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Microwave response of high transition temperature superconducting thin films

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O rder N um ber 9202247
M icrow ave respon se o f high tran sition tem p eratu re superconducting
th in films
Miranda, Felix Antonio, Ph.D.
Case Western Reserve University, 1991
UMI
300 N. Zeeb Rd.
Ann Arbor, MI 48106
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MICROWAVE RESPONSE OF HIGH
TRANSITION TEMPERATURE
SUPERCONDUCTING THIN FILMS
by
FELIX ANTONIO MIRANDA
Submitted in partial fulfillment of the requirements
for the Degree of Doctor of Philosophy
Internal Thesis Advisor: William L. Gordon, Ph.D.
External Thesis Advisor: Kul B. Bhasin, Ph.D.
Departm ent of Physics
CASE WESTERN RESERVE UNIVERSITY
May, 1991
P
L
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CASE WESTERN RESERVE UNIVERSITY
GRADUATE STUDIES
We hereby approve th e t h e s i s o f
Felix A. Miranda_______________
ca n d id a te fo r th e
P h.D .
d e g r e e .:*
Signed :
f
(Chairman)
K>a gfa
Date
}/6
J
/
C -
/ •V
/
1
*We a ls o c e r t i f y th a t w r it t e n ap p roval has
been o b ta in e d f o r any p r o p r ie ta r y m a te r ia l
c o n ta in ed t h e r e in .
1
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M ICROWAVE RESPONSE OF HIGH TRANSITION TEM PERATURE
SUPERCONDUCTING THIN FILMS
Abstract
by
FELIX ANTONIO MIRANDA
We have studied the microwave response of YBa2Cu 30 7.j, Bi-Sr-Ca-Cu-O, and
Tl-Ba-Ca-Cu-O high transition tem perature superconducting (HTS) thin films by
performing power transmission measurements.
These measurements were carried
out in the tem perature range of 300 to 20 K and at frequencies within the range
of 30 to 40 GHz.
Through these measurements we have determined the magnetic
penetration depth (A), the complex conductivity (a =<r1-j<r2), and the surface
resistance (Rs).
An estimate of the intrinsic penetration depth (A~121 nm) for
the YBa 2Cu 30 7.£ HTS has been obtained from the film thickness dependence of
A. This value compares favorably with the best values reported so far (~140 nm)
in single crystals and high quality c-axis oriented thin films.
Furthermore, it wets
observed th a t our technique is sensitive to the intrinsic anisotropy of A in this
superconductor.
Values of A are also reported for Bi-based and Tl-based thin
films.
We observed that for the three types of superconductors, both <rl and <r2
increased when cooling the films below their transition tem perature. This indicates
th at the tem perature dependence of <r1 is not consistent with th a t expected from
ii
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the two-fluid model, and also deviates from the values obtained using the M attisBardeen equations based on the BCS theory.
Values of
frequency and
Rg comparable to or lower than that for copper a t the same
a t 77 K were obtained for the YBa2 Cu 30 7 ^ thin films.
However,
the R s for the Bi-based and Tl-based films wets larger than th at of copper for all
the meetsured
tem peratures. Our Rg measurements were
consistent with those
performed a t 36 GHz on the same films using resonant cavity techniques.
have fabricated a resonant cavity to measure Rg.
We
The measured Rg are in good
agreement with other reported Rg values obtained using resonant cavity techniques
if we assume a quadratic frequency dependence for Rg.
Our analysis shows th at, of the three types of HTS films studied, the
YBa2Cu30 7_£ thin films, deposited by laser ablation and off-axis magnetron
sputtering are the most promising for microwave applications.
iii
b
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TO MY PARENTS,
LUCY AND SANTOS
AND
TO MY WIFE, IVONNE
AND DAUGHTER, MELISSA
iv
kA
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ACKNOWLEDGEMENTS
I would like to thank my thesis advisors Dr. W. L. Gordon, of Case Western
Reserve University, and Dr. K. B. Bhasin, of NASA Lewis Research Center, for
their guidance and encouragement throughout this work.
My deepest thanks to
Dr. D. E. Farrell for his helpful suggestions and advice, as well as to Dr. T. G.
Eck and Dr. P. C. Claspy for their cooperation and participation in my thesis
committee.
The invaluable assistance of Dr. V. O. Heinen, especially during the
final stages of this work, is deeply appreciated.
I am indebted to Mr. J. D.
W arner for all his help and assistance from the early stages of this work to its
completion.
I w ant to express my gratitude to Dr. R. F. Leonard for his support
and attention during this enterprise.
I am thankful to Drs. J. Talvacchio, R.
Kwor, and N. Ianno for providing some of the films analyzed in this thesis.
Special thanks to Mr. E. C. Nordgren for his timely assistance in the experimental
part of this work.
I deeply appreciate the assistance of the technical staff which
facilitated many of the demands of this project.
I also want to thank Mr. C. M.
Chorey, Mr. M. 0 . P atton, and Mr. M. A. Richard, for their constructive
suggestions and for their contribution in creating a very friendly atmosphere in our
work place.
Finally, I would like to acknowledge the contribution of the members
of the Physics Departm ent of Case Western Reserve University and the members
of the Solid State Technology Branch, Space Electronics Division, of the NASA
Lewis Research Center for the support given to me in reaching this goal.
M T ' '1
v
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AGRADECIMIENTO
En la realizacion de toda empresa siempre hay seres, eternos o transeuntes,
cuya contribucion
es
meritoria
de
reconocimiento.
Es
para
estos
que a
continuacion ofrezco humildes h'neas de agradecimiento.
A Dios, Maestro de maestros.
A mis padres Lucy y Santos, por todo su amor, cuidado y respeto, y por el
privilegio que tengo de poder contarme entre sus hijos.
A mi esposa Ivonne, por su amor, tolerancia y apoyo en todas mis empresas, y
a mi hija Melissa por que en su inocencia de nina florece el amor.
A mis hermanos, mi abuela Lola, mis tfos y mis tias, por una nihez y adolecencia
que jam as podran olvidarse.
A mi suegra Iris por ser ejemplo de superacion y vida, y por sus oraciones que
llegan al Padre.
A la familia Boada-Ortiz por una amistad sincera y sin lfmites.
A la familia Norenberg por su cuidado espiritual.
Finalmente, mi gratitud a todos a aquellos seres con quienes he compartiao ia
alegn'a de una sonrisa.
vi
i
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TABLE OF CONTENTS
Chapter
Page
1 General Introduction and Background....................................................................... 1
1.1 In tro d u c tio n ..................................................................................................................
1
1.2 Superconductor-Microwave I n te r a c tio n ..................................................................
5
1.3 High-Tc Oxide S u perconductors............................................................................... 9
1.3.1 The Y-Ba-Cu-0 Superconductor ..................................................................
10
1.3.2 The Bi-Sr-Ca-Cu-0 Superconductor.............................................................
11
1.3.3 The Tl-Ca-Ca-Cu-0 Superconductor ..........................................................
13
1.4 References ..................................................................................................................
14
2 Theoretical Considerations........................................................................................ 18
2.1 In tro d u c tio n ...............................................................................................................
18
2.2 The Two-Fluid M o d e l ..............................................................................................
19
2.3 BCS T h e o r y ...............................................................................................................
21
2.4 Surface Impedance ...................................................................................................
23
2.5 Plane Wave Propagating Through a Thin Film on a Dielectric
Substrate
....................................................................................................................
25
2.6 Determination of Complex Conductivity: Two-Fluid Model
Approximation
..........................................................................................................
30
2.7 Surface R e a c ta n c e .....................................................................................................
32
2.8 References ..................................................................................................................
35
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3 Microwave Transmission Measurements.................................................................. 37
3.1 In tro d u c tio n ...............................................................................................................
37
3.2 Measurement Apparatus and P ro ced u res.............................................................
38
3.3 References .................................................................................................................
43
4 Results and D iscussion............................................................................................... 45
4.1 In tro d u c tio n ...............................................................................................................
45
4.2 YBajCugOy.j Thin F ilm s ........................................................................................
47
4.2.1 Microwave Transm itted Power ....................................................................
47
4.2.2 M aterial Properties of YBa2Cu 30 7. j Thin F i lm s ......................................
57
4.2.3 Magnetic Penetration D e p t h .........................................................................
65
4.2.4 Complex Conductivity ....................................................................................
73
4.2.5 Surface Resistance ...........................................................................................
83
4.3 Bi-Sr-Ca-Cu-O Thin F ilm s ......................................................................................
87
4.4 Tl-Ba-Ca-Cu-0 Thin F i l m s ......................................................................................101
4.5 Closing R e m a rk s..........................................................................................................114
4.6 References ....................................................................................................................118
5 Measurement of The Surface Resistance Using a Resonant
Cavity M ethod............................................................................................................... 124
5.1 In tro d u c tio n ................................................................................................................. 124
5.2 Resonant Cavity F a b ric a tio n ................................................................................... 125
5.3 Definition of Quality Factor Q .................................................................................127
viii
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5.4 Measurement of the Quality Factor Q ..................................................................... 133
5.5 Experimental D e ta ils.................................................................................................140
5.6 R e su lts........................................................................................................................... 141
5.7 References ................................................................................................................... 150
6 Conclusions....................................................................................................................152
Appendices ....................................................................................................................156
A Thin Film Deposition techniques .............................................................................. 156
B Other Sample C h aracterizations................................................................................ 170
C Dielectric Substrates For HTS Thin F ilm s ...............................................................176
D. Evaluation of the Gap P a ra m e te r..............................................................................185
Literature Cited .......................................................................................................... 187
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List of Figures
Figure
1.1
Page
Penetration of an oscillating magnetic field B(w) into
superconductor in
1.2
a bulk
the normal state................................................................
6
Penetration of an oscillating magnetic filed B(ct/) into a bulk supe­
rconductor in the superconducting state.
The penetration depth Ais
defined as a distance in which the fielddecreases
by a factor e' 1
1.3
Crystal structure of YBa 2Cu 30 7.£. (taken from reference 16)
1.4
Crystal structure of Bi2Sr 2CaCu 20 8. (taken from reference 21 ). . . .
1.5
Crystal structure of T l 2Ba 2 Can. 1Cun0 4+2n for n = l, 2, and 3. Metals
6
................... 10
12
atom s are shaded and Cu-O bonds are shown, (taken from reference
28)
2.1
14
Normally incident plane microwave propagating through a thin film
deposited onto a dielectric substrate. Regions I and IV represent the
free space circumscribed by the waveguide, region II represents the
film of thickness d and complex dispersion coefficient a , and region
III represents the dielectric substrate of thickness t and refractive
index n ........................................................................................................................26
3.1
Microwave measurements apparatus
.................................................................. 39
3.2
Side view of a rectangular waveguide propagating the TE 01 mode
w ith its entire cross section covered by a high-Tc superconducting
thin film of thickness d deposited on a dielectric substrate of
x
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thickness t and refractive index n. In this work I~ 16 m W /cm 2, d ~
2000 A, t ~ 5.0 x 10' 2 cm, and 10' 6 < T /I < 1 0 '1
4.1
Transm itted
power
versus
tem perature
for
YBa2Cu 30 7_j thin film (2400 A) on LaA10 3
4.2
Transm itted
power
YBa2Cu 30 7<5 thin
tem peratures
and
versus
film
at
incident
(4000
30.6
A)
GHz.
a
laser
The
ablated
................................................ 50
power for a
on
............................41
LaGaOs
largest
laser
ablated
for
different
error
bars
are
approximately the size of the s y m b o ls ..............................................................52
4.3
Transm itted power versus tem perature for laser ablated YBa2Cu 30 7, j
thin films on LaA103; the thicknesses represented are 828 A (o),
1769 A (A), 2400 A (□), and 4900 A (+ ). The LaA10 3 substrates
for all the films were 20 mils t h i c k .................................................................53
4.4
Transm itted power versus film thickness at different temperatures
corresponding to the film represented in figure 4.3. The maximum
error in the data is approximately the size of the s y m b o l s .................... 54
4.5
Measured relative phase shift A9 for an off-axis magnetron sputtered
YBa 2Cu 30 7.£ thin film (800 A) on YSZ (+ ), and for a laser ablated
YBa 2Cu 30 7_£ thin film (4900 A) on LaA10 3 (A)
4.6
55
dc resistance versus tem perature and its first derivative (dRdc/d T )
for a laser ablated YBa 2Cu 30 7.£ thin film (2400 A) on LaA103.
(Courtesy of Mr. Joseph Warner and Mr. Joseph Meola, NASA
Lewis Research C e n t e r ) .........................................................................................58
xi
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4.7
dc resistance versus tem perature and its first derivative (d R ^ /d T )
for an off-axis magnetron sputtered YBa2Cu 30 7.$ thin film (1000 A)
on MgO. (Courtesy of Mr. Joseph W arner and Mr. Joseph Meola,
NASA Lewis Research C e n t e r ) ........................................................................... 59
4.8
dc resistance versus tem perature and its first derivative (d R ^ /d T )
for a laser ablated YBa 2Cu 30 7_£ thin film (1760 A) on LaA103.
(Courtesy of Mr. Joseph W arner and Mr. Joseph Meola, NASA
Lewis Research C e n t e r ) .........................................................................................60
4.9
X-ray diffraction pattern for a laser ablated YBa 2Cu 30 7,£ thin film
(2400 A) on LaAlOj. (Courtesy of Mr. Ralph Garlick, NASA Lewis
Research C e n t e r .......................................................................................................61
4.10
Scanning electron micrographs a t two different magnifications of the
surface of a laser ablated YBa 2Cu 30 7.£ thin film (828 A) on
LaA103.
(Courtesy
of Mr.
Nicholas Varaljay and Ms.
Bohman, NASA Lewis Research Center)
4.11
Donna
.......................................................63
Scanning electron micrographs a t two different magnifications of the
surface of an off-axis magnetron sputtered YBa 2Cu 30 7.£ thin film
(1000 A) on MgO. (Courtesy of Mr. Nicholas Varaljay and Ms.
Donna Bohman, NASA Lewis Research Center)
4.12
......................................... 64
Surface reactance versus temperature, a t 30.6 GHz, for two laser
ablated films (no.3, 2400 A,
A) and
(no.4,
1769 A, +)
on
LaA10 3 ....................................................................................................................... 68
1
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4.13
Magnetic
penetration
depth
YBa^CugO^ $ thin films.
(A) versus
film
thickness
(d)
for
The solid line represents the second degree
polynomial fit described in the t e x t .................................................................70
4.14
Magnetic penetration depth A versus tem perature for a laser ablated
thin film (2400 A.) on LaAlOg. The dashed line represents a fit
using the tem perature dependence for A according to the two fluid
m o d e l ...........................................................................................................................72
4.15
4.16
Real and imaginary parts of the microwave conductivity a = a l -j<r2
versus tem perature a t 30.6 GHz
fora laser ablated YBa2Cu 30 7. j
thin film (4900 A , T®w=90.8 K)
onL a A l O g ................................................ 74
Real and imaginary parts of the microwave conductivity <r
versus tem perature for a laser ablated YBa2Cu 30 7.£ thin film (1000
A, T “ w= 88.6 K) on LaA103 a t
4.17
33.3G H z .................................................... 74
Real and imaginary parts of the microwave conductivity <r*=<r
for a laser ablated YBa 2Cu 30 7.£ thin film (2400 A, T“ w=91.6 K)
on LaA10 3 a t 34.6 GHz
4.18
..................................................................................... 75
Real conductivity a v obtained from the magnitude and phase of the
transm itted power, for a YBa 2Cu 30 7_£ thin film on LaA103. Solid
line is the real part of the conductivity calculated from M attisBardeen t h e o r y ..........................................................................................................77
4.19
Real and imaginary parts of the microwave conductivity er*=<r1-j«r2
for a laser ablated YBa 2Cu 30 7-(j thin film (2655 A, T“ w=91.2 K)
on LaA10 3 a t 35 GHz
........................................................................................ 78
xiii
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4.20
Real part of the complex conductivity a t 33.3 GHz, calculated from
the magnitude and phase of the transm itted power (o), and from
the magnitude of the transm itted power and the two-fluid model
(+)
4.21
80
Imaginary part of the conductivity at 33.3 GHz, calculated by
measurements of the magnitude and phase of the transm itted power
(o), and from the magnitude of the transm itted power with the twofluid model (+ )
4.22
Surface
resistance,
80
Rg, versus
tem perature
at
36
GHz
for
a
YBa 2Cu 30 7_£ thin film (4000 A) on LaA10 3 as measured by a
microwave power transmission method (+ ) and by a cavity wall
replacement method; NRL( □) and FM (A).
is also plotted for comparison
4.23
The Rg for copper (o)
........................................................................... 86
dc resistance versus tem perature measurement of co-evaporated Bi-SrC a-Cu-0 superconducting films (3000 A) on MgO (+) and LaA10 3
(A). (Courtesy of Mr. Joseph W arner and M r. Joseph Meola, NASA
Lewis Research C e n t e r ) .........................................................................................89
4.24
Scanning electron micrographs for Bi2Sr 2 Ca 1Cu 2Ox thin films (5000
A) on LaAlOj
(a) and MgO (b) substrates. (Courtesy of Mr.
Nicholas Varaljay and Ms. Donna Bohman, NASA Lewis Research
C e n t e r ) ....................................................................................................................... 90
4.25
Scanning electron micrographs for Bi2Sr 2 Ca 1Cu 2Ox thin films (3000
A) on LaA10 3
(a) and MgO (b) substrates. (Courtesy of Mr.
xiv
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Nicholas Varaljay and Ms. Donna Bohman, NASA Lewis Research
C e n t e r ) ....................................................................................................................... 91
4.26
Transm itted power
versus
tem perature for
co-evaporated
Bi2Sr 2C a 1Cu 2Ox thin films (3000 A) on MgO (+) and LaA103 (A)
substrates a t 30.6 GHz
4.27
Relative
phase shift
.........................................................................................93
AO
versus
tem perature
for co-evaporated
Bi2Sr 2C a 1Cu 2Ox thin films (3000 A) on MgO (+) and LaA10 3 (A)
substrates a t 30.6 GHz
4.28
<71 (A) and
........................................................................................ 94
<r2 (+) versus tem perature and
a t 30.6 GHz for a
Bi2Sr 2C a 1Cu 2Ox thin film (3000 A) on a MgO substrate
4.29
(A) and
<r2 (+) versus tem perature and
a t 30.6 GHz for a
Bi2Sr 2C a 1Cu 2Ox thin film (3000 A) on a LaA10 3substrate
4.30
..........................95
...................... 96
Magnetic penetration depth A versus tem perature for a co-evaporated
B ijS rjC ajC ujO ^^ thin film (3000 A) on LaA103. The solid line
represents a fit using the tem perature dependence for A according to
the two-fluid model
4.31
............................................................................................... 98
Magnetic penetration depth A versus tem perature for a co-evaporated
BijSrjCajCujOj^
thin
film
(3000 A)
on MgO.
The solid
line
represents a fit using the tem perature dependence for A according to
the two-fluid model
4.32
Surface
resistance
............................................................................................... 98
(Rg)
at
30.6
GHz
versus
tem perature
for
Bi2Sr 2C a 1Cu 2Ox thin films (3000 A) on LaA10 3 (A) and MgO (+)
xv
k
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substrates, and for copper (□); (♦) represents the theoretical R,
value for Cu a t the shown tem perature and fre q u e n c y ...............................99
4.33
Normalized resistance versus tem perature for laser-ablated Tl-Ba-CaC u-0 superconducting films on LaAlOg. (a) Film thickness, 5000 A;
T f
=
101.8 K. (b) Film thickness 4000 A; Tj® =
99.8 K.
(Courtesy of Mr. Joseph W arner and Mr. Joseph Meola, NASA
Lewis Research C e n t e r ) .......................................................................
4.34
103
Scanning electron micrographs for a 5000 A laser ablated Tl-Ba-CaC u-0 thin film (a), and a 4000 A laser ablated Tl-Ba-Ca-Cu-0 thin
film (b) on LaAlOg.
(Courtesy of Mr. Nicholas Varaljay, NASA
Lewis Research C e n t e r ) ...................................................................................
4.35
104
Scanning electron micrographs for (a) a 5000 A laser ablated Tl-BaC a-C u-0 thin film on MgO, and (b) a 5000 A rf magnetron
sputtered Tl-Ba-Ca-Cu-O thin film on LaAlOg.
(Courtesy of Mr.
Nicholas Varaljay and Ms. Donna Bohman, NASA Lewis Research
C e n t e r ) .....................................................................................................
4.36
105
Tem perature dependence of the power transmission coefficient (a)
and the relative phase shift (b) of 30.6 GHz radiation transm itted
through films T l # l (A),T l# 2 (o), T l# 3 (+ ),
4.37
Tem perature dependence
on
and T l# 4 (□) . . .
and <r2 forsamples
T l # l (a),
and
T l# 2 ( b ) ..............................................................................................................
4.38
109
Tem perature dependence of <rl and <r2 for samples T l# 3 (a), and
T l# 4 ( b ) ..............................................................................................................
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k
107
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110
4.39
Calculated values of the surface resistance Rg versus tem perature a t
30,6 GHz for samples T l # l (A), T l# 2 (o), T l# 3 (+ ), and T l# 4
(□).
Also shown are the
measured
Rg for Cu
(v),
and
its
theoretically predicted value at 77 K (♦), for comparison purposes . 112
4.40
Magnetic penetration depth A for samples T l # l (A), T l# 2 (o), and
T l# 3 (+ ). D ata for sample T l# 4 have been om itted for clarity
4.41
. . 113
Magnetic penetration depth A versus tem perature for sample T l # l.
The solid line represents a fit to the data using the tem perature
dependence for A according to the two-fluid m o d e l...............................
5.1
Top
view
of
the
measurement of Rg.
TEq 13
resonant
cavity
developed
for
114
the
The superconducting sample is place on top of
the cavity replacing the gold plated tablet shown in the figure.
The change in the cavity Q when the sample is used as the end
wall determines the Rg of the superconducting thin f i l m .....................
5.2
126
Coordinate system for a cylindrical cavity of radius a and length
I.
...........................................................................................................................
128
5.3
Tangential fields a t the end plates and side walls of the cavity
. .
130
5.4
Lumped-parameter RLC resonant c i r c u i t ..................................................
134
5.5
Smith chart impedance plot for ideal undercoupled (long-dashed line),
critically coupled (dashed-dotted line), and overcoupled (short-dashed
line) cavity resonator, and displaced impedance plot due to presence
of coupling loss and reactance (dashed-doubled-dot l i n e ) .....................
137
xvii
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5.6
dc resistance versus tem perature
YBa2Cu 30 7.£
superconducting
measurement of laser ablated
films
on
S rT i0 3
and
L aG a0 3
substrates. (Courtesy of M r. Joseph W arner and Mr. Joseph Meola,
NASA Lewis Research C e n t e r ) .....................................................................
5.7
Scanning
electron
micrographs
of
laser-ablated
142
YBa 2Cu 30 7_£
superconducting films on S rT i0 3 (a) and L aG a0 3 (b) substrates.
(Courtesy
of
M r.
Nicholas
Varaljay,
NASA
Lewis
Research
C e n t e r ) .................................................................................................................
5.8
Reflection coefficient above (a) and below (b) T c for the film on
S rT i0 3, and above (c) and below (d) T c for the film on L aG a0 3
5.9
143
144
Smith chart impedance plot for YBa 2Cu 30 7.£ thin film on L aG a0 3
at (a) room tem perature, undercoupled, (b) 77 K, almost critically
coupled, (c) 26 K, o v e rc o u p le d .....................................................................
5.10
Unloaded quality factor Q versus tem perature for YBa 2Cu 30 7.£ thin
films on S rT i0 3 (A) and L aG a0 3 (□)
5.11
146
147
Surface resistance (Rg) a t 58.6 GHz vs tem perature for 1.2 pm films
of YBa 2Cu 30 7 (j deposited by laser ablation onto S rT i0 3 (O), and
LaGaOs (□) substrates, and for the gold-plated cavity (A)
. . . .
A .l
Laser ablation technique
.................................................................................
A.2
Schematic representation of the as deposited multi-layer structure of
148
157
the film (left), and the superconducting film after annealing on the
right; (taken from Ref, 14) . . .
A.3
Co-evaporation set-up for Bi, CaF 2+ S rF 2and Cu
161
................................
xvux
it!•
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163
A.4
rf magnetron sputtering deposition s y s te m .................................................
166
B .l
Fcur-point probe measurement set-up
170
C .l
Surface roughness of LaA10 3 as measured with a profilometer before
and
after
annealing
Czochralski substrate
C.2
for
(a)
flame
........................................................
fusionsubstrate
and
(b)
.....................................................................................
181
Plots of relative resistance versus tem perature for YBa2 Cu 30 7,£ films
on (100) LaA10 3 made by flame fusion and by the Czochralski
method
.................................................................................................................
182
xix
5
L
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List of Tables
Table
Page
4.1
Microwave Measured Param eters of YBCO Superconducting
4.2
Microwave Measurements of A in YBa 2Cu 30 7, j Thin Films ........................
4.3
Magnetic Penetration Depth A of YBa 2Cu 30 7.^ Thin Films on
Film s
LaAlOg ....................................................................................................................
49
66
70
B .l
M aterial Param eters of YBa 2Cu 30 7, j Thin Films ............................................ 174
B.2
M aterial Param eters of Bi and Tl-based thin f ilm s ............................................ 175
C .l
Microwave Substrates for HTS Thin Films ......................................................... 178
xx
k
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Chapter 1
General Introduction and Background
1.1 Introduction
Superconductivity occurs when the conduction electrons order in momentum
space.
