098R, comtr
Z 0h
= l .875 N p /m
181
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Q-factor for conductor loss o f copper: Qc
= 52.516
copper
a c.‘opptr^g
Measured loaded Q-factor and insertion loss o f copper resonator:
Qi._copptr =49.5
S 2l copptr= - 25324 dB
Unloaded Q-factor o f copper resonator: Q,0 _ copper
1
Because
1
Q o _ copptr
1
+
Q c _copptr
1
d _ copper
Qr_copper
-‘opptr^21.
1-10 20
=52.335
Qr_coppcr
1
Q o _ copper
l
1
+-
Q d _ copper
Q
= 6.859x10'
^ c _ copper
Qc
For YBCO resonator:
Thickness ofthe YBCO thin film: f = 3x10"7 m = 0.00118
mil
Thickness of the substrate: A = 5 .0 8 x l0 -4 m = 20 mil
Width o f the transmission line: w = 5.6 mil
Guide wavelength: Xg =0.0319 m
So, Aw = — In
7t
03265 mil
w'=w+Aw = 5.63265 mil
a c_HTsZph _ 1
\i
HTS
2n
1,4 /i.
. h
h
1+ — + — - b p = + i '
w' nw
1 -w
2.098
1+ —
4 t w J.
182
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Measured loaded Q-factor and insertion loss o f the YBCO resonator:
Q l_ h ts
= -2 9 .1 0 2 dB
-10630
Of
Unloaded Q-factor of copper resonator: Q0 ^
1 -1 0
Since Qd m
-Q d
1
Q d _ HTS
Q r_ H T S
Qc
H TS
- + ------- -
Q d _copper
Q t0
HTS
20
H TS
= 6 .8 5 9 x l O -5
Q r _ copper
1
1
hence,
Q r copptr — Q r
HTS
HTS
= 11016
^S-----n . HTS
= 2.489x10Q d _H TS
Q r _H TS
Q-factor for conductor loss o f YBCO: Qc ^
,
=40181
= 0.00245 N p /m
Conductor attenuation constant o f YBCO: a c hts =
Qc
Surface resistance of YBCO: R.j
H TS
a c_HTS^0^
2.098
H T S^t
= 3 .1 6 x 1 0
O
183
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INVESTIGATION FOR SURFACE RESISTANCE OF
YTTRIUM-BARIUM-COPPER-OXIDE THIN FILMS ON
VARIOUS SUBSTRATES FOR MICROWAVE APPLICATIONS
Abstract o f dissertation submitted in partial fulfillment
o f the requirements for the degree o f
Doctor o f Philosophy
By
Hongjun Yao, B.S., M.S.
Fudan University, 1993
Fudan University, 1996
May 2002
University o f Arkansas
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This abstract is approved by:
Dissertation Directors:
0
•
—
///
Dr. Fred D. Barlow
Assistant Professor o f Electrical Engineering
Dr. Gregory J. Salamo
University Professor o f Physics
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ABSTRACT
High temperature superconducting (HTS) materials such as YBCO (YttriumBarium-Copper-Oxide) are very attractive in microwave applications because o f their
extremely low surface resistance. In the proposed all-HTS tunable filter, a layer o f
HTS thin film on a very thin substrate (100 pm) is needed to act as the toractor that
can be rotated to tune the frequency. In order to provide more substrate candidates that
meet both electrical and mechanical requirements for this special application, surface
resistance of YBCO thin films on various substrates was measured using microstrip
ring resonator method.
For alumina polycrystalline substrate, a layer o f YSZ (Yttrium stabilized Zirconia)
was deposited using IBAD (ion beam assisted deposition) method prior to YBCO
deposition. The surface resistance o f the YBCO thin film on alumina was found to be
22 mO due to high-angie grain boundary problem caused by the mixed in-plane
orientations and large FWHM (full width at half maximum) of the thin film. For
YBCO thin films on a YSZ single crystal substrate, the surface resistance showed
even higher value of 30 m ft because o f the mixed in-plane orientation problem.
However, by annealing the substrate in 200 Torr oxygen at 730 °C prior to deposition,
the in-plane orientation of YBCO thin films can be greatly improved. Therefore, the
surface resistance decreased to 1.4 m fi, which is still more than an order higher than
the reported best value. The YBCO thin films grown on LaA103 single crystal
substrate showed perfect in-plane orientation with FWHM less 1 °. The surface
l
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resistance was as low as 0.032 mQ. A tunable spiral resonator made o f YBCO thin
film on LaA 103 single crystal substrate demonstrated that the resonant frequency can
be tuned in a rang as large as 300 MHz by changing the gap between toractor and
substrate. The Q-factor was more than 12,000, which ensured the extraordinarilly high
sensitivity for the proposed all-HTS tunable filter.
2
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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