The origin and nature of this ordering into a coherent macroscopic
quantum mechanical state was explained by Bardeen, Cooper, and Schrieffer in
w hat is known as the BCS theory .1
According to their theory, electrons pairs
form a ground state a t the absolute zero tem perature (T = 0 K), separated from
a continuum of excited states by an energy gap 2A. A t tem peratures greater than
T = 0 K, some of the excited states
are occupied forming an electron gas system
th a t coexists in equilibrium with the electron pairs.
One of the main features of the superconducting state is zero dc electrical
resistivity, an effect th at was first observed in 1911 by the Dutch physicist Heike
•
2
Kamerlingh Onnes, while working with a mercury wire.
By using nuclear
magnetic resonance methods to measure the magnetic field associated with the
currents flowing in a Nb-25%Zr superconducting ring, File and Mills3 determined
an upper lim it to the equivalent resistivity of the wire of 10*22 fl-cm.
However,
the superconducting state implies more than a zero dc electrical resistivity.
is evidenced
by the
fact th at when a
This
magnetic field H is applied to
a
superconducting m aterial in its normal state there will be a total expulsion of the
1
I
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2
magnetic flux originally present in the interior of the sample as it is cooled below
its transition tem perature (Tc).
Therefore, the material behaves as a perfect
diamagnet with zero magnetic induction in its interior.
This effect, first observed
in 1933 by Meissner and Ochsenfeld ,4 is traditionally known as the Meissner effect.
The phenomenon of superconductivity has been observed in many metallic
elements, alloys, semiconductors and intermetallic compounds.
Before 1986, the
range of transition tem peratures T c extended from 0.01 K for some semiconductors
to 23.2 K for the alloy Nb3Ge, which was the highest T c observed until then.
In 1986 Bednorz and Mueller5 brought the attention of many researchers to the
field of superconductivity by their discovery of superconductivity a t a tem perature
of 30 K in the La 2.xBa;tC u 0 4 system.
Subsequently, Wu, et al .6 found a Tc of
around 90 K in the YBa 2Cu 30 7,£ system, elevating T c above the liquid nitrogen
tem perature.
A t the time of this writing the highest accepted T c value reported
has been 125 K in a Tl-based superconducting system discovered by Sheng and
Hermann . 7
Since the discovery of these high-Tc perovskites, many studies have been
performed in an attem pt to elucidate the nature of the superconducting state of
these
materials.
Among
electromagnetic radiation.
these
are
studies
related
to
the
response
to
The study of the electromagnetic response allows the
determination of m aterial parameters such as the magnetic penetration depth (A),
the complex conductivity (<r =
jX g).
r
Knowledge of these
- j<r2), and the surface impedance (Zg = Rg parameters
is very
im portant for
technological
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3
applications, since they are directly related to the losses of electromagnetic energy
in these materials during signal propagation.
In the past, millimeter and microwave transmission and reflection experiments
have been used to study the properties of conventional low transition tem perature
superconducting films.
Glover and Tinkham 8 analyzed the microwave properties
of lead (Pb) and tin (Sn) films and obtained the effective complex conductivity,
and an effective value for the energy gap from the microwave transmission data.
Rugheimer, et al .9 measured the reflection and transmission coefficients of 1. 2 , 0 .8 ,
and 0.4 mm wavelength microwaves through (~50 A) films of Sn and In a t
tem peratures below T c.
They found a good correlation between the transmission
and reflection ratios calculated on the basis of the BCS theory
experimental data.
Subsequent studies by Lehoczky
and their
and Briscoe ,10 based on
measurements of the microwave transmission and reflection coefficients for thin (<
o
150 A) superconducting Pb films, were consistent with the BCS-based M attis and
Bardeen expressions for the conductivity .11
The information obtained from these studies provided strong evidence for the
validity of the
BCS theory.
More recently, Sridhar 12 performed extensive
measurements of the surface resistance (Rg) and reactance (Xg) of superconducting
Sn a t 10 GHz using resonant cavity techniques.
Good agreement between the
experimental results obtained by Sridhar for the surface impedance Zg = Rg + jX g
and the predictions of the BCS theory was obtained over several orders of
m agnitude variation of Zg.
F
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4
In this thesis we present extensive results of the interaction of microwaves with
YBajCujOy.^, Bi-based, and Tl-based
superconducting thin films deposited on
several microwave substrates.
d ata
microwave
power
transm itted
The
through
the
were obtained
films
in
the
by measuring the
normal
and
the
superconducting state and by resonant cavity techniques, as will be discussed in
chapters 2, 3, and 5 of this dissertation.
Our main motivations for this study
were to quantify and understand the physical param eters (such as the magnetic
penetration depth, the complex conductivity, and the surface impedance) of HTS
m aterials a t millimeter wave frequencies.
Based on these parameters we discuss
the suitability of these HTS films for microwave applications.
This dissertation is organized as follows:
# The remainder of this chapter briefly discusses the superconductor-microwave
interaction and provides a brief description of the properties of the Y-Ba-Cu-O,
Bi-Sr-Ca-Cu-O, and Tl-Ba-Ca-Cu-O superconducting systems.
# Chapter 2 introduces the theoretical background for the concepts which are
relevant to this work.
# Chapter 3 describes the cryogenic and microwave measurement equipment and
the procedures used to measure the microwave transmission through the HTS
films.
# Chapter 4 presents the results obtained for the different types of superconduct*
ing systems considered in this study.
# Chapter 5 discusses the measurements of the surface resistance Rs of HTS thin
films a t 58.6 GHz by using resonant cavity techniques.
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5
•
Chapter 6 presents the conclusions drawn from this study, and suggests direc­
tions for further investigations in this area.
# In addition we present a t the end of the thesis several appendices which de­
scribe different film deposition methods, other characterization techniques used,
dielectric substrates for HTS thin films, and details of the calculation of the
gap parameter.
1.2
Superconductor-Microwave Interaction
The two experimental techniques employed in this study to investigate the
properties of the new perovskites superconductors utilize microwave fields as a
probing
mechanism.
We proceed now to give a
brief description of the
superconductor-microwave interaction.
Consider a plane microwave normally incident on a bulk superconductor. There
will be a magnetic field (B(w)) parallel to the surface of the superconductor,
which, in the normal state, penetrates the sample (see figure 1 . 1) and slowly
decreases with depth in the sample (normal skin effect).
When the sample is
cooled below its transition tem perature Tc, the magnetic field is expelled from the
interior of the superconductor due to the Meissner effect,4 decaying exponentially
into it with a characteristic penetration depth A (see figure 1.2), which is typically
»S T '
much less than the normal skin depth (£N).
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6
B((J)
-
1/5
i i
r
Figure 1 . 1:
Penetration of an oscillating magnetic field B(u>) into a bulk
superconductor in th e normal state.
BCU)
-z /x
/
Figure 1.2:
Penetration of an oscillating magnetic field B(w) into a bulk
superconductor in the superconducting state. The penetration depth A is
defined as a distance in which the field decreases by a factor e '1.
5
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7
The Bardeen-Cooper-Schrieffer (BCS) theory ,1 which describes the superconduct­
ing state as one in which paired carriers interact over a large range with respect
to interatom ic distances (~ 3000 A. in typical pure low-Tc superconductors) to
produce a coherent state, has shown th at the Meissner effect arises due to the
existence of a gap ( 2 A) in the energy
spectrum.
In the weak
coupling limit the
half-gap A is related to T c by,
A(0) = 1.764 kBT c
A(T) = 1.74A(0)(1 - t ) 1/2
, T = 0
(1.2.1)
, T -* T {
(1.2.2)
where kB is the Boltzmann constant, and t = T /T c.
Consequently, below T c
screening of B(w) only occurs when hw < 2A. If t o becomes larger than 2A, the
pairing of the carriers responsible for superconductivity is broken and the surface
of the sample is driven to the normal state.
The screening currents th at exclude
B(w) from the inside of the superconductor arise from the response of the
condensate of paired-carriers and the quasiparticles.
From Maxwell’s equations, an ac magnetic field will be accompanied by an
electric field (E(w)) differing in phase from B(w) by jt/2.
The electric field E(w)
will accelerate the quasiparticles resulting in a dissipative quasiparticle current (JN)
with the corresponding energy absorption.
frequencies greater than zero.
absorption will take place.
This effect will persist
for all
If the frequency is zero then E(w=0) = 0 , and no
In the superconducting state the induced screening
g
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8
currents can be related to the field E(w) in term s of the complex conductivity a*
as,
J = JN + Jg = <T*E(o/) = (ffj - jffj)E(w)
(1.2.3)
where <r1 is associated with the quasiparticle current J N and <r2 with the pairedcarriers current J g.
In the normal state
(1.2.3)
the familiar ohmic expression,
reduces to
= <rN and <r2 = 0 , and equation
J
=
<tn E( w).
For the
superconducting state and in cases for which be*; < < 2A, one has <r2 = nge 2/mw,
where ng is the density of paired-carriers and J g is related to B(w) by
V x J g = - B(o/)/p 0 AL2
where AL is the London penetration depth.
all
the
frequencies
for
which
hw
<<
(1.2.4)
The above relation will be valid for
2A.
Since, for
the
new
high-Tc
superconductors (HTS), 2A is in the terahertz frequency range (w ~ 12 THz, for
Tc - 92 K), the expression (1-2.4) is appropriate for their analysis.
Note th at
for a homogeneous superconductor and for T far below T c, a 2 »
Thus, the
<rv
quasiparticle dissipative current J N, whose magnitude is determined by <rv will be
small.
However, the effect of the quasiparticles on the properties of a supercon­
ductor must
be taken
into account, particularly when the suitability of a
superconducting material to be used in microwave devices is determined by the
magnitude of its ac losses.
r
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9
So far we have discussed the microwave-superconductor interaction in term s of
the intrinsic superconducting properties and loss mechanisms of a superconductor.
However, we have not mentioned other factors th a t can contribute to the response
of a superconductor to external high frequency electromagnetic perturbations.
of
the
factors
th at
considerably
affects
superconductor is the type of structure.
the
high
frequency
losses
One
in
a
For the new HTS m aterials, characterized
by a granular nature, the electrical and magnetic properties a t microwave
frequencies (wavelength ~ 1 cm) are sensitive to both the intragranular and the
intergranular media since the wavelengths in this frequency range are much larger
than the superconducting grain sizes (~ few microns).
This effect is certainly
manifested for the HTS in ceramic or bulk form, but its influence is also strong
in thin films, and even in single crystals due to small angle grain boundaries and
twinning.
1.3
High-Tc Oxide Superconductors
In this thesis we concentrated our efforts in the study of the three principal
HTS discovered so far; Y-Ba-Cu-O, Bi-Sr-Ca-Cu-O, and Tl-BarCa-Cu-O.
A brief
v w
n
description of each of these superconducting compounds is now provided.
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10
1.3.1
The Y-Ba-Cu-O Superconductor
Superconductivity a t 90 K was discovered by Wu, et al .6 in the multiphase YBa-Cu-0 system. The phase responsible for superconductivity is YBa 2Cu 30 7,£ with
a T c of 92 K. 13’14 The crystal structure for this phase is shown in figure 1.3.
Note th a t this structure can be viewed as a stacking of three perovskite layers
with a plane of Y ttrium atom s every three layers.
The Y B ajC ugO ^j is oxygen
deficient; neutron studies 15 have shown th a t the oxygen vacancies are ordered
leading to the presence of copper-oxygen chains within the structure.
Q-*
o -»
o-«
• -C
4 0 *
J 4> ®
o
it(j> i*o
© O
1E
k .
Figure 1.3: Crystal structure of YBa 2 Cu 30 7.j. (taken from reference 16 with
permission of the authors).
i*
M
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11
Studies have shown th at the T c of the YBa2Cu 3 0 7.£ system is considerably
affected by small changes in oxygen content .16 In fact, for the YBa 2Cu 30 7.£ phase
to be superconducting S needs to be between 0.0 and 0.7.
17
As 6 changes between
0.0 and 0.7, oxygen is removed from the O-Cu-O chains th at are parallel to the
b axis.
Note th at in this crystal structure the a and b axes are almost of the
same length with
a = 3.822
A and b = 3.891 A, while the c axis 11.677 A
when 6 = 0 .17 Since the a and b axes are not exactly equal, the crystal structure
of the YBa2Cu 30 7.£ is classified as orthorhombic.
1.3.2
The Bi-Sr-Ca-Cu-0 Superconductor
Superconductivity in the Bi-Sr-Ca-Cu-0 (BSCCO) system was discovered by
Maeda, et al ., 18 with T c of about 105 K.
The properties of this system are very
sensitive to both the starting composition and the overall processing procedure.
The superconducting phase consists of two double layers of B i-0 between which
are located layers of Sr-O, Cu-O, and Ca.
In the B i-0 double layers of the
BSCCO superconductors, the Bi ion can have as many as six oxygen atom s as
nearest neighbors.
The
BSCCO
compounds are polytypoids and
have
the
general formula
B i j S r j C a ^ C u ^ y , where n is the number of CuO layers in each half unit cell.
A description of the cation structures of the Bi2Sr 2CuOy (n = l), Bi2Sr 2CaCu 2Oy
(n=2), and Bi2Sr 2Ca 2Cu 3Oy (n=3) is given everywhere. 19,20 In general these
compositions are denoted by their cation ratios; i.e., 2201 (n = l), 2212 (n = 2 ), and
i
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12
2223 (n=3).
Empirically the transition tem peratures of the BSCCO compounds
have been found to increase with increasing number of Cu-O perovskite layers (up
to n=3) in the unit cell.21,22 One of the shortcomings of this system is the
difficulty of obtaining a single-phase m aterial.
zero-dc-resistance tem perature below 100 K.
This can cause a lowering of the
However, the resistivity may begin
decreasing rapidly a t tem peratures as high as 120 K . 18 It has been observed th at
the zero-dc-resistance tem perature can be raised by a PbO addition and by
carefully controlling the composition during the sample preparation process .23,24 For
this thesis we have used BSCCO thin films having the 2212 phase.
The crystal
structure for this phase is shown in figure 1 .4 .
Figure 1.4: Crystal structure of BijS^CaCugOg. (taken from reference 21
with permission of the authors).
I
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13
1.3.3
The Tl-Ba-Ca-Cu-0 Superconductor
Superconductivity in the Tl-Ba-Ca-Cu-0 system was reported by Sheng and
if
Hermann w ith the beginning of the superconducting transition a t ~ 120 K, and
T c(R=0) ~ 107 K.
Later, the zero-resistance state in the Tl-based system was
observed a t a tem perature as high as 125 K.
al.,
20
Mg fl)«V
Torardi, et al.,
MQ
and Hazen, et
identified different phases present in the Tl-based system and found th at the
2201, 2212, and 2223 phases (as described according to the cations ratio) are
responsible for superconductivity below 82, 110 , and 125 K, respectively.
The
Tl 2Ba 2 CaCu 2Ox (2212) phase, with a c-axis length of 29.3 A and with only a two
layer perovskite cell, has a T c of 110 K ,30 and the T l 2Ba 2C a 2Cu 3Ox (2223) phase,
with a c-axis length of 36.26 A and containing an extra Ca and Cu layers, has
a Tc value reported to be as high as 125 K .25
Diagrams of the 2201 , 2212 , and 2223 phases of the Tl-based system are shown
in figure 1.5.
The Tl-based films considered in this thesis were multi-phased, with
the 2212 and the 2223 as the predominant phases.
The T c’s (R = 0 ) for these
films were between 75 and 101.8 K, while the beginning of the transition ranged
from 120 to 105 K.
Although certainly not among the best quality films achieved
at the time of this writing, (Tc ~
115 K has been achieved ),31 the results
obtained from their characterization were very valuable for the purposes and scope
of this thesis.
I
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14
T IjB ijC uO j
TljBajCaCiijOg
^ B iiC iiC iijO to
Figure 1.5: Crystal structure of Tl 2Bt^C an. l Cun0 4+2n for u = 1 , 2 , and
3. M etals atom s sure shaded and C u -0 bonds are shown. (Taken from
reference 28 w ith permission of the publisher.
Copyright 1988 by the
AAAS.)
1.4
References
1. Bardeen, J.; Cooper, L. N.; and Schrieffer, J. R.: T h e o ry o f S u p e rc o n d u c tiv ity ,
Phys. Rev. 108, 1175-1204 (1957).
The Resistance o f P u re M ercu ry a t H eliu m T em peratures.
F u rth er E x p e rim e n ts W ith L iq u id H elium , Leiden Commun. 120b, 657-658
(1911); D isappearance o f th e E lectrical R esista n ce o f M ercu ry a t H elium
Tem peratures, Leiden Commun. 122b, 657-658 (1911).
2 . Onnes, H. K.:
hn
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15
3.
File, J.; and Mills, R. G.: O bservation o f P ersisten t C urrent
S u p erco n d u ctin g Solenoid, Phys. Rev. Lett. 10, 93-96 (1963).
in
4.
Meissner, W.; and Ochsenfeld, R.: Ein n euer E ffe k t bei
S u p ra leitfa b ig keit, Naturwissenschaften 21, 787-788 (1933).
5.
Bednorz, J. G.; and Mueller K. A.: P ossible H ig h -T c S u p e rc o n d u c tiv ity in the
B a-L a -C u-O S y ste m , Z. Physics B 64, 189-193 (1986).
6.
Wu, M. K.; Ashburn, J. R.; Torng, C. J.; Hor, P. H.; Meng, R. L.; Gao, L.;
Huang, Z. J.; Wang, Y. Q.; and Chu, C. W.: S u p e rco n d u c tiv ity a t 93 K
in a N ew M ixed -P hase Y -B a-C u -O C o m pound S y ste m a t A m b ie n t Pressure,
Phys. Rev. Lett. 58, 908-910 (1987).
7.
Sheng, Z. Z.; and Hermann, A. M.: B u lk S u p e rc o n d u c tiv ity a t 120 K in the
T I-C a /B a -C u rO S ystem , Nature 332, 138-139 (1988).
8.
Glover, R. E.; and Tinkham, M.: C o n d u c tiv ity o f Su p erco n d u ctin g F ilm s for
P h o to n E nergies B etw een 0.3 an d 40 K T C, Phys. Rev. 108, 243-256 (1957).
E in tr itt
a
der
9. Rugheimer, N. M.; Lehoczky, A.; and Briscoe, C. V.: M icrow ave Transm issionand-R eflection-C o efficient R a tio s o f T h in Su p erco n d u ctin g T h in F ilm s, Phys.
Rev. 154, 414-421 (1967).
10.
Lehoczky, S. L.; and Briscoe, C. V.: F lu ctu a tio n
E ffe c ts in th e ac
C o n d u c tiv ity o f T hin Superconducting L ea d F ilm s a t M icrow ave
Frequencies, Phys. Rev. B 11, 3938-3951 (1971).
11. M attis, D. C.; and Bardeen, J.: T h eo ry o f T h e A n o m a lo u s S kin E ffe c t in
N o rm a l a n d S u p erconductin g M eta ls, Phys. Rev. I l l , 412-417 (1958).
r
12 .
Sridhar, S: M icrow ave R esponse o f T h in F ilm Superconductors, J. Appl. Phys.
63, 159-166 (1988).
13.
Tarascon, J. M.; Greene, L. H.; McKinnon,
W. R.;
and Hull, G. W.;
S u p e rc o n d u c tiv ity a t 90 K in a M u ltip h a se O xide o f Y -B a-C u, Phys. Rev.
B 35, 7115-7117 (1987).
14.
G rant, P. M.; Beyers, R. B.; Engler, E. M.; Lim,G.; Parkin, S.S.P.;Ramirez,
M. L.; Lee, V. Y.; Nazzal, A.; Vazquez, J. E.;and Savoy, R.
J.:
S u p e rc o n d u c tiv ity A b o v e 90 K in th e C om p o u n d Y B a 2C u3Ox: S tru ctu ra l,
T ra n sp o rt, a n d M agnetic Properties, Phys. Rev. B 35, 7242-7244 (1987).
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.
16
15. Greedan, J. E.; O’Reilly, A. H.; and Stager, C. V.: O xygen O rdering in the
C rysta l S tru c tu re o f the 93-K Superconductor Y B a 2Cu30 7 U sing P ow der
N eu tro n D iffraction a t 298 a n d 79.5 K , Phys. Rev. B 35, 8770-8773 (1987).
16. Tarascon, J. M.; McKinnon, W. R.; Greene, L. H.; Hull, G. W.; and Vogel,
E. M.: O xygen and R are-earth D o p in g o f th e 90-K S u p erco nducting
P ero vskite Y B a 2C u30 7 x , Phys. Rev. B 36, 226-234 (1987).
17. Cava, R. J.; Batlogg, B.; Chen, C. H.; Rietman, E. A.; Zahurak, S. M.; and
Werder, D.: Single-phase 60-K B u lk Su percon ductor in A n nealed
B a 2 Y C u30 7mg (0.3 < S < 0.4 ) W ith C orrelated O xygen Vacancies in the
C urO C haiks, Phys. Rev. B. 36, 5719-5722 (1987).
18. M aeda, H.; Tanaka, Y.; Fukutomi, M.; and Asano, T.: A New H ig h -T c O xide
S u p erconductor W ith o u t a R a re E a rth E lem en t, Jpn. J. Appl. Phys. 27,
L209-L210 (1988).
19. Hanzen, R. M.; Prewitt, C. T.; Angel, R. J.; Ross, N. L.; Finger, L. W.;
Hadidiacos, C. G.; Veblen, D. R.; Heaney, P. J.; Hor, P. H.; Meng, R. L.;
Sun, Y. Y.; Wang, Y. Q.; Xue, Y. Y.; Huang, Z. J.; Gao, L.; Bechtold,
J.; and Chu, C. W.: S u p e rc o n d u c tiv ity in th e H igh-T c B i-S r-C a -C u -0
S yste m : P hase Identification, Phys. Rev. Lett. 60, 1174-1177 (1988).
20. Subramanian, M. A.; Torardi, C. C.; Calabrese, J. C.; Gopalaskrishnan, J.;
Morrissey, K. J.; Askew, T. R.; Flippen, R. B.; Chowdhry, U.; and Sleight,
A. W.: A N e w H igh-T em p erature Superconductor: B i2S r3mXCax C u2O g , y,
Science 239, 1015-1017 (1988).
Kasowski, R. V.; and Hsu, W. Y.: E lectronic S tru c tu re o f
B ijS rjC a C u jO g hig b rT c Superconductors, Phys. Rev. B 38, 204-207 (1988).
21 . Herman, F.;
L. F.; and Hamann, D. R.: E lectronic B a n d
C aSrjB igC ujO g, Phys. Rev. B 38, 5012-5015 (1988).
22 . M attheiss,
P roperties o f
23. Green, S. M.; Mei, Y.; Manzi, A. E.; Luo, H. L.; Ramesh, R.; and Thomas,
G.: E ffec ts o f C om positional
V ariations on
th e P roperties o f
S u p erco n d u ctin g (B i,P b)2Sr2Ca2Cu30 g, J. Appl. Phys. 66 , (1989).
24. Ramesh, R.; Green, S. M.; Mei, Y.; Manzi, A. E.; and Luo, H. L.:
M icro stru ctu re-p ro p erty
C orrelations
in
th e
B i(P b )-S r-C a -C u -0
S uperconducting S ystem , J. Appl. Phys. 6 6 , 1265-1272 (1989).
25. Parkin, S. S. P.; Lee, V. Y.; Engler, E. M.; Nazzal, A. I.; Huang, T. C.;
Gorman, G.; Savoy, R.; and Beyers, R.: B u lk S u p e rc o n d u c tiv ity a t 125 K
in T ljC a jB a jC u jO ^ Phys. Rev. Lett. 60, 2539-2542 (1988).
r
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.
17
26. Wu, P. T.; Liu, R. S.; Liang, J. M.; Lee, W. H.; and Chang, L.: Syn th esis,
T ra n sp o rt, M ag n etiza tio n a n d S tru ctu ra l C haracterizations o f Tl-C a-B a-C urO
S p ecim en s w ith T 0= 123 K an d T onaet= 155 K , Physica C 156, 109-112
(1988).
27. Ihara, H.; Sugise, R.; Hirabayashi, M.; Terada, N.; Jo, M.; Hayashi, K.;
Negishi, A.; Tokumoto, M.; Kimura, Y.; and Shimomura, T.: A N ew HighT c T IB a2Ca3C u4O n Superconductor w ith T c > 120 K , Nature 334, 510-511
(1988).
28. Torardi, C. C.; Subramanian, M. A.; Calabrese, J. C.; Gopalakrishnan, J.;
Morrissey, K. J.; Askew, T. R.; Flippen, R. B.; Chowdhry, U; and Sleight,
A. W.: C rysta l S tru c tu re o f T l 2B a 2Ca3C u3O10, a 125 K Superconductor,
Science 240, 631-634 (1988).
29. Hazen, R. M.; Finger, L. W.; Angel, R. J.; Prew itt, C. T.; Ross, N. L.;
Hadidiacos, C. G.; Heaney, P. J.; Veblen, D. R.; Sheng, Z. Z.; El Ali, A.;
and Hermann, A. M.: 100-K Superco n d u ctin g P hases in th e T l-C a-B a-C u-O
S y ste m , Phys. Rev. Lett. 60, 1657-1660 (1988).
30. Ginley, D. S.; Morosin, B.; Baughman, R. J.; Schirber, E. L., and Kwak, J.
F.: G row th o f C rystals and E ffects o f O xygen A n n ea lin g in th e Bi-Ca-SrC u - 0 a n d Tl-C arB arC u-O Superconductor S y stem s, J. Cryst. Growth 91,
466-470 (1988).
31. Ianno, N. (Private communication).
I
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Chapter 2
Theoretical Considerations
2.1
Introduction
In this chapter we discuss the theory of the microwave interactions with
superconductors.
We begin the chapter w ith a brief description of the two-fluid
model, followed by a short presentation of the BCS theory.
The surface
impedance of a superconductor is discussed, w ith emphasis on the relationship
between the surface resistance (Rs) and the complex conductivity (a* =
- j a 2)-
W ith the exception of some data discussed in chapter 5, all the experimental
d a ta gathered for this study were obtained by measuring the microwave power
transm itted through a thin fllm-substrate combination.
We therefore discuss the
problem of a normally incident plane wave propagating through a thin film on a
dielectric.
From this analysis we obtained expressions for the real and imaginary
parts of the complex conductivity in terms of the magnitude and phase of the
microwave transm itted power.
An alternate ” semi-empirical” method for the
calculation of the conductivity based on the two-fluid model and on the magnitude
of the transm itted power is also discussed.
The chapter ends with a brief
discussion of the determination of the microwave surface reactance (Xg) of a film
in the superconducting state from microwave power
t r a n s m is s io n
measurements.
18
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19
For the analysis of HTS thin films we have used the standard electromagnetic
theory of conduction through a dissipative media (section 2.4) and techniques
implemented
by
superconductors.
others 1’2 (sections
2.6
and
2.7)
for
the
study
of low-Tc
Our contribution has been the formulation and solution of the
problem of microwave transmission through HTS thin films discussed in section 2.5.
2.2
The Two-Fluid Model
In the two-fluid model the superconducting system is assumed to consist of a
fluid of superconducting electrons intermingled but not interacting w ith the fluid
of normal electrons.
The most successful of the two-fluid theories was that
developed by Gorter and Casimir in 1934.3 The basic assumption of this theory
is th a t the superfluid fraction (ng/N ) varies from one a t T = 0 to zero a t T = T C,
where T c is the tem perature of transition to the superconducting state.
The best
agreement with the therm al properties of superconductors was obtained when the
fraction ng/N obeyed the relation
n„/N = 1 - (T /T c) 4
(2.2.1)
When an electromagnetic field is applied to a superconductor, the total current
density associated with the field is the sum of the current densities corresponding
to the normal and superconducting fluids, and is given by
r
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20
J = JN + Jg = - (npjevj^ + ngevg)
where
vN and
vs
are
the
average
drift
(2.2.2)
velocities
for
the
normal
and
superconducting electrons, -e is the electron charge, and nN and ns are the
densities of normal and superconducting electrons, respectively.
Then, using the
equation of motion for the normal and the superconducting electrons with an
electric field of the form & a e]a;t, the total current can be expressed in terms
of a
as
J = JN + Jg = nNe 2rE /m (l + u^r2) - j[n ge2/mw + nNe 2(wr)2/m a;(l + w2 r2)]E
= <x*E
= K
- j* 2)E
(2-2.3)
where r is the mean carrier scattering time for normal electrons.
real p art of a
Note th a t the
involves only the normal electrons, while its ima ginary part
includes contributions from both the normal and the superconducting electrons.
For frequencies below lxlO 11 Hz, we have th at uit «
1 (in general r~ 1 0 ' 13-10' 15
seconds) and, therefore,
a
= nNe 2r/m - jn ge2/mw
= <rN(T /T c) 4 - jffN( l - ( T /T c)4)/w r
r
(2.2.4)
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21
where equation (2.2.1) and <7^ = Ne2r/m , where
is the conductivity in the
normal state, have been used.
We discussed in the previous chapter th at an oscillating magnetic field B(w)
parallel to the surface of a superconductor in its superconducting state decays
exponentially in the m aterial with a characteristic penetration depth A.
The
tem perature dependence of A according to the two-fluid model is given by
A = A0 [ l - ( T /T c)4] 1/2
where A0 = (m /p 0 Ne2) ,/4 is the zero tem perature penetration depth.
(2.2.5)
Observe th at
the penetration depth goes to infinity as the tem perature approaches the transition
tem perature T c, and th a t most of the change in A takes place in the tem perature
range 0.5 < T /T c < 1 .
Using equation (2.2.4), A can be expressed in terms of
«t2 as
A = (1/Mo^ ) 1/ 2
(2.2.6)
2.3 BCS Theory
The BCS theory of Bardeen, Cooper, and Schrieffer4 provided a more rigorous
description of superconductivity than the phenomenological two-fluid model.
This
microscopic theory of superconductivity suggests th at in a superconducting material
attractive forces between the electrons exist in addition to the Coulomb repulsion.
r
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22
An attraction arises from a virtual phonon exchange, producing pairs of electrons
called Cooper pairs.
The average separation distance between the electrons of a
pair is called the coherence length (£0), which for pure low-Tc superconductors is
~ 3000 A.
One of the major predictions of the BCS theory is the existence of an energy
gap (Eg = 2A(T)) in the energy spectrum, which implies th at a minimum energy
of 2A(T) is required to split the pair into two quasiparticie excitations.
The half­
gap A(T) has a value of zero a t T c and increases with decreasing tem perature
reaching a value of
2A(0) = 3.528kBT c
(2.3.1)
at absolute zero.
M attis and Bardeen 5 obtained an expression for the conductivity which can be
presented in a simple way only in limiting cases. For hw < < 2A, the real part
of the complex conductivity is given by 6
° l = <TN2A(kBT)"^exp(-A/kBT)ln(A/W )
(2.3.2)
where <7^ is the normal microwave conductivity, kB is the Boltzmann constant,
and w is the angular frequency.
In this limit <x2 is given by <r2 = ( 1/ a 0wA2),
which agrees with equation (2 . 2 .6 ).
F
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23
2.4 Surface Impedance
For any conductor, there is a direct relationship between the ac conductivity
and its surface impedance.
The surface impedance of a conductor can be defined
in terms of the interaction between the conductor and any electromagnetic
radiation incident upon it.
Consider a plane electromagnetic wave of frequency w
propagating through a vacuum in such a way th at it is normally incident on a
conductor.
The power involved in the interaction between the radiation and the
conductor can be expressed in terms of the tangential magnetic field strength (Bt)
a t the surface of the conductor and the real and imaginary parts of the surface
impedance Zg= R g+ jX g, as follows,
Pab. = (2/i0) ' 1/ SBt 2RsdS
(2.4.1)
Preac = W
(2.4.2)
' ! a * ? * ,* *
In the above equations, Rs and Xg are the surface resistance and the surface
reactance of the conductor, respectively, and the integration is over the surface of
the conductor.
Note that P at,g, the power absorbed by the conductor from the
incident radiation, is determined by Rg.
Similarly, P reac, which is the rate at
which energy is exchanged between the conductor and the radiation ,7 is determined
by Xg. For a superconducting m aterial, it will remain in its superconducting state
if the incident radiation energy hw is less than twice the energy gap (i.e.,
hw<2A).
However,
absorption
is
still
possible
due
to
the
excitation
b
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of
24
quasiparticles a t finite tem peratures, and this determines the surface resistance Rg.
Also, due to the Meissner effect surface currents are generated which cause the
field
to
decay
exponentially
penetration depth
A.
inside
the
superconductor
with
characteristic
The effectiveness of this shielding effect is directly related
with the surface reactance Xg of the superconductor.
The surface impedance of a conductor is im portant because the propagation
properties of transmission lines and the quality factor Q
of resonant cavities and
microstrip circuits are strongly dependent on the surface impedance of the primary
conducting medium forming the propagation structures.
For a good conductor the
surface impedance is given by
z , = O /*0/ * ) 1/2
(2-4-3)
For the case of a superconductor a is complex, and therefore Rg can be expressed
in terms of
K. =
r n
and <r2 " i
[ { [ ( < ' i /< ' n ) 2 +
(V »
n)
T ' S - (■’ J/<’ n ) } / [ K / ' ’ n ) 2 +
K /«
n ) 21
] ‘ /J
(2.4.4)
where RN=("#*o/2 <rN) 1/2 is the surface resistance a t T c. In the limit where <r2 >>
a i (typically, a t low tem peratures compared with T c and for hw < < ^B^c)’ fc^e
surface resistance is approximately,
t
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25
Rs ~ R N(ffl / ff2)(<rN /<T2)1/2 = V ^ M o ) 2*3* !
where the relation <72= (l//x 0wA2) has been used.
(2.4.5)
Note th at in this limit the Rg
of a superconductor increases as the square of the frequency while for normal
conductors the losses increase ju st as the square root of the frequency.
Equation (2.4.5) agrees with experimental results within 30% for low-Tc
superconductors (for example within ~ 5% for Sn) when the BCS expression for
(see equation 2.3.2) is used in equation (2.4.5 ).8
2.5
Plane Wave Propagating Through a Thin
Film on a Dielectric Substrate
Consider a film of thickness d, on a substrate of thickness t and refractive
index n, and
covering the entire cross section of a rectangular waveguide
propagating the T E 10 mode as shown in Fig. 2 . 1 .
Then, for a uniform plane
microwave normally incident on the film and propagating in the z direction, the
wave functions associated with the incident, reflected and transm itted microwaves
in the different propagation regions illustrated in Fig. 2.1 are given by,
= v k*
,
w = V 'jk*
= V Qk‘
,
if>2 = A2e-j“k*
i>3 = A3ei"k*
,
^ = A4e"jnk*
K
= Atreik»
i
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26
where k= 2x/A s and Ag=A[l - (fc/f ) 2]-1^* are the free space wave number and the
wavelength,
respectively,
of
the
microwave
signal
propagating
through
the
rectangular waveguide, f its frequency, and fc the cutoff frequency of the
rectangular waveguide (which in this study is 21.1 GHz).
K
OK
%
We are interested in
nK
*1
tr
Yr
>2
I
II
z=o
\
IV
III
Z=d
Z=d+t
Figure 2 . 1 : Normally incident plane microwave propagating through a thin
film deposited onto a dielectric substrate. Regions I and IV represent the
free space circumscribed by the waveguide, region II represents the film of
thickness d and complex dispersion coefficient a , and region III represents
the dielectric substrate of thickness t and refractive index n.
the m agnitude (T) and phase (0) of the transm itted signal in region IV with
respect to the incident signal in region I.
The boundary conditions of the problem
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27
require th at the wave function $ and its first derivative d 0 /d z be continuous a t
z=0, z= d, and z = d + t, where i> in each of the regions I, II, and III is the sum
of the right-going and left-going wave.
Applying these boundary conditions, we
obtain
Aj + Aj = Atfe^kt [cos(knt) - (j/n)sin(knt)]
(2.5.1)
and
Aj - Ay = Atre*kt [cos(knt) - jnsin(knt)]
- j a 2kdAtre*kt[cos(knt) - Q /n)sin(knt)j
(2.5.2)
In deriving these relations we have assumed th a t d is sufficiently small compared
to Ag so th at we can make the following approximations:
<Jkd = e*nkd = 1
e± ja k d =
l ± ja k d
k
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28
For the typical film thicknesses (d<0.6xl0 ’6 m) and frequencies (f~30 GHz) used
in this study, kd = (2x/Ag)d = 2.7xl0'4.
All the relevant information about the properties of the film which can be
obtained from these measurements is present in the term a 2kd in equation (2.5.2).
In order to express this quantity in terms of the properties of the transm itted
wave (amplitude and phase relative to those of the incident wave), one adds
equation (2.5.1) and (2.5.2). Adding and rearranging gives,
2Aji
r
^ 2cos(knt) - j(n + l/n)sin(knt)
- j a 2kd[cos(knt) - (j/n)sin(knt)] ^
(2.5.3)
Atr/A ; is a complex number th at can be expressed in terms of its magnitude and
phase as,
Atr/Aj = T ,/4e ^ = T ^ -^ c o sfl + jsintf}
(2.5.4)
where T and 9, the magnitude and phase of transm itted wave relative to the
incident wave, respectively, are the quantities which we measured.
Substituting
expression (2.5.4) for Atr/A j into equation (2.5.3), and solving for a 2kd, we obtain
)
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29
(2n/T 1|/2)e*j^ + kt) - 2ncos(knt) -t- i(n_2 + l).9in(knt)
a kd = -------------------------------------------------------------------------------- j[ncos(knt) - jsin(knt)]
(2.5.5)
W riting a 2 as R + jl, we can express R and I in terms of the real and imaginary
parts of the complex conductivity using standard theory for electromagnetic waves
in a conducting media,9
R =
[ 1 + 4™ a/ « « ] [ l - (fc/f ) 2] 1 ,
I = [toffj/w e] [l - (fc/ f )2] _1
(2.5.6)
In the above equation, w= 2 xf, and the factor [1 - (fc/ f ) 2]-1 is introduced to
account for the difference between A and Ag.
Solving equation (2.5.5) for the real
and imaginary parts of a 2, we obtain our working equations,
R =
^ (2 n /T 1^2) [ncos(knt)sin(kt + 0)
-
sin(knt)cos(kt + 0)]
- n(n 2 - l)sin(knt)cos(knt) ^ j kd[n 2cos2(knt) + sin 2(knt)]
I =
(2.5.7)
(2 n /T 1^2) [ncos(knt)cos(kt + 0) + sin(knt)sin(kt + 0)]
- 2n 2cos2(knt) - (n 2 + l)sin 2(knt) ^ j kd[n 2cos 2(knt) + sin 2(knt)]
(2.5.8)
ft
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30
2.6
Determination of Complex Conductivity:
Two-Fluid Model Approximation
Glover and Tinkham 1 combined the power transmission d a ta through thin Pb
films in the microwave and infrared frequency ranges with the two-fluid model to
determine a
for these films.
Later, the two-fluid model was applied successfully
in the microwave characterization of metallic superconductors for hu < < E gap. 10
Since the energy gap for the superconducting copper oxides is in the terahertz
range ( ~ 12 THz, for T c = 92 K), and since so far no theory has been accepted
as fully describing the superconducting state in the HTS m aterials, we have applied
the method used by Glover and Tinkham for the analysis of HTS thin films.
This m ethod allows a determination of the real microwave conductivity in the
normal state <r^ and of a
in the superconducting state, by measuring the
microwave power transm itted through the film-substrate combination.
We now
proceed to describe the method.
The microwave power transm itted through the sample is given by,
8n 2
T = ---------------------------------------------A + Bcos(2 kt)
Csin(2kt)
where k = 2 xn/A
( 2 .6 . 1)
is the wave number, and
A = n 4 + 6 n 2 + 1 + 2(3n 2 + l)g + (n 2 + l)(b 2 + g2)
(2.6.2.a)
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31
B = 2(n 2 - l)g - (n 2 - l ) 2 + (n 2 - l)(b 2 + g2)
( 2 .6 .2 .b)
C = 2(n 2 - l)nb
( 2 .6 .2 .c)
In the above equations, y = g -jb = YZC =
- j<72)dZc, is the dimensionless
complex adm ittance per square of the film, and Zc is the characteristic impedance
of the wave guide ( z c = ZQ[l - (fc/f ) 2] 1^2, and ZQ is the impedance of free
sp ace).
In the normal state
*<rN and <r2—*-0 , and equation (2 .6 . 1 ) becomes,
8n
T n = ------------((fj^dZ ) Q + ffpjdZ R + P
,
x
(2.6.3)
where
Q = (n 2 + 1) + (n 2 - l)cos(2kt)
(2.6.4.a)
R = 2(3n 2 + 1) + 2 (n 2 - l)cos( 2 kt)
(2.6.4.b)
P =
(2.6.4.c)
n 4 + 6 n 2 + 1 - (n 2 - l ) 2cos( 2 kt)
The normal state conductivity of the film can be expressed conveniently in terms
of the power transmission as
_ - R T n ± [(R Th )» - 4QTN(P T „ - 8n2) ] 1/3
N
‘
’
ft
ft
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32
where only the expression with the + sign has physical relevance.
It is convenient
to use the ratio of T g/ T N in the analysis of the superconducting state, where T g
refers to the power transmission in the superconducting state and is given by
equation (2 .6 . 1).
Ts
Hence,
(<TjjdZc)^Q +
+ P
( 2 .6 . 6 )
Tn
A + Bcos(2kt) + Csin(2kt)
Solving (2.6.6) for the imaginary part of the conductivity gives
V 'c
=
{ - 0 ( 2 'cd Zc ^
+ {(<rcdZc)-2[(/J/2 )2 - t] - v a ^ d Z J 1
- K / a c)2 + (Tc/ T g) [l + a(ercdZ c)-1 + ^ d Z J 2} } 1/2}
(2.6.7)
where <rc and T c are the conductivity and the transmissivity a t T = T C, « = R /Q ,
7 = P /Q , and /9=[-2n(n 2 - l)sin(2kt)]/Q . Thus, from the expression for (rx given in
equation (2.4.4), and equations (2.6.5), and (2.6.7) the microwave conductivity of
the films in both the normal and the superconducting states can be determined.
2.7
Surface Reactance
The microwave power transm itted through the high-Tc superconducting thin
films considered in this study can be used to determine their surface reactance, Xs.
k
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33
This param eter is related to the magnetic penetration depth A, which measures the
distance a magnetic field can penetrate into the superconducting material.
Sridhar
was the first to use the microwave power transm itted through thin
Sn films, placed a t one of the end walls of a cylindrical copper cavity, to
determine Xg as a function of tem perature.
Since we were able to measure the
transm itted microwave power directly, we have followed Sridhar’s method for
obtaining Xg. We proceed now to discuss this method.
The microwave power absorbed in the film (Pabs) and the microwave power
transm itted through the film (PtT,„ ,) are given by,
P aba = R 3H( 0 )2/2
(2.7.1)
Ptrans = W ) 8^
(2.7.2)
where Rg is the surface resistance of the film, H(0) is the magnetic field at the
film surface, H(d) is the magnetic field a t the substrate, and ZQ is the impedance
of the substrate.
The impedances of the film (Zf) and the substrates (Z0) can be
defined as,
Zf = Rg + jX g = E(0)/H (0)
(2.7.3)
Z0 = E(d)/H (d)
(2.7.4)
\
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34
where E(0) is the electric field a t the film surface and E(d) is the electric field
at the substrate.
Thus,
P trans = ( V
+ Xg2) jE (d)/E (0) j2 |H(0) | 2/(2Z„)
(2.7.5)
Using the expression for the magnetic field th a t satisfies the boundary conditions
for this case (see figure 2.1), B(z)=B(0)sinh(d-z/A)/sinh(d/A), and Maxwell’s
equations, one can show th at the electric field a t z=d is E (d )/E (0 )~ l/co sh (d /A ),
where A is the magnetic penetration depth.
In the normal state, A—
t he normal
state skin depth, and therefore cosh(d/A)—>1; also for thin films RN> > X N, where
Rn and XN are the surface resistance and reactance, respectively, in the normal
state.
Hence, the power transm itted in the normal state is,
pNtran. =
| H(0) 12RN2/(2Z 0)
(2.7.6)
On the other hand, in the superconducting state the reactance of the film becomes
very large while the absorption in the film becomes very small (i.e., Xg> > R g);
then, at temperatures below but not near T„C (since
near T„C the relation X8.> > R .§
'
does not hold), we have
pStran. = Xg2[l/cosh(d/A )]2 |H(0) | 2/ ( 2 Z Q)
(2.7.7)
II?
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35
Combining (2.7.6) and (2.7.7) one obtains an expression for the surface reactance
Xs in terms
of the transm itted
microwave power in the normal and the
superconducting state,
Xg = fi*cosh(d/A) | P straM/ P Ntran, | W
(2.7.8)
where R N is the normal state surface resistance a t T = T C.
2.8
References
1.
Glover III, R. E.; and Tinkham, M.: C o n d u c tiv ity o f S u p erco n d u ctin g F ilm s
fo r P h o to n Energies B etw een 0.3 and 40 K g T c, Phys. Rev. 108, 243-256
(1957).
2.
Sridhar, S: Microwave R esponse o f T h in -F ilm Superconductors, J. Appl. Phys.
63, 159-166, (1988).
3.
Gorter, J. C.; and Casimir, H. B. G.: T h e th erm o d yn a m ics
Su p erco n d u ctin g S ta te , Physik. Z. 35, 963-966 (1934).
4.
Bardeen, J.; Cooper, L. N.; and Schrieffer, J. R.: T h eo ry o f S u p erco n d u ctivity,
Phys. Rev. 108, 1175-1204 (1957).
o f th e
5. M attis, D. C.; and Bardeen, J.: T h eo ry o f th e A n o m a lo u s Skin E ffect in
N orm al a n d S uperconductin g M etals, Phys. Rev. I l l , 412-417 (1958).
6.
Hinken, J. H.: Superconductor Electronics: F u n d a m en ta ls
A p p lica tio n s, 23 (Springer-Verlag, New York, 1989).
and M icrow ave
7. Sridhar, S.: M icrow ave D yn am ics o f Q uasiparticles and C ritical Fields in
Su p erco n d u ctin g F ilm s, Ph.D. thesis, California Institute of Technology,
(1983).
8. Halbritter, J.: Com parison B etw een M easured and C alculated R F Losses in the
Su p erco n d u ctin g S ta te , Z. Physik 238, 466-476 (1970).
k
R eproduced w ith perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
36
9. Jackson, J. D.: Classical E lectrod ynam ics, Sec. Ed., 296 (John Wiley and Sons,
Inc., New York, 1975).
10. Gittlem an, J. I.; and Rosemblum, B.: M icrow ave P roperties o f Superconductors,
IEEE Proc. 52, 1138-1147 (1964).
r
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Chapter 3
Microwave Transmission
Measurements
3.1
Introduction
The high transition tem perature superconducting (HTS) thin films analyzed in
this
study
were
prepared
by
several
researchers
using
different
deposition
techniques, including laser ablation, co-evaporation, and dc off-axis magnetron
sputtering.
A brief description of all the deposition techniques used is given in
appendix A.
resistance
O ther groups have also extensively characterized the films using dc
versus
tem perature
measurements,
Scanning Electron Microscopy (SEM).
X-ray
diffraction
analysis,
and
The details and results are summarized in
appendix B.
The main source of experimental data upon which the analysis and conclusions
of this thesis are based were the measurements of the transm itted microwave
power.
It was found th at for the film thickness used in this study (~ 800 to
6000 A), and for the maximum power levels available (~ 16 mW ), the m a x i m u m
observed change in the reflected power on cooling the film through its transition
tem perature was approximately 20 times the noise power.
However, we did not
use the fractional reflection coefficient d ata for our analysis because it has been
shown th at it is less sensitive to changes in the real and imaginary parts of the
37
h
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38
complex conductivity (<r = <r1-j<r2) than the transmission coefficient.1 Furthermore,
we found th at it was more difficult to account for systematic errors (such as linear
contractions of the waveguides network components while cooling the system) in
the reflection d a ta than in the transmission data.
Similar observations were made
earlier by other researchers who measured the transm itted and reflected microwave
power of low-Tc superconducting thin films (~ 20 to 150 A).1,2 These researchers
found th at the fractional change in the reflected power on cooling a film from the
normal to the superconducting state is larger for thinner films than for thicker
ones.
However, we have not examined thinner films since good HTS films of
o
_
thickness less than 500 A are difficult to obtain.
The deposition factors affecting
the quality of HTS thin films have been discussed by others.3
3.2
Measurement Apparatus and Procedures
A schematic of the configuration used to measured the microwave power
transm itted through the HTS thin films is shown in figure 3.1.
The main
components of the experimental apparatus are a HP-8510B autom atic network
analyzer, a closed cycle helium gas refrigerator, and a tem perature controller
(LakeShore Cryotronics, model DRC 91C), which are controlled by a HP 9000-216
computer.
The network analyzer is coupled to the refrigerator by Ka-frequency
band (26.5 to 40.0 GHz) rectangular waveguides.
The measurement technique is
based on comparing the reflected and the transm itted signals against the incident
F
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3
■
—E o m
HP directional
coupler model
R752D
model 2518A
39
as
ills
X a o
ip
helium gas
closed cycle
refrigerator
1 |2
g^a
? S o
I <n
HP directional
coupler model
R752D zone line
I 3
3 s
CM
Isolator
HPR36SA
X «
HP directional
coupler model
R752D
IEEE Dala bus
X ca c\i
31
Figure 3.1: Microwave measurements apparatus.
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40
microwave signal produced by a 0.01 to 20 GHz synthesized sweeper whose output
is doubled to the Ka-frequency band.
Through the use of a directional coupler
the incoming signal is divided, with part of it directed toward a mixer and used
as a reference signal and the rest of the signal directed toward the sample.
A
second directional coupler is used to direct a portion of the signal reflected from
the sample to a second mixer.
The fraction of the original signal which is
transm itted through the sample is also directed to a third mixer by means of a
directional coupler.
A 0.01 to 26.5 GHz synthesized sweeper is used as a local
oscillator to feed the three mixers.
The intermediate frequency signals from these
mixers are fed into the network analyzer.
The network analyzer compares the
power and phase of the reflected and transm itted signals with th at of the reference
signal to determine the reflection and transmission coefficients. The data measured
in this way are then stored by the computer for subsequent analysis.
All the measurements were performed under vacuum (usually less than 10
m torr), in a custom made aluminum vacuum chamber designed to fit on top of
the external shield of the refrigerator and to give access to the set up of
waveguides connecting the network analyzer with the refrigerator.
In order to
preserve the vacuum, natural mica windows were used a t the coupling points
between the external waveguides and the waveguides inside the chamber.
Mica
was selected for the windows because of its very low loss, thermally stable relative
dielectric constant, and its transparency to microwave signals in the tem perature
and frequency ranges considered in this study.
Inside the vacuum chamber the
sample was oriented perpendicular to the microwave source by clamping it between
I
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41
two waveguide flanges thermally connected to the cold head of the refrigerator
through a copper plate.
A thin layer of In was used between the holding flange
and the film in order to improve both therm al and electrical contact between
them.
The film side of the sample was directed toward the incident microwave
signal, as show by the schematic in figure 3.2.
The system was calibrated before
the beginning of each measurement cycle. The calibration was performed using the
Hewlett Packard WR-28 Calibration Standards Kit R11644A consisting of a thru,
a short circuit, a shielded open circuit, and loads which provides corrected
transmission and reflection measurements.
THIN
According to Hewlett Packard,4
SUBSTRATE 7
FILM-7
/
/
//
/
/
Figure 3.2: Side view of a rectangular waveguide propagating the TEQ1
mode with its entire cross section covered by a high-Tc superconducting
thin film of thickness d deposited on a dielectric substrate of thickness t
and refractive index n. In this work I ~ 16 m W /cm 2, d ~ 2000 A, t ~
5.0 x 10*2 cm, and 10'6 < T / I ■< 10"1.
*
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the
42
measurement repeatability (sweep-to-sweep) using a through or short as the device
under test is within 0.005 dB for the magnitude and 0.5 degrees for the phase of
the transm itted and reflected signals.
The noise level for our measurements was
determined to be below -60 dB after the calibration.
Corrections for background
attenuation and phase, obtained by measuring the transm itted power as a function
of tem perature in the absence of the sample, were made by subtracting this
contribution from the d a ta obtained with the sample in place.
Measurements
made with the bare substrates were used to determine any tem perature dependence
of their dielectric constant.
Results of these measurements are given in Refs. 5
and 6.
The
microwave
power
transmission coefficient T
was
measured
with
a
repeatability of ± 5% over the entire tem perature range. This error was estimated
by measuring several samples repeatedly, with the samples being removed and
replaced between each set of measurements.
A run started a t room tem perature,
with measurements taken during cooling.
The tem perature of the film was
measured by two silicon diodes (LakeShore Cryotronics, model DT-470-LR-13),
which were placed in a 1/8 inch diameter hole on top of each of the sample’s
supporting flanges.
The accuracy of these diodes is ± 1.0 K from 1.4 to 100 K,
and 1% of the actual tem perature in the range from 100 to 325 K.
The
difference in the tem perature readings of the two sensors was less than 0.2 K over
the entire tem perature range. An additional sensor was located next to the heater
on the cold head of the refrigerator and was used to control the tem perature of
the cold head.
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43
To determine if there were any effects due to a therm al gradient between the
sample and the tem perature sensors, the tem perature dependence of the power
transmission coefficient was measured for a few samples during cooling and also
while warming to tem peratures above T“ w.
It was found th a t the maximum
difference in the measured power at a given tem perature for the two measurements
was less than 6%, and typically was less than 3%.
This difference was in the
sense expected from a tem perature gradient, but can be neglected for the purposes
of this study.
To investigate any possible warming of the sample as a result of the incident
microwave power ( ~ 16 m W ), power transmission measurements were performed
a t other incident power levels (1.0 mW and 0.1 mW ).
Since no shift of the T“ w
within a resolution of 0.5 K was observed for the different power levels employed,
we concluded th a t any change in the tem perature of the film due to absorbed
microwave power can be neglected.
3.3
References
1. Lehoczky, S. L.; and Briscoe, C. V.: F luctu atio n E ffects in th e ac C o n d u c tiv ity
o f th in Su p erco n d u ctin g L ead F ilm s a t M icrow ave Frequencies, Phys. Rev.
B 11, 3938-3951 (1971).
2.
Rugheimer, N. M.; Lehoczky, A.; and Briscoe, C. V.: M icrow ave Transm issionand-reflection-coefficient R a tio s o f T h in Su p erco n d u ctin g film s, Phys. Rev.
154, 414-421 (1967).
3.
Venkatesan, T.; Wu, X. D.; D utta, B.; Inam, A.; Hedge, M. S.; Hwang, D.
M.; Chang, C. C.; Nazar, L.; and Wikens, B.: H igh-T em perature
S u p erc o n d u ctiv ity in U ltrathin F ilm s o f Y B a 2Cu30 7mX, Appl. Phys. Lett. 54,
581-583 (1989).
I
R eproduced w ith perm ission o f the copyright owner. F urth er reproduction prohibited w itho ut perm ission.
44
4.
Hewlett Packard: M illim eter-w a ve V ector M ea su rem en ts U sing the H P 8510A
N e tw o rk A nalyzer: P ro d u ct N o te no. 8510-1, 10 (1984).
5.
M iranda, F. A.; Gordon, W. L; Heinen, V. O.; Ebihara, B. T.; and Bhasin,
K. B.: M ea su rem en ts o f C o m p lex P e r m ittiv ity o f M icrow ave S u b stra tes in
th e 20 to 300 K T em p era tu re R a n g e F rom 26.5 to 4 0 .0 G H z, Advances in
Cryogenic Engineering 35, Plenum Publishing Corporation, 1593-1599 (1990).
6.
M iranda, F. A.; Gordon, W. L.; Bhasin, K. B.; Ebihara, B. T.; Heinen, V.
O.; and Chorey, C. M.: C o m plex P e r m ittiv ity o f L a n th a n u m A lu m in a te in
th e 20 to 300 K T em p era tu re R a n g e F rom 26.5 to 40.0 G H z, Microwave
Opt. Tech. Lett. 3, 11-13 (1990).
R eproduced w ith perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
Chapter 4
Results and Discussion
4.1
Introduction
In this chapter we present the results of the interaction of microwaves with
YBa2Cu20 7.£, Bi-Sr-Ca-Cu-O, and Tl-Ba-Ca-Cu-0 superconducting thin films, as
studied by performing power transmission measurements.
While resonant cavity
measurements are limited to the determination of the surface resistance (Rg), and
in some cases a relative measurement of the penetration depth (A), the power
transmission technique allows the determination of A and the complex conductivity
(a
= tr1 - ja 2), from which the Rg can be directly
calculated. Furtherm ore, since
it has been suggested th a t the loss mechanisms are due
to the entire film and not
just the surface of the film,1 this technique is appropriate to study the effect of
the loss mechanisms on the microwave properties due to the entire film.
We have been able to obtain values for A, particularly for the YBa2C u30 7 ^
thin films, which are in good agreement with the best values reported so far for
single crystals and high quality c-axis oriented thin films.
In addition, the
anisotropy of A was also observed by measuring this param eter in c-axis and a-axis
oriented films.
However, our principal achievement consists in having been able
to use the film thickness dependence of A to estim ate the intrinsic value of A for
the YBa2Cu30 7.^ superconductor.
This intrinsic value of A, which is the value
expected in the absence of grain boundary effects and other non-superconducting
45
I
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46
inhomogeneities, was obtained by extrapolating
dependence of A to zero.
the
values of the thickness
To the best of our knowledge, this is the first time
th a t such a value of A is reported for any of the HTS superconductors.
In general, a HTS thin film is considered a ’’good” film if it has a transition
tem perature (T^c) of at least 90 K for YBa2Cu30 7.^ films, of 105 K for the highT c phase and 80 K for the low-Tc phase of Bi-based films, and > 120 K for Tlbased films.
For a HTS thin film to be suitable for microwave applications, the
most im portant property is an Rs lower than th a t of good conductors such as Cu
and Au, a t tem peratures < 80 K.
In addition, the film m ust have a zero field
critical current density greater than 1 x 10s A /cm 2 a t 77 K.
Good films must
also have an in-plane A of ~ 1400 A, which to date is the best reported value.2,3
Finally, the ratio of <r1/<r2 m ust be very small for the film (for example, <r1/«r2
< 10'2) a t tem peratures < 80 K.
We begin the chapter with the results for the Y B a jC u jO ^ HTS thin films,
which was the system in which most of our work was done.
This system is
im portant for microwave applications because of the easiness of single-phase
fabrication, the dem onstrated low Rg values for thin films a t 77 K (best value so
far, ~ 8 mil at 87 GHz),4 and high zero-field critical current density in these
films a t 77 K (Jc > 1 x 106 A /cm 2).5
Bi-based and Tl-based thin films.
We then present similar results for the
The chapter ends with a comparison of the
microwave properties of the three HTS materials.
*n
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47
4.2
In
YB2Cu30 7_^ Thin Films
this
section we discuss
the
results
of the
microwave-superconductor
interaction following the analysis presented in section 2.5.
This allowed us to
calculate transport param eters such as the magnetic penetration depth (A), the
complex conductivity (a ), and the surface impedance (Zg = Rg - jX g), which are
of great importance for microwave applications. The analysis performed, and the
results obtained from our study of HTS YBa2Cu30 7)j thin films are now discussed.
4.2.1
Microwave Transmitted Power
The magnitude (T) and phase shift (9) of the microwave transm itted power
for the different YBa2Cu30 7_$ superconducting thin films were measured with
decreasing tem perature.
The films (828 to 10 000 A thick) were deposited onto
LaA103, MgO, YSZ, and LaGaO^ substrates by sequential evaporation, laser
ablation,
and
dc
magnetron sputtering
tem perature of all the
(see appendix
A).
The
films was determined by dc-resistance
transition
(R<jc) versus
tem perature measurements (hereinafter called T^c) as described in appendix B, and
by microwave power transmission measurements. Using the microwave transmission
measurements, we defined T™w as the tem perature just above th a t a t which
d T /d T changed by more than 5% from its normal state value.
value agreed well with
In general this
the onset tem perature obtained by the
R dc versus
tem perature measurements, with T^c a few degrees lower than T“ w.
However, it
was found th at for some samples the T^c values varied by a few degrees as a
hR eproduced with perm ission o f the copyright owner.
F urth er reproduction prohibited w ith o u t perm ission.
48
function of contact position across the film, a fact that may be explained in terms
of the different paths th at the current can take between the various current
contacts.
Therefore, due to the advantage provided by the microwave technique
employed to measure the transm itted power in which basically the whole sample,
within the limits of the magnetic penetration depth, can be probed, we consider
T™w as the more representative value of the superconducting transition tem perature
of the sample.
The T™w and other transport param eters for these films
determined from microwave measurements are summarized in table 4.1.
In general, the tem perature dependence of T and 9 was similar for all the
films.
However, there were appreciable differences in the microwave power
transm itted through the films mainly because of differences in their m aterial
composition and quality.
In fact, for sequentially evaporated films the transm itted
power and the calculated conductivity data showed th at these films were of such
poor quality (<72 a t 70 K more than an order of magnitude lower than th at for
laser ablated films)6 th at no further analysis was performed on this type of film.
The metallic character of the films is evidenced by the positive slope of T for
T > T™w (see figure 4.1).
At T™w, the transm itted power decreased abruptly
and kept falling with decreasing tem perature, leveling off a t low temperatures.
It
was observed th at the value of T™w, the abruptness of the transition a t T “ w, and
the tem perature at which the power started to level off were closely related to the
film quality, as determined by the values of Rg, A, and <
jv
Films th at exhibited
a sharp transition in the microwave power transmission attenuation, with a leveling
\
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
swr*
TABLE 4.1
Microwave Measured Parameters of YBCO Superconducting Filins
S.N.
SU B ST R A T E . D.M.
LA
d(A )
T™W(K)
Rf}w( n )
/>^^(/l n -c ^ ,)
^NW(#*m )
* (A )
Rs*"(m n )
4900
90.8
0.68
379
5.57
7.8
29 0 7 7
800
92
0.37
111
3.02
26.5
45 0 7 7
1
L aA I0 3
2
YSZ
3
L a A lO j
LA
2400
9 1 .6
0.51
216
4.24
13.6
3.3 0 8 0
4
L aA 103
LA
1769
91.7
0.58
274
4.72
10.7
32 ©77
5
L a A lO j
LA
828
9 2.5
0.61
313
5.12
9.4
112 © 77
6
L aA 1 0 3
LA
1762
9 4 .0
0 .96
758
7.89
3.9
566 0 7 7
7
M gO
1000
9 4 .0
0.67
373
5.57
7.9
1 5 .3 0 7 7
8
L aG aO j
LA
4000
94 .0
0.95
752
7.91
3.9
13 © 77
9
L aA 103
LA
1000
8 8.6
0 .45
164
3.66
17.9
43 ©77
10
M gO
LA
3500
9 3.2
0 .7 0
408
5.83
7.2
86 © 77
11
L a A lO j
2600
9 3 .6
0 .52
222
4.26
13.2
6 .9 © 77
12
L aA 103
LA
2665
88.8
0 .60
294
4.97
10.0
47 © 77
13
L aA 103
LA
2655
9 1.2
0.7 0
400
5.79
7.4
29 © 78
14
L aA 103
LA
2655
91.4
0.8 0
524
6.62
5.6
132 © 77
OAMS
OAMS
OAMS
S .N .= S a m p le n u m b e r, D .M .= D ep o sitio n M e th o d , L A = L ase r A b la te d , O A M S = OfT-axis M a g n e tro n S p u tte re d
R
i T
^ r
c alc u la te d a t T ” w
@ co lu m n in d ic a te s te m p e ra tu re in K a t w hich th e R s eff w as m easu red .
50
off a t tem peratures typically below 50 K, usually had small values of Rs a t liquid
nitrogen tem peratures.
They also had small values of A and high values of a 2.
Different power levels (~0.1, 1.0, 16 mW) were used in probing the samples.
Note th a t, although for low power levels and low tem peratures the d a ta became
noisier, the transm itted to incident power ratio was the same for all incident
powers as shown in figure 4.1 for a laser ablated thin film (2400 A) deposited on
a LaA lO j substrate.
This indicated th a t the superconducting state was not
altered by the incident power, a t least for the different power levels used in this
-is
-is
■20
■25
-30
ac
INCIDENT POWER
•35
-40
+ , 0.1 m W
-45
a
-50
, 1.0 mW
o , 16 mW
-55
-60
-65
+
50
1S0
250
300
TEMPERATURE CKJ
Figure 4.1: Transm itted power versus tem perature for a laser ablated
Y B a^C ujO ^j thin film (2400 A) on LaA103.
r
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51
study.
In addition, this also implies th at, in principle, the superconducting
properties of the thin films can be well characterized a t these low microwave
powers, since the films always remained in a state of near equilibrium.7
The
absence of any appreciable shift of T™w within a resolution of 0.5 K support this
argum ent.
This behavior was typical of the films considered and was independent
of thickness.
Figure 4.2 shows a plot of transm itted power versus incident power
for a thin film (4000 A) deposited by laser ablation on a L aG a03 substrate.
The
expected linear relation between the incident and the transm itted power is followed
reasonably well in both the normal and the superconducting state.
Figure 4.3
shows a plot of the microwave power transm itted a t 33.3 GHz through four
YBa2Cu30 7.£ thin films of different thickness, deposited by laser ablation on
LaA103 substrates of equal thickness.
As expected, more power is transm itted as
the thickness of the film becomes smaller.
From figure 4.4 one can see th at, for
o
films of thickness less than approximately 3000 A, the power transm itted through
the film decreases exponentially with thickness for temperatures below 70 K, even
though the T^c of the films varied by 5 K.
The estim ated attenuation coefficient
for the films in this thickness range varied from ~4 x 105 cm '1 a t 300 K to 1
x 10
7
cm
1
a t tem peratures below 70 K.
The non*exponential behavior seen at
T > 80 K in figure 4.4 is due to the different quality and T c’s of the films.
It
was observed that for films with thicknesses larger than ~ 3000 A the exponential
functional dependence of the power transm itted on film thickness was not well
sustained, as shown in figure 4.4.
r
This is expected, since it has been shown by
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52
2
E
c
a
H
298
200
100
i-5
,-2
10“
Incident pow er, mW
Figure 4.2: Transm itted power versus incident power for a laser ablated
Y B ajC ujO y^ thin film (4000 A) on LaGaOs for different tem peratures and
a t 30.6 GHz. The largest error bars are approximately the size of the
symbols.
others8 th a t as the films becomes thicker it is more difficult to preserve the strong
c-axis orientation; i.e., the number of a-axis oriented grains increases as the
thickness increases.
Since the shielding produced by currents flowing along the c-
axis is poorer than th a t produced by currents along the a or b axes, the amount
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53
-s
ta
ooo O o o ooo ❖ o o ooo o o
O O
-is
A A A AAA A
A A AAA
a
a
a
AAA AAA
:
□ a am
□ □ a am □
+
+
+
+++
++t‘~
+ + + +++ + + +■ + + +
-2 0
□ □ □ cm a n
-3 5
-55
-6 0
■m1
1S0
50
250
200
TEMPERATURE CK)
Figure
4.3:
Transm itted
powerversus
tem perature
for
laser
ablated
Y B a jC u g O ^ thin films on LaA103; the thicknesses represented are 828 A
(o), 1769 A (A), 2400 A (D), and 4900 A (+ ). The LaAlOj substrates for
all the films were 20 mils thick.
of power transm itted will be larger with more a-axis orientation.
It was also
observed that the tem perature a t which the normal to the superconducting state
transition begins (i.e., T “ w) was approximately 2 K higher for the thinnest film
than for the thicker ones, which all show approximately the same T™w. However,
broadening of the transmission curve is more evident in the thinner film, which
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54
♦~r I i i i i i i i > i r\ n n i I i i i i it i i i I i i i n
i i i i I i | 11 i v i i i | r r m i i i i i
-10
-20
+ ,298 K
■.TOOK
uoe —30
S IX K
♦. tOK
V, SO K
:-«0
□ , TOK
*, « K
50K
-50
-60
70^
I I I -LI I I j - I ^ J 1 I-L
1000
1
1 1 1
Z000
1
1 1 1 1 ' 1 1 1 1 1 1 1 1 * ' ' _! I 1 1 1 1 1 1 I I t t t
3000
4000
5000
t
t t t i
6000
THICKNESS (A)
Figure
4.4:
Transm itted
power
versus
film
thickness
at
different
tem peratures corresponding to the films represented in figure 4.3.
The
maximum error in the d ata is approximately the size of the symbols.
may be caused by the presence of a large number of weak links, as has been
observed by other researchers for R jc versus tem perature d a ta on similar films.®’10
Figure 4.5 shows the measured relative phase shift (AO = 0RT - 0(T)) versus
tem perature for a laser ablated thin film on LaAlOg and an off-axis magnetron
sputtered thin film on YSZ (films no. 1 and 2, respectively, of table 4.1).
th at in the normal state AO is basically constant.
Note
Below the transition an abrupt
change in AO takes place, leveling off a t tem peratures below 85 K for the film on
YSZ and continuing to decrease with decreasing tem perature for the film deposited
I
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55
-20
-1G0
-180
200
100
250
300
Figure 4.5: Measured relative phase shift A9 for an off-axis magnetron
sputtered YBa2Cu30 7.^ thin film (800 A) on YSZ (+ ), and for a laser
ablated YBa2Cu30 7_g thin film (4900 A) on LaA103 (A).
on LaA103.
The change in A0 observed for the film on YSZ is consistent w ith
th at expected for conventional superconductors, since its absolute value is less than
the t / 2
value expected for a totally superconducting thin film (ffj > > <r1).
However, for most of the YBajCu30 7>^ thin films considered in this study the
change in A0 became greater than x /2 a t some tem perature below T ^ w, as shown
by the film on LaA103 in figure 4.5.
A similar effect was also observed by
Nichols, et al.11 in transmission experiments with thin films of YBajCu30 7.^
(thickness ~ 10 000 A and T^0 ~ 80-85 K).
They explained this phenomenon in
terms of leakages through the films due to
pin-holes, micro-cracks, normal
insertions and other possible leakage sources in the film.
However, since we have
seen this effect on high quality superconducting YBa2Cu30 7.)j thin films, and failed
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56
to observe it in Bi-Sr-Ca-Cu-0 and Tl-Ba-Ca-Cu-0 thin films, as will be discussed
later, we believe th at the behavior is not exclusively caused by leakage sources,
but rather by an intrinsic, and so far not understood, mechanism taking place in
the YBa2Cu30 7.£ thin films.
The constraints imposed by this effect on the
determ ination of <r1 in the superconducting state will be discussed later.
In order to study the effect th at an externally applied dc magnetic field H has
on the microwave power transmission through the films, we have measured the
power transm itted through an off-axis magnetron sputtered thin film ( ~ 1000 A)
in a dc H field up to 50 G.
The field was generated by a pair of Helmholtz’s
coils and was oriented parallel to the film’s surface.
An externally applied
magnetic field could affect the superconducting state of the film, in particular the
intergranular material which may be driven to the normal state by the applied
field.
Thus, one would expect an increase in the microwave power transm itted
through a superconducting film in an applied dc magnetic field as compared to a
film in no applied field.
It has been observed th at the dc magnetic field dependence of the microwave
absorption in YBa2Cu30 7.£ is characterized by extreme sensitivity to low magnetic
fields, hysterectic behavior with change in direction of H field sweep, and remanent
absorption.12 More detailed studies on bulk13 and thin film14 YBa2Cu30 7_£ have
revealed changes in parameters such as A and a
when the sample is in an
externally applied dc H field, even as low as 4 G.
These studies attributed the
observed changes to intergranular effects.
r
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57
We found th at the dc magnetic field had no observable effect on the
microwave
transmission
superconducting state.
through
the
film
in
both
the
normal
and
the
We attributed this to the high quality of the film
employed, for which the possibility of the appearance of field induced vortices in
the intergranular material is very low, diminishing the effect th at these could have
in T and 9.
Therefore, it is not unexpected th at we did not observed any effect,
since the 50 G field is well below the value of the lower critical field for
YBa2Cu30 7.£ superconductors (~ 400 G ).15
4.2.2
Material Properties of YBajCxijO7_g Thin
Films
Figures 4.6 to 4.8 show the Rdc versus T curves for three of the YBa2Cu30 7.£
thin films considered in this study.
Also shown is the first derivative of Rdc with
respect to T, since it indicates more clearly the beginning of the transition.
The
d a ta shown in figure 4.6 correspond to a laser ablated thin film on LaA103 (no.
3 in table 4.3).
of 0.4 K.
The film was 2400 A thick and its T^c was 90.6 K with a AT
This film has the highest T^c among all the YBa2Cu30 7_£ films
analyzed in this work.
The data of figure 4.7 correspond to an off-axis magnetron
sputtered thin film on MgO (no. 7 in table 4.1).
The film was 1000 A thick and
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58
1.5
1.0
o
o
3
.5
85
90
95
TEMPERATURE. K
100
M i
85
90
95
100
TEMPERATURE, K
Figure
4.6: dc resistance versus
tem perature
and
its
first derivative
(dRdc/d T ) for a laser ablated YBa2Cu30 7.£ thin Sim (2400 A) on LaA103.
(Courtesy of M r. Joseph W arner and Mr. Joseph Meola, NASA Lewis
Research Center).
its TgC was 87.2 K with a A T of ~ 3 K.
This broadening may be due to the
large lattice mismatch between MgO and YBa2Cu30 7.£ (see appendix C).
Of
particular interest is the broadness of the- trace for the Sim shown in Sgure 4.8
(no. 6 table 4.1), which, due to the observed high onset tem perature, we believe
may be the result of c-a axes mixed orientation.
It has been shown16 th at, for
a-axis oriented Sims, the T^c can be lowered because of tensile stresses affecting
the Sim during cooling which leads to lattice dilation.
In order to compensate for
R
m
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59
IS
35 —
cm
12
9
1
S
=
I j6_ m as
«
30 __
85
90
95
100
TEMPERATURE# K
25 —
o
o
J
o 3
o
0
20 —
15
« * jo o o o o o
^ c P 0^
_
0
0
o
0
10
0
0
o
5
1 1 1---1---1__1__
0 QCCoicCOoJc'St^0----- ------- ------85
86
87
88
89
90
91
92
TEMPERATURE, 1C
Figure 4.7: dc resistance
93
versus tem perature and
94
its
95
first derivative
(dRdc/d T ) for an off-axis m agnetron sputtered YBa2Cu30 7_£ thin film (1000
A) on MgO. (Courtesy of Mr. Joseph W arner and M r. Joseph Meola,
NASA Lewis Research Center).
this lattice dilation oxygen has to be released from the Cu-O chains producing a
decrease of Tjjc.
These stresses arise from the difference in therm al expansivity
of the YBa2C u30 7.£ along the c-axis (~25 x 10'6/K ) 16 and th at of LaA103 (~
11 x 10'6/K ).17
Another factor th a t could lower the T^c of an a-axis oriented
film is the presence of slip-planes, although we could
instrum entation limitations.
not investigate this due to
Most of the samples studied showed predominantly
c-axis orientation (see figure 4.9), although evidence of a-axis alignment was found
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60
10
9
8
7
6
5
TEMPERATURE, K
5
2
1
0
20
30
40
50
60
70
80
90
Figure 4.8: dc resistance versus tem perature
and
100
110
TEMPERATURE, K
its
first derivative
(dRdc/d T ) for a laser ablated YBa2Cu30 7.£ thin film (1760 A) on LaA103.
(Courtesy of Mr. Joseph Warner and M r. Joseph Meola, NASA Lewis
Research Center).
in sample no. 6 of table 4.1, in agreement with the observed broadness in the Rdc
versus T behavior for the sample, as shown in figure 4.8.
A shortening of the
length of the c-axis for this film was observed from the x-ray diffraction pattern.
This shortening is due to an oxygen deficiency, and is consistent with the
explanation for the lowering of T^c discussed above.
The mosaic spread of the YBa2Cu30 7.£ films was determined from X-ray
diffraction rocking curves (RCs).
I
We did not observe any substrate effect on the
.....................................................
R e p ro d u c e d w ith p erm is sio n o f th e c o p yrig h t o w n er. F u rth e r re p ro d u ctio n pro hib ited w ith o u t p erm is sio n .
61
m
U A iO ,
LaAIO
La AIO
( 100)
WAX
20 , DEG
Figure 4.9: X-ray diffraction pattern for a laser ablated YBa2Cu30 7_£ thin
film (2400 A) on LaA103. (Courtesy of Mr. Ralph Garlick, NASA Lewis
Research Center).
RC of the films.
More details are given in section B.2 of appendix B.
The
surface morphology of the samples was studied by scanning electron microscopy
(SEM), as discussed in appendix B.
For the laser ablated samples the surface of
the film was smooth, as shown in figure 4.10 for a film on LaAlOj.
This is in
contrast to observations made by other researchers th a t there are particulates on
the surface of high quality laser ablated YBa2Cu30 7-($ thin films.4 However, a view
over a larger area of the film
(figure 4.10.b) does show structural inhomogeneities
in the film which may be caused by the substrate’s structural defects.
These
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62
inhomogeneities can affect the transport properties of the
film by increasing the
surface resistance Ra and the penetration depth A.
Figure 4.11 shows SEM for an off-axis magnetron sputtered film on MgO.
is
evident
th at
this
film
is
not
as
smooth
as
the
laser
ablated
It
ones.
Superconducting grains with sizes between 1-3 p m are distributed uniformly over
a smooth surface, which also shows a uniform distribution of dips (figure 4.11.b).
These dips may be caused by negative-ion (oxygen) resputtering, as has been
observed by other researchers.18,19 The effect of these surface grains on the
microwave properties of the film is still not well understood, since it has been
observed th a t the degree of surface roughness does not always correlate with
R..20’21
k
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63
Figure 4.10: Scanning electron micrographs a t two different magnifications
of the surface of a laser ablated YBa2Cu30 7.£ thin film (828 A) on
LaA103.
(Courtesy of M r. Nicholas Varaljay and Ms. Donna Bohman,
NASA Lewis Research Center).
L
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64
Figure 4.11: Scanning electron micrographs a t two different magnifications
of the surface of an off-axis m agnetron sputtered YBa2Cu30 7.£ thin film
(1000 A) on MgO. (Courtesy of Mr. Nicholas Varaljay and Ms. Donna
Bohman, NASA Lewis Research Center).
L
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65
4.2.3 Magnetic Penetration Depth
One of the parameters of most relevance in the evaluation of the suitability
of the new HTS thin films for microwave applications is the magnetic penetration
depth (A).
This parameter, which is a measure of how far a magnetic Held can
penetrate into the superconducting m aterial, can give information not only about
the fundamental mechanisms for superconductivity in these new materials, but also
necessary information for the design of superconductor-based microwave integrated
circuits.23 To date, values of A for Y B a jC u g O ^ single crystals and ceramics have
been reported using various experimental techniques, such as muon-spin-rotation
I*n o t\A AP
and low-field dc magnetization measurements. ’ ’ ’ Others have determined this
param eter in HTS thin films from microwave measurements.8,11,23,26*30 Table 4.2
shows a summary of the values of A for Y B ajC ugO j.j thin films measured by
others using different microwave techniques.
Observe th at the largest and smallest
values of A shown in table 4.2 differ by more than one order of magnitude.
This
range of values for A depends on factors such as film quality, film thickness, and
measurement technique, among others.
However, it is evident from the d ata in
the table th at the smallest values of A have been obtained for laser ablated films.
In particular, the group from W uppertal
on
has measured A values which compare
very well with those reported for single crystals of YBa2Cu30 7.£.2,3
The magnetic penetration depth A can be calculated from the transm itted
power using equation (2.7.8) of chapter 2, and the relation for the surface
reactance Xg = p0wA, where « is the angular frequency and p0 is the permeability.
r
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j« r” l
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
T A B L E 4.2
M IC R O W A V E M E A SU R E M E N T S O F A IN Y B a jC u g O ,^ TH IN FILM S
M E AS. T E C H N IQ U E
i f (K )
Pow er T ransm ission
M easu rem en ts'
ref. no. 10
80-85
electron
beam
co-evap.
Pow er T ransm ission
M easurem ents,*
ref. no. 26
56-70
ion-beam
sp u tterin g
M icrostrip
R esonator,b
ref. no. 8
80.6-86.5
rf-sputt.
electron
beam
co-evap.
D .M .
SU BSTRATE
d (A)
A l20 3, M gO ,
YSZ
10 000
9.0
25000
a t 30 K
650-5500
60
4000, 55 K
1700, O K
Rockwell
1200-1700
1-25
2554-3651
at 0 K
Stanford
148
3 0 0 0 ,4.2K
Stanford
1700-4400
87
1600, 0 K
W uppertal
S rT iO j, M gO 1600-3900
87
1400-1700
at OK
4000-6000
101.3
1900, 0 K
4000
148
2800-3800
at 0 K
M gO
M g O ,Z r0 2
L aA lO ,
R esonant
Cavity,*
ref. no. 29
87
reactive
m agnetron
co-sputt.
SrTiO.3
R esonant
Cavity,*1
refs. no. 28,30
an d 31
88
Laser
ablation
S rT iO ,
R esonant
Cavity,*
refs, no 23 an d 27
88-91
91
88
Laser
A blation
electron
beam evap.
S r T i0 3
L aA IO ,
S rT iO ,
10 000
F (GHz)
A (A )
GROUP
IBM
05
UCLA
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
urarH
D .M . = deposition m eth o d , d = film thickness, a: A calculated from A =
b: F ittin g o f d a ta for (c /v h) to (c/v h)2 = *r + 2(*r/td )(A 0Y (T )M (T ))2, w ith AQY (T ) = A0(1 -(T /T C)4) ,/2 . M (T )A (T )/t =
c o th ( t/A ( T ) ) ,a n d v pll = :ffnL /n .
c: A calculated from A = Xt /w /i0.
d: F ittin g o f d a ta w ith tem p eratu re dependence for A given by th e BCS theory in weak coupling lim it. D a ta obtained from resonant
frequency sh ift, A f = - irp0f2A A /G §. AA is m easured w ith respect to th e norm al s ta te skin d ep th 6, AA = 6 - A.
e: R g/R fl = (2 )'1/ 2|p 0urrNA2|3/ 2( T /T c)<[l - ( T /T c)'*|‘3^2. A djusting Ae u ntil th is equation converges w ith experim ental Rt / R N d a ta .
o>
68
Figure 4.12 shows the surface reactance versus tem perature for two of the films
investigated in this study (films no. 3 and 4 of table 4.1).
Note th a t film no. 3
exhibits a strong shielding of the microwave field, as deduced from the sharp decay
of Xg a t tem peratures ju st below T“ w, and the slow change of Xg with decreasing
±±t
'20
30
* t t t t t t * *****
40
50
S0
TEM PERA TU RE,
70
90
30
K
Figure 4.12: Surface reactance versus tem perature, a t 30.6 GHz, for two
laser ablated films (no.3, 2400 A, A) and (no.4, 1769 A, + ) on LaA103.
tem perature a t tem peratures below approximately 80 K.
On the other hand, Xg
of film no. 4 decays slower than th at for film no. 3 a t tem peratures below T®w,
and shows a slower transition.
b
This suggests that the shielding of the microwave
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69
fields is weaker than th at exhibited by film no. 3, implying a larger penetration
depth.
The rapid decrease of Xg for film no. 3 a t tem peratures ju st below T™w
and its small variation with decreasing tem perature for tem peratures below 80 K,
suggest the suitability of this type of film for microwave device applications.
Furthermore, a similar behavior for Xg observed for films deposited by off-axis
magnetron sputtering (for example, film no.2 of table 4.1), is evidence of the
appropriateness of both deposition techniques for the fabrication of high quality
YBa2Cu30 7.£ superconducting thin films.
To find the magnetic penetration depth, we solved equation (2.7.8) for Xg by
using an initial trial value for the penetration depth of A=100 A.
Using the
resulting Xg in the expression Xg= /iQwA, we calculate a new value for A.
This
value was then used in equation (2.7.8) and the process was repeated until the
value of A changed by less than 0.1% between iterations.
The values of A
obtained in this way for films of different thickness (d) on LaA103 and a t 30 K
are listed in table 4.3.
The uncertainty of the individual values of A was
approximately ten percent.
Observe th at the calculated values of A agree very
well w ith those obtained by others for YBa2Cu30 7. j thin films (see table 4.2), and
for single crystals.2,3 A plot of A versus film thickness is shown in figure 4.13.
Note th a t the anisotropy of A is evidenced in this plot by the observed increase
of A with increasing film thickness.
As mentioned in the previous section,
A
observations by others
have shown th at as the films become thicker it is more
difficult to preserve their strong c-axis orientation, resulting in an increase of the
number of a-axis oriented grains.
r
This produces a less effective shielding of the
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70
TABLE 4.3
MAGNETIC PENETRATION DEPTH A OF Y Ba,Cu30 7.£ THIN FILMS ON LaA103
S a m p le n o .
D e p o sitio n M e th o d
1
3
4
5
6
9
11
12
13
14
la se r a b la tio n
la se r a b la tio n
la se r a b la tio n
lase r a b la tio n
lase r a b la tio n
lase r a b la tio n
d c m a g . s p u tt.
la se r a b la tio n
la se r a b la tio n
la se r a b la tio n
d (A)
A (30 K , n m )
4900
2400
1769
828
1762
1000
2600
2665
2655
4000
250
160
170
150
610
120
180
140
170
260
600
700
600
500
<= 400
300
200
100
0
500
1000 1500 2000 2500 3000 35 0 0 40 0 0 45 0 0 5000 5500 6000
d. A
Figure 4.13: M agnetic penetration depth (A) versus film thickness (d) for
Y B a ^ C u jO ^ thin films.
The o represents an a-axis oriented film and the
n r
solid line represents the second degree polynomial fit described in the text.
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w ith o u t perm ission.
71
external field, resulting in an increase of A.
A stronger verification of this
argum ent is given by the large value of A observed in figure 4.13 for film no. 6
of tables 4.1 and 4.3, which, as pointed out earlier, is a predominantly a-axis
oriented film.
Taking the ratios between the A for film no. 6 and those
corresponding to films 4 and 9 of table 4.3, which have a comparable thickness,
yields A6/A 4«3.6 and A6/Ag»5, respectively.
These ratios are consistent with the
value of Ac/Aab» 5 previously reported by others for single crystals and high purity
YBa2Cu30 7. j superconductors.2,25,31
The solid line in figure 4.13 represents a fit to the d ata using a second degree
polynomial regression analysis.
This polynomial was net chosen based upon any
expected functional dependence of A on the film thickness, but was chosen because
it provided the best fit to the data.
This gives an intrinsic value of A,
corresponding to zero film thickness, of A(d=0) = 121 ± 32 nm.
This value of
A represents the smallest possible value th at can be obtained for a c-axis oriented
film free from grain-boundary effects and other non-superconducting inhomogeneities;
i.e., it is the intrinsic value for the low tem perature penetration depth of the
YBa2Cu30 7.£ superconductor.
To our knowledge, this is the first time th at this
value has been estimated experimentally for any of the HTS superconductors.
The tem perature dependence of A for a laser ablated film on LaAlOj (no. 3 of
table 4.1) is shown in figure 4.14.
Using the expression for the tem perature
dependence of A in the two-fluid model approximation (see equation 2.5.5), we
determined AQ by fitting the measured penetration depth A, using a standard least-
r
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72
.3
as
H
—
.2
LU
o__
LU
LU
z
_q _
q O -9 -
0 - 2 2 2 - 2 -°-°-2
.1
ta
0
20
30
50
60
TEMPERATURE. K
70
80
90
Figure 4.14: Magnetic penetration depth A versus tem perature for a laser
ablated thin film (2400 A) on LaAlOj. The dashed line represents a fit
using the tem perature dependence for A according to the two-fluid model.
square fit to equation (2.5.5).
It was found th a t a strong deviation from the
measured d a ta occurred for T /T c >
0.95.
Therefore, all the fits to the
experimental data were carried out for T /T c < 0.95.
Values of A0, obtained from
the two-fluid model approximations for the film in figure 4.14 and for film no. 4
of table 4.3, were ATFM(0)=150±11 nm and ATFjtl(0 )= 1 7 0 ± ll nm, respectively.
The agreement of these values with previously reported ones is evident.
Therefore, the power transmission technique presented here provides a fast and
non-destructive
r
alternate
technique
for
the
determ ination
of
the
magnetic
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73
penetration depth in HTS thin films.
We have shown th at the technique is
sensitive to the intrinsic anisotropy of A as well as to the overall film quality.
4.2.4
Complex Conductivity
As discussed in chapter 2, one can obtain the microwave complex conductivity
from the magnitude and phase of the microwave transm itted power.
Figures 4.15
to 4.17 show the real and imaginary parts of the microwave complex conductivity
as a function of tem perature for some of the films considered in this study.
The
behavior of Oy and <r2 as a function of tem perature for a laser ablated thin film
(4900 A) on LaA103 is shown in figure 4.15.
Observe th at in the normal state
<r1 exhibits a metallic-like behavior with decreasing tem perature (see insert in figure
4.15), while
a<t
remains
v e rv
close to zero,
a s e x p e c t e d f n r a. g o o d p r » n d _ « c tn r
T K i.
behavior in the normal state was typical of all the HTS YBa2Cu30 7.£ thin films
considered in this work.
Note th a t both Oy and <r2 increase rapidly upon cooling
the sample through the transition tem perature T “ w.
Observe the maximum
reached by Oy and its subsequent rapid decrease at tem peratures not far from
T™w, and the monotonic increase in <r2 with decreasing tem perature.
A similar
behavior for Oy and <r2 ju st below the beginning of the transition was observed by
Nichols, et al.,11 in YBa2Cu30 7.$ thin films (~ 10 000 A) deposited on A120 3,
YSZ, and MgO substrates, and
Y B a jC u jO ^ on MgO.
more recently
by
Golosovski,
et a l.14 for
Nichols, et al. suggested th at this behavior is consistent
I
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50 100 150 200 250 300
TEMPERATURE, K
70
80
90
100
110
TEMPERATURE. K
Figure 4.15: Real and imaginary parts of the microwave conductivity a* =
a \ - iff 2 versus tem perature a t 30.6 GHz for a laser ablated Y B a ^ C ^ O ^ j
thin film (4900 A, T “ w=90.8 K) on LaA103.
6 .8
3.8
^^OCCCOCOCXDo o o o
l A .V A V A M A M
90
OOO*
AAA-A £
£
ICO
Figure 4.16: Real and imaginary parts of the microwave conductivity <r*=al
- ]ff 2 versus tem perature for a laser ablated YBa2Cu30 7.£ thin film (1000
A, T“ w=88.6 K) on LaAlQ3 a t 33.3 GHz.
k
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75
I
85
75
95
10 5
Figure 4.17: Real and imaginary parts of the microwave conductivity a*=
a \ ' i ff2 f°r a ^aser ablated YBa2Cu30 7-(j thin film (2400 A, T ^lw=91.6 K)
on LaA103 a t 34.6 GHz.
with
th at
expected for a homogeneous superconductor which, for decreasing
tem peratures, exhibits both an increasing energy gap and an increasing density of
quasiparticle states a t the gap edge, such as a Bardeen-Cooper-Schrieffer (BCS)
superconductor.
A comparison of
for our films was made w ith the calculated
obtained from the M attis-Bardeen theory,32’33 which is based on the BCS
theory and is given by
o f * = <rN[2A(kBT)- 1]exp[-A /ka T ]ln (A /W ) ,
F
fiw<< 2A
(4.2.4.1)
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76
where ffN is the normal microwave conductivity a t T = T “ W, kg the Boltzman’s
constant, w=2jrf is the angular frequency, and A is the energy gap.
The value
of A(T) in equation (4.2.4.1) was obtained by numerical integration of the
expression34
(N(O)V)*1 = /Jj^tanh [1/40(£2 + A2),/4](? 2 + A2)-,/4d f
(4.2.4.2)
where, in the BCS theory, N(0) is the density of states at the Fermi level, V is
the interaction potential, hi/ is the cutoff energy, 0 = 1/kgT , and £=e-/t is the
single particle energy relative to the Fermi energy (see appendix D for further
details).
Figure 4.18 shows a comparison of o 1 as measured for the film of figure 4.15
W TJ
(no. 1 table 4.1) and a j
as calculated using equation (4.2.4.1).
It is evident
th at the tem perature behavior for the experimentally measured value for <ri
deviates from th a t expected using the BCS theory.
One can claim a qualitative
agreement between the two parameters at tem peratures just below T™w, but even
this agreement is lost as one moves far from T“ w. According to the BCS theory
the increase in <r1 upon cooling through the transition tem perature is accompanied
by an increase in nuclear spin relaxation rate (1 /T j) above the normal value
because of the increase of the density of quasiparticles a t the gap edge.
temperatures
both
<r1 and
( 1 /T J
decrease
exponentially
to
zero
A t lower
as
the
quasiparticles above the gap are frozen out.35 However, Warren, et al.36 have shown
*H
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77
1.0x10s
0 .9
0. 8
0 .7
6
0.6
CO
o
O.'l
0 .3
0.2
0
10
20
30
40
50
60
70
80
90
100
110
TEMPERATURE. K
Figure 4.18: Real conductivity <r1, obtained from the m agnitude and phase
of the transm itted power, for a YBa2Cu30 7_£ thin film on LaA103.
Solid
line is the real p u t of the conductivity calculated from M attis-Bardeen
theory.
th at 1 /T 1 for quasiparticles on the chain-forming C u (l) and planar Cu(2) lattice
sites decreases rapidly upon cooling through T c.
Therefore, if the observed
behavior for <r1 is a consequence of the intrinsic superconducting state of the film,
this type of response may be due to a non-isotropic energy gap or to a
superconductor which does not behave according to the BCS theory.
However, if
the behavior is intrinsic to the material, one would expect th a t the tem perature
dependence of
would be the same for all the YBa2Cu30 7.£ HTS thin films
considered, independent of the deposition technique and substrate employed in the
film fabrication.
Unfortunately, the d ata for some YB ajC u-jO ^j films on LaA103
and other substrates contradict this hypothesis.
In these films it is observed that
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78
both <T1 and <r3 increase as the film is cooled through its transition tem perature,
but the rapid decrease in
observed for the films in figures 4.15-4.17 was not
Instead <rl levels off at tem peratures below 80 K changing slowly at
observed.
low tem peratures, as shown in figure 4.19 for a film on LaA103.
This behavior
has also been observed in Bi-based and Tl-based films, as we will show later in
this thesis.
One can explain the variability of behavior for <?i(T) by taking into account
the granular nature of the YBa2Cu30 7, j HTS thin films.
Ho, et al.37 have
suggested th a t these HTS films can be visualized as composed of superconducting
20
h—
O
S
+ REAL
o IMAGINARY
* *6. o
15
10
UJ
5
0
20
30
40
50
60
70
80
90
100
110
TEMPERATURE, K
Figure 4.19: Real and imaginary parts of the microwave conductivity
9 =<VJ>2 f°r a laser ablated YBa2Cu30 7.£ thin film (2655 A, T“ w=91.2
K) on LaA103 a t 35 GHz.
I
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79
regions embedded in a normal conducting matrix.
When the grains undergo the
superconducting transition as the film is cooled through its T c the microwave
electric field will be excluded from the superconducting regions.
The exclusion of
the microwave electric field from the superconducting regions will enhance the
effective current density in the intergranular normal regions, thus causing an
apparent increase in the conductivity <rt of the film.
Since the distribution of the
non-superconducting inclusions through the film varies from film to film, the
response of the films, as determined from the tem perature dependence of
also be different from film to film.
will
In addition, the variation of T c from grain
to grain may also contribute to this effect.
Figure 4.20 shows a plot of the real conductivity versus tem perature for a dc
magnetron sputtered film (1000 A thick, T®w=94
K) calculated
using the
magnitude of the transm itted power and the two-fluid model approach, and from
the measured T and A#.
Note th at in the normal state the values of
by the two methods are in excellent agreement.
obtained
However, in the superconducting
state there is marked discrepancy between the tem perature dependence of a 1
predicted by the two-fluid model and th at obtained from T and AO.
Nevertheless,
we observed th a t the values of <r2 38 calculated by the two methods are in very
good agreement as shown in figure 4.21.
Therefore, the technique consisting of
combining the magnitude of the transm itted power with the predictions of the twofluid model seems to be suitable for obtaining a 2 in the superconducting region,
which is a useful parameter in the modeling of microwave devices,38,39 but it is
k
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80
4X105
3
2
0 0 000 o O O ooo o O o 000 OS
1
0
50
100
150
200
TEMPERATURE. K
250
300
Figure 4.20: Real p art of the complex conductivity a t 33.3 GHz, calculated
from the m agnitude and phase of the transm itted power (o), and from the
magnitude of the transm itted power and the two-fluid model (o ).
i. o7
00
i/i
©
-
1 .0
Figure 4.21: Imaginary part of the conductivity a t 33.3 GHz, calculated by
measurements of the magnitude and phase of the transm itted power (o),
and from the m agnitude of the transm itted power with the two-fluid model
(o ).
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81
rather poor in providing a reliable description of the tem perature dependence of
a x in the superconducting state.
Using equation (2.2.6) and the measured values of <r2 we have calculated a
penetration depth A for the films analyzed in this work.
We found th at the
values for A determined in this way were not only larger than those for A shown
in section 4.2.3, but also were distributed throughout a larger range of values.
The larger A values calculated from <r2 are a manifestation of the effects of grain
boundaries, crystal defects, and the intrinsic anisotropy of these materials which
lower the value of <r2, thereby increasing A.
The calculation of the microwave conductivity by microwave power transmission
measurements allowed us to determine the normal state resistivity, pN.
Since
previous measurements of HTS materials have shown th at the microwave and the
dc conductivities are nearly equal in the normal state,26’37 we have used the
microwave conductivity to determine pN.
Values of pN a t T“ w for a number of
films considered in this study, are given in table 4.1.
Note th a t the normal state
resistivities we obtained, 111-400 fid -cm a t T “ w for c-axis oriented samples, are
in close agreement with values reported by other researchers (~ 100-200 fid -cm) for
YBa2Cu30 7, j thin films.4,28,40 However, they are large when compared with
recently reported values of approximately 65-90 fid -cm a t tem peratures around 100
K, obtained for very high quality YBa2Cu30 7.£ thin films on LaA103 and MgO
substrates.41
The normal state surface resistance (RN) at T®w was determined from the
normal state resistivity a t th at same temperature, p ^ w by using the normal skin
¥
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82
effect formula,28’42 R jj= (/t0wp^w/2 ) 1A. The values so obtained are shown in table
4.2.
The value of pN can also be used to determine the carrier mean free path,
t, by using the expression
tpN ss •^(25re2/h )(s2/3ir2)1^3}' 1
(4.2.4.3)
where s is the density of free carriers (cm*3), e is the electronic charge and h is
Planck’s constant.
The above expression, which is based on a free electron model,
has been used by others15’42,43 to obtain the carrier mean free path of Iow-Tc as
well as high-Tc superconductors.
From the work of Bardeen, et a l.15 the density
of carriers (holes) for the Y B a jC u jO ^ superconductor is approximately 9 x 1021
^ <3
cm* .
Using this value in equation (4.2.4.3) gives
fpN = 0.294 /ifl-cm«ftm
(4.2.4.4)
We have used the values of pjj a t T™w, p™w, in equation (4.2.4.4) to determine
the value of the carrier mean free path for the films under consideration.
The
resulting values for ( are given in table 4.1.
The obtained
( values are
consistent
al.15 for
YBa2Cu30 7.^
with
superconductor.
those
reported
by
Bardeen, e t
the
Since the film thicknesses employed in this study are much larger
than I, the effect of surface scattering on I is negligible.
Therefore, we believe
k
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83
th at the value of the mean free path was limited either by grain-boundary
scattering or by scattering a t the twin boundaries.
4.2.5 Surface Resistance
The surface resistance of the films was calculated by using the values of
and <r2 obtained from power transmission measurements in equation (2.4.4) of
chapter 2.
For the actual calculations we have used RN and
as the surface
resistance and the real conductivity, respectively, of the film in the normal state
and a t T=T™W.
We have already mentioned th a t for many of the films
considered in this study we could not determine
T®w.
a t tem peratures far below
Although the values of <r1 obtained within this limited tem perature range
below T™w allowed us to compare its behavior as a function of tem perature with
th at predicted by the M attis-Bardeen equations, for most of the films studied we
were unable to determine Rg a t tem peratures far below T “ w.
Values of Rg calculated a t tem peratures around 77 K and a t 30 GHz are given
in table 4.1.
The smallest values of Rg a t 77 K were obtained for a laser ablated
YBa2Cu30 7_£ thin film (2400
A;
no 3 table 4.1) on LaAlOj, Rg~3.3 mfi, and an
off-axis magnetron sputtered YBa2Cu30 7 (j thin film (2600 A; no. 11 table 4.1) on
LaA103, Rg~6.9 mfl.
These values are lower than for pure copper (Rg~16 mil
a t 77 K and 30.6 GHz), and are also in good agreement with those reported for
very
high quality
YBa2Cu30 7_^ thin
films deposited
by
off-axis magnetron
sputtering onto LaA103 substrates (~500 pH a t 10 GHz and 77 K; and ~4.7 mfl
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84
a t 30 GHz, calculated by using Rgocf2 dependence, where f is the frequency)41.
However, they are still somewhat larger than the best value reported to date for
a laser ablated YBa2Cu30 7.£ thin film on S rT i0 3, whose measured value was ~8
mfl a t 87 GHz, which corresponds to a value of ~ 1 mG at 30 GHz assuming the
iy
j
Raocf dependence.
We observed also th at for the films of thickness below 1000 A (for example
film no. 2 and no. 5 of table 4.1) Rg becomes larger than for most of the other
thicker films considered in this study.
However, this effect was not directly
correlated with the T c values, i.e. a high value for Rg did not necessarily imply
a low value for T c (see film no. 2 table 4.1).
For the overall range of thicknesses
considered, no clear correlation between Rs and the thickness of the film was
observed.
The large value of Rg observed for film no. 6 of table 4.1 is a
consequence of its a-axis being aligned normal to the substrate.
Rg results from the poor shielding currents along the c-axis.
The increase in
The difficulty in
establishing a strong correlation between Tc and Rg for the samples considered in
this work is a consequence of the differences in the type, average size and location
of impurities and lattice defects from film to film.
To date, most of the Rg measurements of YBa2Cu30 7.£ HTS have been
performed using resonant cavity techniques.4,44’45 Although this technique provides
a direct measurement of Rg, it does not provide information related to other
im portant transport parameters in the superconducting state such as <r* and A.
Furthermore, it has been observed th at the values of Rg for YBa2Cu30 7.^ thin
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85
films vary by more than an order of magnitude in measurements made a t different
laboratories.1
In view of this, we have measured the Rg of three laser ablated YBa2Cu30 7 (j
thin films
(~ 2 6 6 0 -4 0 0 0
A) on LaA103 by microwave power
resonant cavity measurements.
t r a n s m is s io n
and
All three films were measured by Dr. Harvey
Newman, of the Naval Research Laboratory (NRL) in W ashington D.C., using a
TE0U-mode copper cavity resonant a t
36
GHz.
One film was also measured by
Dr. William Wilber, of Fort Monmouth (FM) in New Jersey, using a T E 01l-mode
copper cavity resonant a t
35
GHz.
Figure 4.22 shows Rg versus tem perature for the film (~4000 A thick)
measured by both NRL and FM.
purposes.
25 mR
The Rg of copper is also shown for comparison
This film had a T^c=84.2 K and a T™w=90 K.
at
80 and
Rg values of 177 and
50 K, respectively, were obtained by using the power
transmission method.
The scatter of the d ata below ~ 50 K is due
of an input power of
only 1 mW.
Similarly, R# values of 528 mfl at
13 mR a t 50 K, were measured a t NRL.
to our use
80 K,and
The Rg values (scaled to 36 GHz
assuming an f2 dependence) measured a t Fort M onmouth were 127 mR at 78 K,
and 23 mR a t 48.5 K.
The uncertainty in this d a ta is ± 20% below 50 K.
The
time elapsed between the Rg measurements shown in figure 4.19 was one and a
half m onth, with the NRL
measurement last.
measurement performed first and our microwave
Note th at both techniques give an Rg th at decreases rapidly
when the sample is cooled through T™w and then levels off a t lower tem peratures
r
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86
tn
£
©
X
10
50
50
80
90
Figure 4.22: Surface resistance, Rs, versus tem perature a t 36 GHz for a
YBa2Cu30 7_£ thin film (4000 A) on LaA103 as measured by a microwave
power transmission method (+) and by a cavity wall replacement method;
NRL
(□) and FM (A).
The R, for copper (o) is also plotted for
comparison.
showing a residual surface resistance th at changes very slowly with decreasing
tem perature.
Although there is an appreciable discrepancy between the R, values
obtained by the two techniques a t tem peratures not far below T “ w, they agree
within a factor of 2 a t lower temperatures.
A similar behavior was observed for
the other two samples, and the results obtained are presented in reference 46.
It has been observed th at for thin films a t tem peratures not far below T c A>
5000 A.6,28 The largeness of this
value relative
to
the
film thickness of
approximately 4000 A suggests th at a large amount of microwave energy is leaking
¥
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87
through the substrate.
This leakage would result in an overestimation of Rg.
the cavity technique a t tem peratures close to
In
this leakage is strongly
dependent on the average power stored in the cavity.
At low tem peratures
compared with T“ w, due to a smaller A one would expect less leakage and a
weaker dependence of the leakage on the energy stored in the cavity.
In this
tem perature range the measured Rg values should be closer to the actual Rg values
of the film.
The better agreement between the Rg values of figure 4.22 a t lower
tem peratures is consistent with this argument.
The good correspondence between
the three measurements suggests th a t the microwave transmission power technique
can be used as an alternative technique for the determ ination of Rg in HTS thin
films.
4.3
Bi-Sr-Ca-Cu-O Thin Films
The discovery of the Bi-Sr-Ca-Cu-0 superconductor brought to the high-Tc
superconductivity domain a superconductor with a T c > 100 K (for its high-Tc
phase), great stability w ith respect to thermal cycling, and relatively insensitive to
w ater and moisture.
Due to these features this superconducting oxide could be
suitable for microwave applications.
Although
millimeter wave
studies
of
YBa2Cu30 7.£ thin films have been performed in the frequency range from 26.5 to
a
40.0 GHz,
to the best of our knowledge no similar studies have been performed
for the Bi-Sr-Ca-Cu-0 superconductors a t these frequencies. M otivated by this fact
we have studied several co-evaporated Bi-Sr-Ca-Cu-0 superconducting thin films
F
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88
deposited on LaA103 and MgO substrates by performing power transmission
measurements in the aforementioned frequency range.
Since, to this date,
deposition of thin films of the high-Tc phase of the Bi-based HTS is very difficult,
our studies were performed on films with a lower T c phase (T^c ~ 80 K).
However, study of the low-Tc phase can still provide information related to the
microwave properties of the
Bi-based superconducting system.
As for the
YBa2Cu30 7.£ thin films, we have calculated the microwave complex conductivity
for these films as well as their magnetic penetration depth and surface resistance.
We have analyzed four co-evaporated Bi-Sr-Ca-Cu-O superconducting thin films
( ~ 5000 A and 3000 A thick) deposited on MgO and LaA103 substrates.
All the
films have a zero-dc-resistance tem perature of approximately 80 K with a transition
width A T~10 K, as shown in figure 4.23 for the 3000 A films.
Inspection of the
o
films by SEM revealed th at for the 5000 A films the surface morphology of the
film on MgO (B i# l) was smoother than for the one deposited on LaA103 (B i#2),
as can be seen in figure 4.24.
Note th at there are voids in the film deposited on
MgO probably due to hydrolization of C aF2 and SrF2 during the first step of the
annealing process.
A similar effect has been observed in YBa2Cu30 7.£ thin films
deposited by sequential evaporation.48 On the other hand the film on LaA103 is
characterized by randomly oriented grains uniformly scattered across the film’s
surface.
o
Similar micrographs for the 3000 A films on MgO (B i#3) and LaA103
(B i#4) are shown in figure 4.25.
These films were deposited by KalKur, et. al.49
almost a year after films B i# l and B i#2 were deposited.
Two main features are
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89
3 5 .a
3a.0
~
U1
X
25 .0
X
o
20 .0
Ld
CJ
z
X
15.0
cn
1-4
U1
O'
Ld
ie.0
taa
Isa
200
300
TEMPERATURE CK)
Figure 4.23: dc resistance versus tem perature measurement of co-evaporated
Bi-Sr-Ca-Cu-0 superconducting films (3000 A) on MgO (+ ) and LaAIOa
(a). (Courtesy of Mr. Joseph Warner and Mr. Joseph Meola, NASA Lewis
Research Center).
noticed immediately.
First, film B i#4 exhibits a better connectivity (i.e., grain
coupling) than th a t shown by film B i#2 on figure 4.24 and second, the number
of particulates and misoriented grains on film B i# 4 are fewer than for its
counterpart of figure 4.24.
Both factors should result in the improvement of the
microwave transport properties of the films.
The morphology of film B i#3 shown
in figure 4.25 also shows differences from the film B i# l shown in figure 4.24, as
h
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90
Figure 4.24:
Scanning electron micrographs for Bi2Sr2C axCu2Ox thin films
(5000 A) on LaAIO.
(a) and MgO (b) substrates. (Courtesy of Mr.
Nicholas Varaljay and Ms. Donna Bohman, NASA Lewis Research Center).
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91
Figure 4.25: Scanning electron micrographs for Bi2Sr2Ca1Cu2Ox thin films
(3000 A) on LaAlOj
(a) and MgO (b) substrates. (Courtesy of Mr.
Nicholas Varaljay and Ms. Donna Bohman, NASA Lewis Research Center).
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92
judged by the moce evident plate-like grain structure typical of this compound.
However, the voids and gaps observed in film B i# l are still observed in film
B i#3.
Since these voids are a signature of poor connectivity between the grains,
they will be deleterious for the microwave properties of the film. X-ray diffraction
patterns for both films as measured by others (see appendix B) showed th at the
films
were c-axis oriented.
However,
a
broadening
of the
rocking curve
corresponding to the (0012) X-ray diffraction peak of the B i# 4 Him was observed.
This broadening could be due to the presence of tw in domains on the LaAlOj
substrate, as has been observed in YBa2Cu30 7,£ thin films on LaA103,41 and also
in Bi2Sr2C a1Cu20 8+x thin films deposited on LaGaO3,S0 an isomorphic substrate
to LaA103.
Figure 4.26 shows the microwave transm itted power versus tem perature a t 30.6
GHz for the B i#3 and B i# 4 films.
The transm itted power decreases slowly with
tem perature and then decreases abruptly upon going through the superconducting
transition.
For the film on MgO the transition is almost completed a t 80 K, with
the transm itted power barely changing for lower tem peratures. On the other hand,
for the film on LaA103, the power attenuation with respect to its value at the
beginning of the transition is twice as large as for the film on MgO leveling off
only a t temperatures below 60 K. The tem perature dependence of the transm itted
power observed for films B i# l and B i#2 was similar to th at exhibited by film
B i#3.
Figure 4.27 shows the tem perature dependence for the relative phase shift, AO
= 0RT - 0(T), associated with the power d a ta shown in figure 4.26.
r
It is readily
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93
-ta
-15
_
, + + -H-+ + + +
-H4-
aA^4A * A *
0 -3 0
-4 5
-5 5
se
150
300
TEMPERATURE <K)
Figure 4.26:
Transm itted power versus tem perature for co-evaporated
Bi2Sr2C a1Cu2Ox thin films (3000 A) on MgO
(+) and LaA103
(A)
substrates a t 30.6 GHz.
apparent th a t for both films A9 is almost tem perature independent in the normal
state while a negative A0 appears upon transition to the superconducting state.
A dram atic change of A0 takes place between 90 and 80 K a t which it levels off
and continues to change slowly with decreasing tem perature.
In figure 4.26 we
showed th a t the transm itted power for the film deposited on LaA103 is attenuated
considerably upon cooling the film through its transition tem perature suggesting an
effective shielding of the microwave fields.
However, the broadening and leveling
off shown by the A 9 d a ta in figure 4.27 indicates th at the power losses in the film
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Further reproduction prohibited w itho ut perm ission.
94
sa
2a
-40
-60
20
30
50
70
80
110
90
TEMPERATURE CIO
Figure 4.27:
Relative phase shift Ad versus tem perature for co-evaporated
Bi2Sr2Ca1Cu2Ox thin films (3000 A) on LaAlOj
(A) and MgO (+)
substrates.
film are still high, which implies th at Rg remains relatively large, as will be
considered later.
Figures 4.28 and 4.29 show the <rv and <r2 as determined from the magnitude
and
phase of the
microwave
power transm itted through
the
films.
Both
param eters exhibit the same behavior observed previously for thin films of
YBa2Cu30 7.£, with <r1 and <r2 increasing upon cooling through the transition
tem perature.
The same behavior has also been observed in similar measurements
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95
+++
A A A tA tA* A*1* £a a
^ '
> *4.a
-i.B,
30
20
40
90
90
Figure 4.28: a x (A) and <r2 (+) versus tem perature and a t 30.6 GHz for
a Bi2Sr2Ca1Cu2Ox thin film (3000 A) on a MgO substrate.
at
60
GHz
deposition.
07
on
Bi-Ca-Sr-Cu-O
thin
films
fabricated
by
reactive
ion-beam
Just as for the YBa2Cu30 7.^ films, the behavior of a l deviates from
th at expected from the empirical two-fluid model.
In the superconducting state
reaches a maximum a t temperatures around 73 K and 45 K for the films on
MgO and LaA103,
tem peratures.
respectively, and then starts to decrease slowly a t low
From both figures we can see th at the values for <rL and <r2 in the
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96
>. + 7 . 0
++
♦ 3 .8
-I.
30
50
50
70
80
30
TEMPERATURE CK)
Figure 4.29: <tx (A) and <r2 (+ ) versus tem perature and a t 30.6 GHz for
a Bi1Sr2C a1Cu2Ox thin film (3000 A) on a LaAlOj substrate.
superconducting state for the film deposited on LaA103 are approximately an order
of magnitude larger than those for the film on MgO.
This correlates very well
with the better connectivity and apparent higher density observed in the film
deposited on LaA103 as compared with that on MgO.
This also shows the
importance of achieving good grain coupling during the deposition processes
employed in the preparation of HTS thin films.
for films B i# l and B i#2.
The same behavior was observed
However, the actual values of a j and <t2 obtained by
the measurement of T and 9 were smaller (as much as an order of magnitude for
r
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97
the film on LaA103)
than those corresponding to films B i#3 and B i#4.
A
detailed discussion of the results of the interaction between the incident microwave
power and films B i # l and B i#2, in terms of the power transmission and the twofluid model is given in reference 51.
for
The fact of having a very large value of <r1
the film on LaA103 fits well with the model of the film consisting of
superconducting regions growing in a normal conducting m atrix proposed by Ho,
*17
et al. ; i.e., the better the superconducting properties of the grains, the more
complete the exclusion of the microwave electric field from the superconducting
regions will be.
Furtherm ore, due to the better connectivity between grains there
are less intergranular normal regions and therefore current density in these regions
will be greater causing a greater increase of a 1 for the composite film.
true,
If this is
one should see a larger penetration depth A for the film on MgO than for
the film on LaA103.
Using equation (2.2.6) values of A of 3.48 and 1.31 /im at
77 K, and of 2.50 and 0.48 p m a t 20 K were obtained for the (3000 A) films on
MgO and LaA103, respectively.
The values of A a t 77 K for these films were
less than half the values of the penetration depth corresponding to films B i# l and
B i#2.
This was expected due to the better surface properties exhibited by films
B i#3 and Bi#4.
Following the explanation given in Section 4.2.3, we have determined A from
Xg.
The data for films B i# l and B i#2 are shown in figures 4.30 and 4.31.
Values of A a t 77 K of 0.37 and 1.05 ^m , and a t 20 K of 0.24 and 0.86 p m
were obtained for the films on LaA103 ' and MgO, respectively.' As betore, we
performed a least squares fit to the equation (2.2.5) corresponding to the two-fluid
F
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98
US
£
=L
28
38
78
88
38
Figure 4.30: M agnetic penetration depth A versus tem perature for a co­
evaporated Bi2Sr2C a1Cu2Ox thin film (3000 A) on LaA103. The solid line
represents a Fit using the tem perature dependence for A according to the
two-fluid model.
1
I
• ia
28
38
68
78
98
Figure 4.31: M agnetic penetration depth A versus tem perature for a co­
evaporated B ijSrjC ajC ujO j. thin film (3000 A) on MgO. The solid line
represents a fit using the tem perature dependence for A according to the
two-fluid model.
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99
model (TFM ) tem perature dependence of A, in order to determine AQ. As for the
case of YBa2Cu30 7.£, we found th a t strong deviations
from the measured data
occurred at T /T c > 0.95, and thus all fitting was performed a t T /T c < 0.95.
Values of AoTFM = 857 ± 23 nm and A0 TFM = 233 ± 27 nm were obtained for
the films on MgO and LaA103, respectively.
These values are larger than those
obtained for the thin films of YBa2Cu30 7.£ discussed previously in section 4.2 of
this thesis.
Generally, one expects the large values of A to be reflected in the
magnitude of the surface resistance Rg since these two param eters are directly
correlated to one another.
using equation (2.4.4).
Figure 4.32 shows the tem perature for Rg calculated
Also shown is the Rg of copper measured by a TE011
resonant cavity technique, and the theoretical value for the Rj^ of copper a t a
tem perature of 77 K and 30.6 GHz, calculated from R ^ = ( fiQu ip /2 )'^ and using />Cll
at 77 K = 0.2 fiQ-cm.
en
It is evident th a t Rg for both films is greater than that
of Cu a t all temperatures.
deposited on
However
it is also very clear th a t Rg for the film
LaA103 is lower than th a t for the film on MgO.
Note th a t for
both cases the appearance of a residual surface resistance, which prevents the films
from reaching Rg values as low as or lower than those for copper.
Note th a t once
more the film deposited on LaA103 appear to be a better superconductor than its
counterpart
on
MgO,
superconducting state.
by
having
a
smaller
surface
resistance
Rg in
the
This is true, even though the film deposited on MgO seems
to have a better single crystallinity than the film on LaA103 as deduced from the
rocking curve FWHM.
The same feature was observed for films B i# l and Bi#2.
This suggest th at it is more advantageous to use the LaA103 rather than MgO
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100
as a
dielectric substrate
for Bi-based HTS films growth
and
for practical
microwave applications.
+ +++ + + + + + +++
O
AAA AA
30
70
80
110
Figure 4.32: Surface resistance (Rs) a t 30.6 GHz versus tem perature for
Bi2S r2C a1Cu2Ox thin films (3000 A) on LaA103
(A) and MgO (+)
substrates, and for copper (□); (♦) represents the theoretical Rs value for
Cu a t the shown tem perature and frequency.
I
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101
4.4
Tl-Ba-Ca-Cu-0 Thin Films
Of the three principal copper-oxides superconducting systems (i.e., Y-Ba-Cu-O,
Bi-Sr-Ca-Cu-O, and Tl-Ba-Ca-Cu-O) the system th a t has shown superconductivity
a t the highest tem perature (~ 125 K ),53 is the Tl-Ba-Ca-Cu-O compound.
The
high T c value exhibited by this system has stim ulated great interest concerning its
microwave characterization because of the possibility of applying this HTS in
microwave devices.
An im portant criteria, at least from the stand point of
microwave applications, is the thermal stability of the transport parameters of the
superconducting m aterial a t liquid nitrogen tem peratures.
It has been observed
th at for YBa2Cu30 7.£ the surface resistance Rg and the complex conductivity a*
=
-j<r2 are still changing rapidly a t 77 K.
However, both Rg and a* are
expected to vary only slightly below 90 K for the Tl-based superconductor, because
of its
higher
transition
tem perature.
This
fact
may
make
the
Tl-based
superconductors a better choice for microwave applications a t tem peratures near
the liquid nitrogen temperature.
We describe here the results of a microwave power transmission study of four
Tl-Ba-Ca-Cu-O films a t 30.6 GHz.
The films (~ 4000-5000 A thick) were
deposited by other researchers on LaA103 and MgO substrates (~ 20 mils thick)
by laser ablation, and by rf magnetron sputtering on LaA103 (~ 10 mils thick)
as described in appendix A.
The samples were characterized by others (see
appendix B) using dc resistance versus tem perature measurements, scanning electron
microscopy (SEM), and X-ray diffraction.
f
Zero-dc-resistance was attained at 101.8
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102
K for the 5000 A laser ablated film on LaA103 (hereinafter called sample T l # l) ,
at 99.8 K for the 4000 A laser ablated film on LaA103 (hereinafter called sample
T l# 2 ), a t 83 K for the 5000 A laser ablated film on MgO (hereinafter called
sample T l# 3 ), and a t 83 K for the rf magnetron sputtered film on LaA103
(hereinafter called sample T l# 4 ).
The dc-resistance versus tem perature curves for
samples T l # l and T l# 2 are shown in figure 4.33.
Note that the T^° values for
these two samples are considerably higher than those for samples T l# 3 and T l# 4 .
However all the samples show a dc-onset tem perature within 105 and 110 K,
which is consistent with the observed T™w.
The X-ray diffraction patterns of the samples show th at the films were
polycrystalline.
Typically, the (2223) and the (2212) phases were present.
More
details are given in appendix B.
Figures 4.34 and 4.35 show SEM micrographs for the Tl-based films analyzed
in this work.
Samples T l # l and T l# 2 exhibit plate-like grains, as typically
observed for Tl-based HTS thin films, with varying orientation in the a-b plane.
The platelets are smooth, varying in size from 2 to 8 /im.
The plate-like grain
structure is even more evident in the laser ablated film on MgO (sample T l# 3 )
as can be seen from figure 4.35a.
The grains size for this film are approximately
10 to 15 p m , and are characterized by ” step-like” features which result in and
increase in the Rg of the film.
In addition, the film is characterized by empty
spaces or voids which may account for the low T^c value measured for this film.
Figure 4.35b shows the SEM micrograph for the rf magnetron sputtered sample
(sample T l# 4 ) after the post deposition annealing process.
r
The micrograph shows
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103
1.0
1
£
£E
<2
atn
CC
50
100
150
200
250
300
Temperature (K)
1.0
1
w
<
aa
rr
100
150
200
250
300
Temperature (K)
Figure 4.33: Normalized resistance versus tem perature for laser-ablated TlBa-CarCu-O superconducting films on LaAlOg. (a) Film thickness, 5000 A;
T cdc = 101.8 K. (b) Film thickness 4000 A; T cdc = 99.8 K. (Courtesy of
Mr. Joseph W arner and Mr. Joseph Meola, NASA Lewis Research Center).
I
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104
Figure 4.34: Scanning electron micrographs for a 5000 A laser ablated TlBa-Ca-Cu-0 thin film (a), and a 4000 A laser ablated Tl-Ba-Ca-Cu-O thin
film (b) on LaAlOj.
(Courtesy of Mr. Nicholas Varaljay, NASA Lewis
Research Center).
t
L
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105
Figure 4.35: Scanning electron micrographs for (a) a 5000 A laser ablated
Tl-Ba-Ca-Cu-O thin film on MgO, and
(b) a 5000 A rf magnetron
sputtered Tl-Ba-Ca-Cu-O thin film on LaA103. (Courtesy of Mr. Nicholas
Varaljay and Ms. Donna Bohman, NASA Lewis Research Center).
r
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106
some evidence of deviation of grain orientation parallel to the surface, and also of
randomly distributed defects in the form of pinholes.
Characteristics grain sizes
between 2 and 5 /im were observed for this sample.
Note th at the connectivity
between grains is much better for samples T l # l and T l# 2 than for samples
T L # 3 and T l# 4 .
This aspect may very well be responsible for the higher T^c
exhibited by the T l # l and T l# 2 films.
Figure 4.36.a shows the tem perature dependence of the 30.6 GHz power
transmission magnitude for the four samples. The slopes of the power transmission
in the normal state follow th at of the dc resistance in the same region.
As for
the previous HTS systems considered, the magnitude of the transm itted power
drops abruptly at temperatures just below T“ w.
Note th at films T l # l , 2, and
3 are quite similar in their power transmission properties.
In contrast film T l# 4
behaves definitely different, exhibiting a transmission change which occurs over a
broader interval of tem peratures and does not level off as was observed for the
power transmission curve observed for the other three films.
Figure 4.36.b show the relative phase shift A d for the 30.6 GHz radiation
transm itted through the samples.
Phase changes of over 75°, and approaching 90°,
the value expected for a fully superconducting film
for samples T L # 2 and T l # l , respectively.
< < 1), were observed
The phase change is more gradual for
sample T l# 3 , while for sample T l# 4 it takes place over a
tem perature range.
much broader
Note th at we have been able to measure the phase shift to
temperatures down to 20 K.
As we have seen already this is in contrast with
many of the YBa2Cu30 7.^ thin films which, due to their large microwave signal
\
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107
□□
GOO hiti Q □ □ 11n QD .
. j, j, M
•29
>39
se
Cfl
49
29
9
-6 9
» --t.- i
.
I
sa
» .
» >
I_..
.
.
.
I
158
280
T D ra v m jR C (K)
Figure 4.36: Tem perature dependence of the power transmission coefficient
(a) and the relative phase shift (b) of 30.6 GHz radiation transm itted
through films T l # l (A), T l# 2 (o), T l# 3 (+ ), and T l# 4 (□).
k
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108
attenuation, prevented us from determine the phase shift accurately a t temperatures
far below T“ w.
Figures 4.37 and 4.38 show ff1 and <r2 for the samples under discussion.
Note
th at in the normal state the conductivity for films T I#1, 2, and 3 exhibit a
metallic-like behavior as for the YBa2Cu30 7.£ and Bi-Sr-Ca-Cu-O systems, already
discussed.
Values for <r1 of 1.4 x 10s and 3.5 x 10s S /m were obtained for
sample T l # l a t room tem perature and a t T“ w, respectively.
the ffj '3 close to zero for all the films.
In the normal state
The increase in <r^ and
in going
through the T™w into the superconducting state, observed for all the previously
discussed HTS thin films, is also manifested in these samples.
Observe th at, for
sample T l # l , <rL goes through a maximum at 107 K and saturates a t temperatures
below 100 K, while for samples T l# 2 and T l# 3 o l continues to increase leveling
off a t tem peratures below 105 and 90 K, respectively.
For sample T l# 4 , <rl
increases below T™w and continues increasing monotonically with decreasing
tem perature.
On the other hand, <r2 is close to zero in the normal state as
expected for a good conductor, increases rapidly as the tem perature is lowered
below T “ w and continues increasing at a slower rate a t tem peratures below
approximately 95 K.
The <r2 shows a similar behavior for samples T l # l , 2 and
3, by increasing rapidly below T™w and leveling off at low temperatures. This
feature is more pronounced for sample T l # l , which starts to level off at
tem peratures of ~ 95 K, and less pronounced for sample T l# 3 , which begins to
I
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109
1.0x10s
ttA &
|
a x* a -.
0.0
i
u
-0.5
60
70
80
90
100
110
120
130
Temperature (K)
0.8x10®
0.6
o2
f
SG.
|
0.4
3
•3
o
<’t^w*’sSSS5*^
O
-
0.2
60
70
80
90
100
110
120
130
Temperature (K)
Figure 4.37: Tem perature dependence of <r^ and o2 f°r samples T l # l (a),
and T l# 2 (b).
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110
°
A 02
> «4.a —
***
A A A A A A
(a)
, J m in m lM .tm M L n u ttt! » ..iM i iin in n n li n m i.« lm m .» L M » im lm » ....l.im ...,l ...,.....1 ...t..M .l....M ...i ....o ...1 ....M « t,
«
19
29
28
-18
59
S8
79
U0
90
100
110
120
130
140
IISO
TEMPERATURE <JO
i| iii»iuu|»m iu u |u iiiin nu iiiim n nu uii{ iu» »n i)|nn i
29
30
48
50
88
78
89
90
180
1 10
1 20
1 30
1 40
158
TETffERRTURE CIO
Figure 4.38: Temperature dependence of a j and <r2 f°r samples T l# 3 (a),
and T l# 4 (b).
k
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I ll
level off a t tem peratures below 30 K.
The <r2 for sample T l# 4 shows a
qualitatively different behavior, increasing slowly with decreasing tem perature and
reaching values of only 2 x 10s S /m a t 30 K.
The Rg for the Tl-based films can be calculated from equation (2.4.4) of
chapter 2.
The calculated surface resistances of the four samples are compared in
figure 4.39 with th a t of copper as measured by a resonant cavity technique.
Also
given is the theoretically expected value for the Rg of copper a t 77 K and 30.6
GHz.
The smallest Rg values for the films correspond to sample T l # l , with an
Rg a t 77 K of approximately 62 mft.
Samples T l # l , 2, and 3 show a residual
surface resistance larger than th at of copper a t all temperatures.
This residual
resistance has been explained, for the case of YBa^CugOy.^ superconducting thin
films,54 in terms of the grains being separated by weak links which enhance the
microwave energy losses.
Figure 4.40 shows the values of the penetration depth A corresponding to
samples T l # l , 2, and 3.
We have not plotted the data corresponding to sample
T l# 4 for clarity; this sample has values of A~ 1.8 /im a t 20 K.
In general, these
values of A were approximately a factor of Vfc the values for A calculated from the
measured <r2, using equation (2.2.6).
As for the YBa2Cu30 7_(j and Bi-Sr-Ca-Cu-0
thin films, we have made a fit to the d ata of samples T l # l , 2, and 3, using the
tem perature dependence for A according to the two-fluid model (see equation 2.2.5).
It was found th at for films T l # l and T l# 2 the d ata agrees well with the
empirical two-fluid model, as shown in figure 4.41 for sample T l # l .
From this
analysis we calculated a zero-temperature penetration depth value for samples T l # l
i
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112
tjiiin iw |M !m t« |u n im i|iiiTm H |n m n n |m
C3
af
++* ++H-++«"W'W+'
19
29
39
49
SB
69
79
19
t l n
I...
99
19 9
t t . .........
1 19
12 9
139
TEMPERATURE CK)
Figure
4.39:
Calculated
values
of
the
surface
resistance
Rg versus
tem perature a t 30.6 GHz for samples T l # l (A ), T l# 2 (o), T l# 3 (+ ), and
T l# 4
(□).
Also shown are the measured Rg for C u
(v), and its
theoretically predicted value a t 77 K (♦), for comparison purposes.
and T l# 2 of A0 = 1004 ± 24 nm and A0 = 1113 ± 24 nm, respectively.
For
sample T l# 3 we obtained A0 = 1011 ± 49 nm, although for this sample we
observed th at the fit to the experimented d a ta was not as good as for the T l # l
and T l# 2 samples.
However, using the following expression for A(T),
A(T) = A0[2(l - T /T c)]-,a
for
T —» T c
(4.4.1)
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113
S
©.
2
© © © © © © © © c©
©«©©<
A A A A A A A A A A A 1 1 * *1* '
+++ + ++^ +
t
9
^
2a
39
7a
40
aa
99
no
Figure 4.40: Magnetic penetration depth A for samples T l # l (A ), T l# 2 (o),
and T l# 3 (+ ). D ata for sample T l# 4 have been om itted for clarity.
which is valid in the BCS theory clean lim it,55’25 we obtained an excellent
agreement with the experimental data.
was Aq = 926 ± 9 nm.
The resulting A0 value for sample T l# 3
Nevertheless, these A0 are way above those measured by
muon spin rotation, AQ = 185 nm, in the Tl-based superconducting compound.56
The largeness of A may be the result of the poor connectivity between the
superconducting grains, as shown by the SEM in figures 4.34 and 4.35.
This poor
connectivity between grains has caused low critical current density values in zero
field ( ~ 5 x 104 A /cm 2 a t 77 K) obtained for similar Tl-based films,57 and may
be the cause of the low T^c values measured in our films when compared with
those reported by others (T6c > 106 K).58,59
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114
g
4.
t.s
AA
38
50
80
90
100
Figure 4.41: M agnetic penetration depth A versus tem perature for sample
T l # l . The solid line represents a fit to the d a ta using the tem perature
dependence for A according to the two-fluid model.
4.5 Closing Remarks
We have studied the microwave response of YBa2Cu30 7_j, Bi-based, and Tlbased HTS thin films.
We have measured the transm itted power as a function
of tem perature, incident power, and film thickness.
We found th a t the microwave
transmission properties are weakly dependent on tem perature in the normal state,
but change drastically upon transition to the superconducting state.
In particular,
the transmission decreases and there is a negative relative phase shift with respect
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115
to the phase a t room tem perature when the sample is cooled through its transition
tem perature.
The magnetic penetration depth for all films was determined from the surface
reactance of the films.
We found th at the smallest penetration depth values were
obtained for the YBa2Cu30 7_£ films whose values of A were consistent with the
best values reported by others so far.
We were able to verify experimentally the
intrinsic anisotropy of A for this HTS superconductor by measuring this parameter
in c-axis and predominantly a-axis oriented thin films.
As expected from the
intrinsic anisotropy of these HTS materials, the value of A for the a-axis oriented
film was larger than the values obtained for c-axis oriented films.
In fact, the
ratio of A for an a-axis oriented film to th at of c-axis oriented films agrees very
well with
that reported
superconductor.
by others for single crystals of the
YBa2Cu30 7.j
We also observed th a t A increased with increasing film thickness
which is consistent with the increase of the number of a-axis oriented grains and
other structural and material defects with increasing film thickness.
From the
thickness dependence of A we were able to estim ate, for the first time, the
intrinsic value of A for the YBa2Cu30 7 ^ superconductor.
This value is consistent
with th at expected from measurements of A in single crystals by other techniques.
The A values for the Bi-based films and Tl-based films were larger than those
obtained for the Y B a jC u jO ^ films, and for the Tl-based films the calculated A
values were larger than the best reported values up to date.
We have seen that
these large values may be associated with the poor grain connectivity exhibited by
these films.
f
Values for A were also determined from the measured <r2.
It was
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116
found th at the values of A calculated in this manner were larger than those
obtained from Xg.
The microwave complex conductivity was determined in both the normal and
the superconducting state.
The largest values for the conductivity in the normal
state were obtained for the YBa2Cu30 7.£.
observed th a t both
state.
For the three types of HTS films we
and <r2 increased upon transition to the superconducting
This implies th at the tem perature dependence of
predictions of the two-fluid model.
dependence of
deviates from the
In addition, we found th a t the tem perature
is not consistent with th a t expected from the M attis-Bardeen
equations, and the BCS theory.
YBa2Cu30 7_j thin films.
The largest values for <r2 were measured for the
We found that for the Bi-based and Tl-based films we
were able to measure ffl for all measurable tem peratures below T “ w, while for
most of the YBa2Cu30 7.£ films we were unable to measure <r1 for temperatures
far below T“ w.
We have calculated the surface resistance Rg for the three types of HTS films
studied.
We found th at for high quality YBa2Cu30 7 ^ thin films the Rg values
at 77 K compared fairly well with those reported by other researchers for similar
films and were equal or smellier them th at for copper a t the same frequencies and
tem perature.
However, for the Bi-based and Tl-based films the calculated Rg
values were larger than those of Y B ajC ujO ^^ thin films and copper for all the
tem peratures considered in this study.
O ur analysis suggests th a t, among those studied, the laser ablated and dc offaxis magnetron sputtered YBa2Cu30 7,^ thin films are the most promising for
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117
microwave
applications.
However,
we
believe
th at
improvements
in
the
superconducting properties of Bi-based and Tl-based HTS thin films could be
achieved by using ” in-situ” deposition techniques.
In our case, the fabrication of
both the Bi-based and the Tl-based films included a post-deposition heat treatm ent.
It has been observed th at YBa2Cu30 7.£ thin films preparation processes which
include a post-deposition annealing, such sis sequential evaporation, yield films
which are of lower quality than those deposited by " in-situ” techniques such as
laser ablation.
The merits of our experimental technique have been tested against widely
accepted characterization techniques, such as resonant cavity measurements.
The
consistency of the Rg values measured using both techniques support the validity
of our method.
The strength of our technique is th at it allows the calculation of
several transport param eters, such as A, a , and Rg, from one single measurement,
an attribute rarely found in any other probing technique actually employed in HTS
films research.
The versatility of our technique rests not only in yielding values
for A, a , and Rg in good agreement w ith those obtained by other techniques, but
also in being sensitive to the intrinsic anisotropy of these materials, as evidenced
by the A results for YBa2Cu30 7.£ thin films.
N
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118
4.6
References
1.
Talvacchio, J.; and Wagner, G. R.: H ig h -T c F ilm D evelo p m en t for E lectronic
A p p lic a tio n s, in Superconductivity Applications for Infrared and Microwave
Devices, SPIE Proc. 1292, 2-12 (1990).
2.
Harshmann, D. R.; Schneemeyer, L. F.; Waszczak, J. V.; Aeppli, G.; Cava,
R. J.; Batlogg, B.; Rupp, L. W.; Ansaldo, E. J.; and Williams, D. LI.:
M a g n etic P en etra tio n D ep th in S in g le-C rysta l Y B a 2C u30 7m^ Phys. Rev. B
39, 851-854 (1989).
3.
Krusin-Elbaum, L.; Greene, R. L.; Holtzberg, F.; Malozemoff, A. P.; and
Yeshurun, Y.: D irect M ea su rem en t o f th e T em pera tu re-D ependent M agnetic
P en etra tio n D ep th in Y -B a-C u-O C rysta ls, Phys. Rev. Lett. 62, 217-220
(1989).
4.
Klein, N.; Muller, G.; Piel, H.; Roas, B.; Schultz, L.; Klein, U.; and Peiniger,
M.: M illim e ter W ave Surface R esista n ce o f E p ita x ia lly G row n Y B a 2C u30 7mj
T h in F ilm s, Appl. Phys. Lett. 54, 757-759 (1989).
5.
Qiu, X. G.; Cui, C. G.; Zhang, Y. Z.; Li, S. L.; Zhao, Y. Y.; Xu, P.; and
Li, L.: C ritical C urrent M ea su rem en ts in Y B a 2C u30 7_x T hin F ilm G rown
L a A 1 0 3 su b stra te, J. Appl. Phys. 68, 884-886 (1990).
6.
M iranda, F. A.; Gordon, W. L.; Bhasin, K. B.; Heinen, V. O.; W arner, J. D.;
and Valeo, G. J.: M illim eter W ave Transm ission S tu d ies o f Y B a2C u30 7m$
T h in F ilm s in th e 26.5 to 40.0 G H z F requency R ange, Superconductivity
and Applications, Plenum Press, 735-748 (1990).
7. Sridhar, S.: M icrow ave D ynam ics o f Q uasiparticles a n d C ritical F ields in
Su p erco n d u ctin g F ilm s, Ph.D. Thesis, California Institute of Technology,
(1983).
8. Anlage, S.; Sze, H.; Snortland, H. J.; Tahara, S.; Langley, B.; Eom, C. B.;
and M. R. Beasley: M easurem en ts o f th e M agnetic P enetratio n D epth in
Y B a 2C u30 7_g T hin F ilm s b y th e M icro strip R eso n a to r Technique, Appl.
Phys. Lett. 54, 2710-2712 (1989).
9. England, P.; Venkatesan, T.; Wu, X. D.; Inam, A.; Hedge, M. S.; Cheeks, T.
L.;
and
Craighead,
H.
G.:
Intrinsic
Superconductor/N orm alM e ta l/S u p e rc o n d u c to r-like W eak L in k s in Y B a 2C u30 7 x T hin F ilm s, Appl.
Phys. Lett. 53, 2336-2338 (1988).
10. Dubson, M. A.; Herbert, S. T.; Calabrese, J. J.; Harris, D. C.; Patton, B. R.;
kft
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w ith o u t perm ission.
119
Garland, J. C.: N onrO hm ic D issip a tive R eg im e in th e S uperconducting
Transition o f P oiycrystallin e Y jB a 2C u3Ox, Phys. Rev. Lett. 60, 1061-1064
(1988).
11. Nichols, C. S.; Shiren, N. S.; Laibowitz, R. B.; and Kazyaka, T. G.:
M icrow ave S tu d ie s T hrough F ilm s o f Y B a 2C u30 7mfr Phys. Rev. B 38,
11970-11973 (1988).
12. Blazey, K. W., Muller, K. A.; Bednorz, J. G.; Belinger, W.; Amoretti, G.;
Buluggiu, E.; Vera, A.; and M atacotta, F. C.: Low -F ield M icrow ave
A b so rp tio n in th e S u p ercon ducting C opper O xides, Phys. Rev. B 36, 72417243 (1987).
13. Wu, D. H.; Shiftman, C. A.; and Sridhar, S.: F ield V ariation o f the
P en etra tio n D ep th in C eram ic Y ^ a j C u j O ^ Phys. Rev. B 38, 9311-9314
(1988).
14. Golosovsky, M.; Davidov, D.; Rettori, C.; and Stern A.: M a g n etic Field
M o d u la tio n E ffects on th e M icrow ave Transm ission T hrough Superconducting
T hin F iim s o f Y-B a-C u-O , Phys. Rev. B 40, 9299-9302 (1989).
15. Bardeen, J.; Ginsberg, D. M.; and Salamon, M. B.: E xcito n ic S u p erc o n d u c tivity
in L a yer S tructures, Novel Superconductivity, eds. S. A. Wolf, and V.
Kresin, Plenum Press, 333-339 (1987).
16. Ramesh, R.; Chang, C. C.; Ravi, T. S.; Hwang, D. M.; Inam, A.; Xi, X. X.;
Li, Q.; Wu, X. D.; and Venkatesan, T.: S tru c tu ra l P erfection o f Y-B a-C uO T h in F ilm s C ontrolled b y th e G row th M echanism , Appl. Phys. Lett. 57,
1064-1066 (1990).
17. Phillips, J. M.; Siegal, M. P.; Perry, C. L.; and M arshall, J. H.: Com parison
o f B a 3 Y C u30 7 ^ F ilm s on N d G a 0 3 and L a A lO ^ to be published in IEEE
Trans, on Magnetics (1991).
18. Shah, S. I.; and Carcia, P. F.: S u p e rc o n d u c tiv ity and R e sp u tte rin g E ffe cts in
R f S p u tte re d Y B a 2C u30 7,x T h in F ilm s, Appl. Phys. Lett. 51, 2146-2148
(1987).
19. Migliuolo, M.; Belan, R. M.; and Brewer, J. A.: A bsence o f N egative Ions
E ffe c ts D uring O n -A xis Single T arget S p u tte r D epositions o f Y -B a-C u-O
T h in F ilm s on S i(l0 0 ), Appl. Phys. Lett. 56, 2572-2574 (1990).
20. Venkatesan, T.: Private Communication.
21. Talvacchio, J.: Private Communication.
k
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w ith o u t perm ission.
120
22. Chorey, C. M.; Bhasin, K. B.; Warner, J. D.; Josefowicz, J. Y.; Rensch, D.
B.; and Nieh, C. W.: An E x p erim en ta l S tu d y o f High T c S u percon ducting
M ic ro strip T ransm ission L ines a t 35 G H x a n d th e E ffe ct o f F ilm
M orphology, Presented a t the ” 1990 Applied Superconductivity Conference” ,
sponsored by the Institute of Electrical and Electronics Engineers, Aspen,
Colorado, September 24-28, 1990.
23. Drabeck, L.; Carini, J. P.; Gruner, G.; Hylton, T.; Char, K.; and Beasley, M.
R.: P ow er-law T em p era tu re D ependence o f th e E lectro d yn a m ic P roperties
in O riented Y B a 3C u30 7,g a n d Y 2 B a 4C u g0 16_g F ilm s, Phys. Rev. B 39,785788 (1989).
24.
Chi, H.; Nagi, A. D. S.: M a g n etic P en etra tio n D ep th
Superconductors, Phys. Rev. B 40, 7361-7363 (1989).
of
H ig h -T c
25. Schilling, A.; Hulliger, F.; and O tt, H. R.: M e a su re m en t o f th e London
P enetration D ep th on Y B a 3C u4O g a n d Y B a 3C u30 7 P olycrystals, Physica C
168, 272-278 (1990).
26. Kobrin, P. H.; Ho, W.; Hall, W. F.; Hood, P.J.; Gergis, I. S.; and Harker, A.
B.: M illim eterw a ve C o m p lex C o n d u c tiv ity o f so m e E p ita x ia l Y B a 3C u30 7mg
F ilm s, Phys. Rev. B 42, 6259-6263 (1990).
27. Drabeck, L.; Gruner, G.; Chang, J. J.; Inam, A.; Wu, X. D.; Nazar, L.;
Venkatesan, T.; Scalapino, D. J.: M illim ete r-w a re Surface Im pedance o f
Y B 3C u30 7mg T hin F ilm s, Phys. Rev. B 40, 7350-7353 (1989).
28. Klein, N.; Muller, G.; Orbach, S.; Piel, H.; Chaloupka, H. Roas, B.; Schultz,
L.; Klein, U.; and Peiniger, M.: M illim e te r W a ve Surface R esista n ce and
L ondon P en etratio n D ep th o f Y B a 3Cu$0 7 g T hin F ilm s, Physica C 162-164,
1549-1550 (1989).
29. Hylton, T. L.; Beasley, M. R.; Kapitulnik, A.; Carini, J. P.; Drabeck, L.; and
Gruner, G.: Surface Im pedance S tu d ies o f th e H ig h -T c O xide
Superconductors, IEEE Trans, on Magnetics 25, 810-813 (1989).
30. Klein, N.; Chaloupka, H.; Muller, G.; Orbach, S.; Piel, H.; Roas, B.; Schultz,
L.; Klein, U.; and Peiniger, M.: T h e E ffe ctiv e M icro w a ve Surface Im pedance
o f High- T c T h in F ilm s, J. Appl. Phys. 67, 6940-6945 (1990).
31. Piel, H.; and Muller, G.: T h e M icrow ave Surface Im pedance o f H ig h -T c
Superconductors, presented at the ” 1990 Applied Superconductivity
Conference”, sponsored by the IEEE, Aspen, Colorado, September 24-28,
1990; Also to be published in the IEEE Trans, on Magn. (1991).
f
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.
121
32. M attis, D. C.; and Bardeen, J.: T h eo ry o f the A n o m a lo u s Skin E ffec t in
N orm a l a n d Superconductin g M eta ls, Phys. Rev. I l l , 412-417 (1958).
33. Tinkham, M.: Intro d u ctio n to S u p e rc o n d u c tivity , (Krieger, M alabar, FL, 1985).
34. Bardeen, J.; Cooper, L. N.; and Schrieffer, J. R.: T h eo ry o f S u p erc o n d u ctiv ity,
Phys. Rev. 108, 1175-1204 (1957).
35. Hebei, L. C.; and Slichter, C. P.: N uclear S pin R ela xa tio n in N orm al and
Superco nducting A lu m in u m , Phys. Rev. 107, 901 (1957); 113, 1504-1519
(1959).
36. W arren, W. W.; W alstedt, R. E.; Brennert, G. F.; Espinosa, G. P.; and
Rameika, J. P.: E vidence fo r T w o P a irin g E nergies from N uclear SpinL a ttic e R elaxation in S uperconducting B a 2 Y C u 30 ^ f i Phys. Rev. Lett. 59,
1860-1863 (1987).
37. Ho, W.; Hood, P. J.; Hall, W. F.; Kobrin, P.; Harker, A. B.; and DeWames,
R. E.: M illim eter-w ave C om plex C o n d u c tiv ity M ea su rem en ts o f Bi-C a-Sr-C uO Supercondu cting T hin F ilm s, Phys. Rev. B 38, 7029-7032 (1988).
38. Bhasin, K. B.; W arner, J. D.; Chorey, C. M.; Ebihara, B. T.; Romanofsky,
R. R.; Heinen, V. O.; M iranda, F. A.; and Gordon, W. L.: M icrow ave
C o n d u c tiv ity o f Laser A b la te d Y B a 2Cu30 7_ j S u p erco n d u ctin g T hin F ilm s
and Its R elation to M icro strip Transm ission L ine P erform ance, NASA CP
10043 , 78-81 (1990).
39. Bhasin, K. B.; W arner, J. D.; Romanofsky, R. R.; Heinen, V. O.; Chorey, C.
M.; Kong, K. S.; Lee, H. Y.; and Itoh, T.: P erform ance a n d M o d eling o f
S upercondu cting R in g R esonators a t M illim eter-w a ve Frequencies, IEEE
MTT-S International Microwave Symposium Digest 1, 269-272 (1990).
40. Hu, Q.; and Richards, P. L.: D esign A n a ly sis o f a H igh T c S u percon ducting
M icrobolom eter, Appl. Phys. Lett. 55, 2444-2446 (1989).
41. Newman, N; Char,
C. B.; Geballe,
F ilm s w ith L o w
Phys. Lett. 57,
K.; Garrison, S. M.; Barton, R. W.; Taber, R. C.; Eom,
T. H.; and Wilkens, B.: YB a2C u30 7mg Sup ercond ucting
M icrow ave Surface R esista nce O ver Large A reas, Appl.
520-522 (1990).
42. Sridhar, S.: M icrow ave R esponse o f T h in F ilm Superconductors, J. Appl. Phys.
63, 159-166 (1988).
43. Larson, D. C.: P hysics o f T hin F ilm s, 6, 83 (1971).
r
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.
122
44. Carini, J. P.; Awasthi, A. M.; Beyermann, W.; Gruner, G.; Hylton, T.; Char,
K.; Beasley, M. R.; and Kapitulnik, A.: M illim eter-w ave Surface R esista nce
M ea su rem en ts in H ig h ly O riented Y B a 2Cu30 7mg T hin F ilm s, Phys. Rev. B.
37, 9726-9729 (1988).
45. Sridhar, S.; and Kennedy, W.: N ovel T echnique to Measure th e M icrow ave
R esponse o f High T c Superconductors B etw een 4.2 and 200 K , Rev. Sci.
Instrum. 59, 531-536 (1988).
46. Bhasin, K. B.; W arner, J. D.; M iranda, F. A.; Gordon, W. L.; and Newman,
H. S.: D eterm in a tio n o f Surface R esistance a n d M a g n etic P en etra tion D ep th
o f S u p erconducting Y B a2Cu30 7 j T hin F ilm s b y M icrow ave P o w er
Transm ission M ea surem ents, to be published in IEEE Trans, on Magnetics
(1991), and NASA TM-103616 (1990).
47. Maeda, H; Tanaka, Y; Fukutomi, M.; and Asano, T.: A N e w H ig h -T c O xide
Superconductor W ith o u t a R are E arth E lem en t, Jpn. J. Appl. Phys. 27,
L209-L210, (1988).
48. Valeo, G. J; Rohrer, N. J.; W arner, J. D.; and Bhasin, K. B.: Seq u en tia lly
E va p o ra ted T hin Y-B a-C u-O Superconductor Film s: C om position a nd
P rocessing E ffects, American Institute of Physics, Proceedings no. 182, 147152 (1989).
49. Kalkur, T. S.; Kwor, R.; Jernigan, S.; and Smith, R.: C oevaporated Bi-Sr-CaCu O xide Superco n d u ctin g F ilm s and T heir P attern in g , presented at the
Conf. Sci. Technol. Thin Films Supercond., Colorado Springs, CO, 14-18
November (1988).
50. Balestrino, G.; Foglietti, V.; Marinelli, M.; Milani, E.; Paoletti, A.; and Paroli,
P.: T ra n sp o rt C ritical C urrent D en sity in E pita xia l B i2Sr2Ca1C u2Og+x
F ilm s: E ffe cts O f th e S u b stra te T w inning, Appl. Phys. Lett. 57, 2359-2361
(1990).
51. M iranda, F. A.; Bhasin, K. B.; Heinen, V. O.; Kwor, R.; and Kalkur, T. S.:
M icrow ave c o n d u c tiv ity o f superconducting B i-Sr-C a-C u-O thin film s in the
26.5 to 40.0 G H z frequency range, Physica C 168, 91-98 (1990).
52. Ashcroft, N. W.; and Mermin, N. D.: Solid S ta te P hysics, Holt, Rinehart and
Winston, 8 (1976).
53. Torardi, C. C.; Subramanian, M. A.; Calabrese, j . C.; Gopalakrishnan, J.;
Morrissey, K. J.; Askew, T. R.; Flippen, R. B.; Chowdhry, U.; and Sleight,
A. W.: C rysta l S tru c tu re o f T l ^ a 2C a2Cu3O 10, a 125 K Superconductor,
Science 240, 631-634 (1988).
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.
123
54. Hylton, T. L.; Kapitulnik, A.; Beasley, M. R.; Carini, J. P.; Drabeck, L.; and
Gruner, G.: W ea kly C oupled G rain M o d el o f H igh-frequency Losses in High
T c S u p ercondu cting T h in F ilm s, Appl. Phys. Lett. 53, 1343-1345 (1988).
55. Muhlschlegel, B.: D ie T herm odynam ischen F u n ktio n en des Supraleiters, Z. Phys.
155, 313-327 (1959).
56. Lichti, R. L.; Chan, K. C. B.; Cooke, D. W.; and Boekema, C.: C oupling
S tre n g th s and F lu x P in n in g in O xide Superconductors, Appl. Phys. Lett.
54, 2361-2363 (1989).
57. Ianno, N. J.: P ulsed Laser D eposition o f Tl-Ca-Ba- C u-O film s a t 248 n m ,
Presented a t the 2nd Conf. on the Science and Technology of Thin Films
Superconductors, Denver, Co. March 29- April 1, 1990.
58. Olson, W. L.; Eddy, M. M.; James, T. W.; Hammond, R. B.; Gruner, G; and
Drabeck, L.: P reparation o f S u p ercondu cting Tl-C arB a-C u T hin F ilm s by
C hem ical D eposition, Appl. Phys. Lett. 55, 188-190, (1989).
59. Chang, L. D.; Moskowitz, M. J.; Hammond, R. B.; Eddy, M. M.; Olson, W.
L.; Casavant, D. D.; Smith E. J.; and Robinson, M.: M icrow ave Surface
R esista n ce in Tl-based Superco n d u ctin g T h in F ilm s, Appl. Phys. Lett. 55,
1357-1359 (1989).
t—
k
R eproduced w ith perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
Chapter 5
Measurement of Surface Resistance
Using a Resonant Cavity Method
5.1 Introduction
In the selection of conductors to be used for microwave applications one of the
parameters th at must be known is the surface resistance (Rg) of the material.
This param eter is of importance since it determines the losses and signal distortion
in transmission lines, resonators, and interconnects.
Microwave loss measurements
are ideal for probing the nature of the superconducting state in the new high
transition tem perature (high-Tc) superconductors.
only
can be used as a
probe which directly
Therefore, Rg measurements not
provides information
on the
mechanisms of superconductivity in these superconducting copper oxides, but also
yield an im portant figure of merit in the determ ination of their suitability for
microwave applications.
One of the simplest ways to measure the Rg is to place the superconductor in
a high-Q resonant cavity.
In this technique the sample to be tested can actually
be physically placed inside the cavity a t the microwave magnetic or electric field
maximum, or it can be mounted as one of the end walls of the resonant cavity.
In both cases, the Rg of the sample under study can be determined by measuring
the change in cavity Q from th at without the sample.
124
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125
In this study we have used a TE013-mode, gold-plated copper cavity resonant
a t 58.6 GHz to measure the Rg of high-Tc superconducting thin films.
To the
best of our knowledge, our Rg measurements have been the first performed a t this
frequency in the new high tem perature superconducting (HTS) materials.
We were
interested in determining how the microwave losses a t the surface of these
superconducting thin films compare with those of very good conductors such as
copper and gold, which are generally used in the fabrication of microstrip
transmission lines due to their low microwave losses.
In the followings sections of this chapter we will briefly discuss the cavity
fabrication process, the theoretical aspects and experimental techniques employed
in the measurements of the cavity Q, and the Rg results for some of the
superconducting samples considered in this work.
5.2
Resonant Cavity Fabrication
For this work we have fabricated a cylindrical resonant cavity operating in the
TE013 resonant mode.
The cavity was made of oxygen free high conductivity
copper (OFHC) and was gold plated afterwards to avoid oxidation.
the cavity taken during the fabrication process is shown in figure 5.1.
A picture of
The cavity
was designed to resonate a t 60.0 GHz, having a diameter of 0.500 inches and a
length of 0.335 inches.
The cavity is coupled to the microwave source through
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126
Figure 5.1: Top view of the TE013 resonant cavity developed for the
determination of Rg. The superconducting sample is placed on top of the
cavity replacing the gold plated tablet shown in the figure. The change in
the cavity Q when the sample is used as the end wall determines the Ra
of the superconducting thin film.
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127
a coupling iris 0.060 inches in diameter and 0.020 inches long.
The expression for
the resonance frequency is given by1
u mnp = c O ^ r ^ X ' ^ / a ) 2 + (p x /l)2]
’/i
(5.2.1)
where m = 0,l,2,... is the radial mode number, n= l,2,3... and p= l,2,3,... the
azim uthal and z-axis mode numbers respectively,
Bessel’s equation J m(x)=0, a is the cavity radius,
'
is
and
fcft
the n
root of the
Iis the length of the
cavity.
The main advantage of the TE01p modes for this type of measurement is th at
in this configuration the currents circulate azim uthally,2 therefore diminishing the
risks of leakages of microwave energy to the exterior of the cavity.
Furthermore,
when combined with the wall-replacement technique for Rg measurements this
selection of modes keeps the field structure relatively
undisturbed when the cavity
end wall is replaced by the superconducting sample.
5.3
Definition of Quality Factor Q
The coordinate system for the cylindrical cavity is shown in figure 5.2.
For
a T E mode the transverse wave equation for ip=Hv subject to the boundary
condition dip
~3F
has the solution,1
^ W ) = J m( ' W ) e±im^
F
(5.3.!)
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128
► y
X
Figure 5.2: Coordinate system for a cylindrical cavity of radius a and
length (.
with,
'W = X 'mn/ a
(5.3.2)
The resonant frequencies for the T E mnp modes are given by equation (5.2.1).
The field equations for the T E 01p family of modes are,
H *= H oJ o (<l o i ^ / a )s i n ( P ,r* / 0
(5-3.3)
Hp=pxaH oJ o(q01p/a)co s(p irz/0 /lq 01
(5.3.4)
E^=j2rfMoaHoJ o(q01p/a)sin (p * -z/Ij/q ^
(5.3.5)
k
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129
where q01=3.8317 is the first zero of J t and p is the longitudinal mode number.
Note th at the electric field E tangential to the surface is always azimuthal and
therefore the
currents
will
always be
azimuthaily
directed,
leading
to
the
advantages discussed in section 5.2 .
The quality factor (Q) of
the resonant cavity is defined as,
(jfm axim um energy stored inside the cavity)
Q = — ------------------------r r - .
j -------------------------power dissipated
(5.3.6)
Thus, in order to evaluate the Q of the cavity one m ust determine the maximum
energy stored in the electromagnetic fields inside the cavity and the am ount
power dissipated through the
walls of the cavity.
of
The maximum energy stored
inside the cavity is given by
U=V4/e | E | 2dV
(5.3.7)
V
and for the case under consideration E is given by equation (5.3.5).
u = V4c/ q/ qT/ 5 |
=
Thus,
| rd^drdz
V 4 c /o /o T / o { 4 T f2 ^ o a 2 1H o 12 j 02(ck u r / a ) s in 2 (I1,rz/ O / q ^ J r d t f d r d z
= (4T3a 2cfVo/qjji)/J5rdr{ IH0 12J o2(q01r/a ) /js in 2(nxz/|)dz}
T3a S f V ol|H o | 2(-Jo(q01)J 2(q01))
fc
M
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130
The problem of calculating the power dissipated at the cavity walls can be
divided in two parts by first considering the power loss a t the side walls of the
cavity and then the loss a t its end walls.
Note th at the latter should also be
separated for the case in which one of the end walls is replaced by the
superconducting sample.
In all cases, the power loss per unit area is given by
Vi | Ht | 2R s, where Ht is the tangential component of the magnetic field H a t the
wall and Rg is the surface resistance of the m aterial of which the cavity is made.
In the equations below, we define Rgl as the surface resistance of the cavity metal,
and Rg2 as the surface resistance of the thin film.
First, we are going to calculate the power dissipated a t the end walls of the
cavity w ithout the sample in place.
The tangential field is Hy as shown in figure
5.3.
r
Figure 5.3:
cavity.
Tangential fields a t the end plates and side walls of the
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131
Using (5.3.4) we have
P «,= VS«,l/|H t |*dS
s
= V y W f d ^ r d r IH0 12Jo2(q01r/a )n 2ir2a2cos2(nirz/1)
= ir3n2a2 1H„ | 2 Rgi;5 Jo2(q01r/a )rd r
(Moi)2
= ^ W lH pl2 R.iK.OW-^qoi))
(5>3<9)
2(*qoi)2
To account for the power dissipated a t both end walls we ju st have to
multiply (5.3.9) by 2.
The power dissipated at the side walls of the cavity can be calculated using
Ht= H 1 as given by equation (5.3.3).
Hence,
P sw= V5rR9l/ | H , | 2ds
= V & a IH o 12/o/oT{j2(qoir/a)9in2(nW*)}dzad*
=
IH0 12a J2(q0i ) ^
(5.3.10)
Therefore, from (5.3.6), (5.3.8), (5.3.9), and (5.3.10) we have th at the Q-factor
for the test cavity is given by
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132
u 0x 3a * d 2fi0t | H0 12(-J0(qoi) J 2(qoi))
Q i =■
(qoi|Hor)Rsl{%aJ2(qoi)lx +
(5.3.11)
which can be w ritten as
8(xlaf)3e/i*(-Jo(q0i)J ,(q Oi))
Q t = --------------------------------------------------------------------
(5.3.12)
" 4T2a3n2J0(qoi)J2(qoi)]
From equation (5.3.12) it is very clear that by measuring Qx one can obtain
the surface resistance Rgl of the m aterial of the cavity walls.
When one of the
end walls of the cavity is replaced by the superconducting thin film, equation
(5.3.12) becomes
_
8(Tfaf)3e/i2(-Jo(q01)J2(q01)
^■1 [2 ^ C<loi*^0 C*Joi))*1 * ^(Tn)2a3^o((loi)^ 2 ((loi)[®»l
^§ 2!
(5.3.13)
where Rg2 is the surface resistance of the thin Him.
Observe th a t in the
denominator of (5.3.13), the contributions of the two end walls of the cavity to
the total dissipated power have been separated since Rgl * Rg2.
For our cavity we have,
t = depth of the cavity = 8.509xl0'3 meters
i?
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133
a = cavity radius = 6.350xl0‘3 meters
f = resonant frequency = 58.598125 GHz
p = longitudinal mode number = 3
q ^ = the first zero of J j = 3.8317
Also,
H0 = permeability of free space = 1.257xl0*6 H /m
e0 = perm ittivity of free space = 8.854xl0'12 F /m
J o f o o i ^ ^ l ) = -0.1622
Jo(%i) = 0-1622
Thus, the general procedure is to first obtain Rgl from the
and other
param eters of the cavity w ithout the sample in place, and then to determine Rg2
from Rgl and the quality factor Q2 corresponding to the cavity w ith one of its
end walls replaced with the thin film.
5.4 Measurement of the Quality FactorQ
In this section we are going to discuss how to determine the quality factor Q
of the cavity.
Basically, we will follow Ginzton’s impedance method,3,4 in which
the Q-factor of the cavity is determined by measuring the reflection coefficient.
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134
A microwave resonant cavity can be represented by a conventional lumpedparam eter RLC resonant circuit, as shown in figure 5.4.
Standard circuit analysis
for the input impedance gives
(5.4.1)
I, =
1 + jQ (
where Q = R / wqL, and wQ= (l/L C )
-1 )
(J
The input impedance is real and reaches its
maximum absolute value (Z.=R) a t w=wQ.
To calculate Q, one m ust determine
O
O
<o
Figure 5.4:
Lumped-parameter RLC resonant circuit.
I
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135
w0 and the two frequencies w1 (< w j and u/2 (> u 0) a t which |Z j| falls to 0.707
of its maximum value; i.e.,
<j„
Q =-
(5.4.2)
Since the microwave cavity must be coupled to a transmission line while the
measurements are performed, the input impedance Z> will be modified.
In general,
the coupling between the resonator and the transmission feed line contains resistive
and reactive components.
Therefore, the resonant circuit will be loaded by these
lossy components which, in addition to the characteristic impedance of the
transmission line, will result in a loaded quality factor (Q jJ different from the
unloaded quality factor (Q) characteristic of the resonator when not perturbed by
the coupling mechanisms.
For this situation one finds,
Q = Ql (1 + «)
(5.4.3)
where it is the coupling coefficient, which is defined as the ratio of the impedance
of the resonant cavity at resonance to the characteristic impedance of the
transmission line.
The coupling coefficient it is related to Tr, the cavity reflection
«r*’i
coefficient a t resonance (u/=as0), by
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136
it - 1
rr =
(5.4.4)
I T T
For w#wfl the reflection coefficient, T, is given by,
(4 t t ) •
T =
where a = 1 - w0/« .
________________________
1 + j2QLa
Note th a t when * = 1, T = 0, which indicates th at the
resonator is perfectly matched to the source.
C ritical Coupling.
(5.4.5)
This condition is referred to as
In general we can have three different coupling conditions.
These are,
1. Critical Coupling:
2.
Tr
= 0, => it = 1
Resonator Undercoupled: it
= (1 - |rr|)/(l + |Fr | ),
=> * <
1
it
= (1 + |rr|)/(l - |rr|),
=> it >
1
3. Resonator Overcoupled:
Thus, it can be determined by measuring the magnitude of the reflection coefficient
a t resonance.
The state of coupling of the cavity can be determined using the
Smith C hart impedance plot.
is given in figure 5.5.
A simple representation of a standard Smith chart
The Smith chart was developed by P. H. Sm ith5,6 to
facilitate the graphical solution of transmission-line problems.
This chart consists
of a plot of the normalized impedance, Z(z)/Z0 = r + jx, with the magnitude and
r
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137
+j
0.0
Figure 5.5: Sm ith chart impedance plot for ideal undercoupled (long-dashed
line), critically coupled (dashed-dotted line), and overcoupled (short-dashed
line) cavity resonator, and translated impedance plot due to presence of
coupling loss and reactance (dashed-doubled-dot line).
F
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138
angle of a generalized complex reflection coefficient in a unity circle.
is useful for the analysis of a lossless line as well as a lossy line.
The chart
To determine
the impedance of the loaded transmission line at any particular position in moving
along the line toward (away from) the load, one ju st performs a simple counter­
clockwise (clockwise) rotation on the chart.
The Smith chart of figure 5.5 consist
of sets of r and x circles bounded by the r= 0 circle.
Also shown are plots of the
impedance locus corresponding to the three different possible coupling conditions
for a resonator.
In calculating QL, one m ust always consider the coupling effects,
regardless of the particular degree of coupling of the resonator. In general, the
coupling loss (a ) modifies the location of the half-power frequency points thus
changing QL-
These losses also result in a slightly different
circumstances, the reflection coefficient a t
k.
Under this
frequencies far from the resonant
frequency is given by
r
RL ‘
R l/^o * 1
RL + Zo
iJ
a
+
1
=
9 - 1
(5.4.6)
9 + 1
Therefore, the value of 9 can be calculated by measuring the reflection coefficient
at frequencies far from resonance according to,
<r =
1 * lr J
I_ Z _
(5.4.7)
i + |rj
F
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139
The losses’ effects can be also perceived as a linear displacement on the Smith
chart impedance plot by an amount a.
These losses result in the magnitude of
the reflection coefficient no longer approaching one a t frequencies away from
resonance. Furtherm ore, the coupling coefficient becomes k ' = ( R l + z L) / z 0 = «
+ <r. Therefore, when the losses’ effects are taken into account, the expression for
the unloaded Q as a function of QL given in (5.4.3) becomes
Q = Ql [(1 + « ') / ( l + <r)l
which reduces to (5.4.3) when a tends to zero.
(5.4.8)
The loaded quality factor
is
given by equation (5.4.2), i.e. by measuring the upper and lower frequencies a t the
half-power level, which is the level a t which |Z j| falls to 0.707 of its maximum
value.
The half-power level reflection coefficient can be expressed in term s of the
effective coupling coefficient
k'
and the coupling loss a as,
Pyk = % { [ ( « ' * ! ) / ( * ' + i ) ] 2 + [(* - ! ) / ( * + I ) ] * }
(5.4.9)
In summ ary, equation (5.4.8) allows the determ ination of the unloaded quality
factor Q of the resonant cavity, by measuring the loaded quality factor QL and
knowing the effects of the losses in the coupling of the cavity with the driving
source.
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140
5.5
Experimental Details
In order to create the appropriate conditions for the experiment to be
successful, a number of experimental details were routinely observed.
run
the
cavity was ultrasonically
cleaned by immersing
it
Before each
in acetone for
approximately 15 minutes, with a subsequent rinse in alcohol to remove any
rem anent acetone film.
This process was done in order to remove any layers of
dust or oxides th at could have accumulated on the cavity walls while not in use.
The presence of any oxides or impurities on the cavity walls may lower the
quality factor Q of the cavity.
In all cases the sample to be studied was held in place as the top end wall
of the cavity by pressing it against the cavity with a stainless steel cross bar
which was bolted to the body of the cavity.
This mechanism allows for the
measurement of films of different thicknesses and provides a good contact between
sample and cavity.
The temperatures of the sample and the cavity were
monitored by three silicon diodes sensors (LakeShore
DT-470-LR-13).
These
diodes have an accuracy of ± 1.0 K from 1.4 to 100 K, and 1% of the actual
tem perature in the range from 100 to 325 K.
One of the sensors was placed very
close to the sample in order to record the sample’s tem perature during the
reflection coefficient measurement process.
The second sensor was placed a t the
bottom of the cavity in order to detect the tem perature difference across the
cavity.
It was found th at the tem perature difference between these two sensors
was less than 1 K a t 90 K.
Finally a third sensor was placed close to the heater
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141
on the cold head of the refrigerator, and it was used as a reference for the
tem perature controller to keep the tem perature of the cold head a t a particular
preselected temperature.
5.6
Results
We have measured the Rg of two predominantly c-axis oriented polycrystalline
YBa2Cu30 7.£ films deposited on S rT i0 3 and L aG a03 substrates by pulsed laser
ablation.
The films were analyzed by x-ray diffraction, dc resistance versus
tem perature measurements, and scanning electron microscopy (SEM) (see appendix
B).
Zero dc resistance was attained a t 90.0 and 88.9 K for the films on S rT i0 3
and L aG a0 3, respectively (see Fig.5.6).
A typical critical current density for films
on S rT i0 3 a t 77 K was 2xl06 A /cm 2 using a 1 /iV /cm measurement criteria.
The resistivity a t 300 K for the films on S rT i0 3 and L aG a03 was 130±30 and
220±50 /if!-cm, respectively.
The uncertainties arise from the irregular geometry
of the samples and uncertainties in the film thicknesses.
The x-ray diffraction
pattern revealed th at both films are predominantly c-axis oriented.
Figure 5.7
shows SEM micrographs for the two films which indicates the polycrystalline
character of the samples.
The Rg was measured, as explained above, by looking
at the change in the Q factor of the cavity when one of its end walls is replaced
by the superconducting film sample.
Using an HP-8510 network analyzer and
<5 i
Ginzton’s impedance method, ’ the Q factor for the cavity was determined from
r
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142
1.0
o
YBCO ON S rT iO ,
□ YBCO ON LaGaOi
0.8
x
<
£
os
§
_
8
0.6
UJ
<_)
z
sto
0 .4
to
LU
OS
0.2
50
100
150
200
250
300
TEMPERATURE, K
Figure 5.6:
dc resistance versus tem perature measurement of laser ablated
Y B a^C ujO f.j superconducting films on SrTiOs and L aG a0 3 substrates.
(Courtesy of M r. Joseph W arner and M r. Joseph Meola, NASA Lewis
Research Center).
the reflection coefficient.
Figure 5.8 shows the reflection coefficients (Su ) in the
normal and the superconducting states for the two samples under consideration.
The two main features in this figure are the narrowing and increase of the
resonance peak a t low tem peratures when compared to its shape and magnitude
a t room tem perature, and the frequency shift of the resonance peak w ith decreasing
tem perature.
The narrowing and increase of the peak is the result of the increase
in the quality factor Q of the cavity due to the reduction in losses in the thin
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143
Figure 5.7:
Scanning electron micrographs of laser-ablated YBa2Cu30 7.£
superconducting films on SrTiOj (a) and L aG a03 (b) substrates. (Courtesy
of Mr. Nicholas Varaljay, NASA Lewis Research Center).
film when cooled through its transition temperature.
result of a change in volume of the cavity.
The frequency shift is the
The maximum frequency shift
observed was less than 5% of the resonance frequency, therefore having a negligible
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144
42
Reflection coefficient, dB
58.575 GHz, -6.2996 dB
58.777 GHz, -33.271 dB
-10
-14
-2 0
-28
-3 0
-42
Start 58.500
Stop 59.000
Start 58.500
Stop 59.000
30
20
10
58.509 GHz, -7.0891 dB
50.775 GHz. -25.459 dB
0
-10
-14
-20
-28
-30
-42
Start 58.500
Stop 59.000
Frequency, GHz
Figure 5.8:
Start 58.650
Stop 58.900
Frequency, GHz
Reflection coefficient above (a) and below (b) T c for the film
on SrTiOs, and above (c) and below (d) T c for the film on LaGaOs.
k
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145
effect in the final determination of Rg.
Figure 5.9 shows a plot of the Smith
impedance chart for the case in which the end plate of the cavity was replaced
with the YBa^Cu-jO^j thin film on L aG a03.
is undercoupled.
At room tem perature, the cavity
Observe th a t due to the coupling losses the impedance circle is
displaced from the expected position in the absence of losses (see Fig. 5.5).
Note
that as the tem perature is lowered two main features become evident at once.
The degree of coupling becomes stronger.
critically coupled.
At T = 77 K the cavity is almost
At 26 K the cavity is overcoupled.
In addition, the effects of
coupling losses are reduced as indicated by the shifting of the impedance locus
with decreasing tem perature.
Both features are the result of the improvement in
the quality factor Q of the cavity as the tem perature is lowered.
Figure 5.10 shows a plot of the unloaded Q versus tem perature for the samples
under discussion.
and
then
Note that the Q increases slowly with decreasing tem perature,
increases abruptly
as
the
cavity
is cooled
below
the
transition
tem perature of the superconducting film.
Figure
5.11
shows
the
measured
Rg curves
for
the
two
films
under
consideration. Also plotted is the experimental surface resistance of the gold-plated
reference cavity for comparison.
The Rg values for the two films are comparable
in the normal state, while the Rg for the film on S rT i0 3 decreases faster than
that for the film on L aG a03 a t temperatures just below T c.
Using the normal
skin depth formula, Rg=(w/*0p / 2 ) w e obtained values for the resistivity, p, and
skin depth, 6, a t 300 K of approximately 118 p d -c m and 2.3 p m for the Rim on
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146
Ref. 1.0 units
1 200.0m units/
V 588.98m « 610.05m a
Ref. 1.0 units
1 200.0m units/
V 940.0mfl 006.44m a
Start 58.500 GHz
Stop 59.000 GHz
Start 58.650 GHz
Stop 58.900 GHz
Ref. 1.0 units
1 200.0m units/
V 1.3277 fl -381.41m n
Start 58.650 GHz
Stop 58.900 GHz
Figure 5.9: Smith chart impedance plot for YBa2Cu30 7<j thin film on
L aG a03
a t (a) room tem perature, undercoupled, (b) 77 K , almost
critically coupled, (c) 26 K, overcoupled.
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147
14
12 —
^
YBCO ON SrTiOg, Tc - 90.0 K
YBCO ON LaGaO* Tc - 88.9 K
10
o
8
S
4
0
% °8
50
b
E^0
100
150
200
TEMPERATURE. K
250
300
Figure 5.10: Unloaded quality factor Q versus tem perature for YBa2Cu30 7_j
thin films on S rT i0 3 (A) and L aG a03 (□).
S rT i03, and 158 p(l cm and 2.7 p m for the film on L a G a 0 3.
strong oscillatory
Note th a t the
behavior of R3 as a function of tem perature in the normal
state, observed for films on S rT i0 3 by other researchers,7 was not observed in our
case.
This is not unexpected due to the greater film thicknesses employed here.
In the superconducting state the films on S rT i0 3 and L aG a0 3 exhibit a drop of
Rg to values of 103±15 and 144±20 mil a t 77 K, and 82±15 and 116±20 mfl a t
i>
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148
1.0
T
oGpa0a
V)
os
10-1
%
10
-2
50
100
150
200
250
300
TEMPERATURE/ K
Figure 5.11:
Surface resistance (Rg) a t 58.6 GHz vs tem perature for 1.2
/im films of Y B ajC ujO y.j deposited by laser ablation onto S rT i0 3 (O ), and
LaGaO j (□) substrates, and for the gold-plated cavity (A).
70 K, respectively.
The surface resistance a t 77 K for the film on S rT i0 3 was
less th an th at of the gold-plated cavity, while for the film on L aG a03 Rg is the
same as for the gold-plated cavity.
Since we are operating a t a fixed frequency,
we cannot study the frequency dependence of Rs directly from our measurements.
I
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149
Nevertheless, a comparison with Rg values reported by other researchers in similar
types of films and a t different frequencies was very helpful in formulating a
frequency dependence trend for Rg.
For this we used the results obtained by
a
Klein, et al.
for c-axis textured layered samples of YBa2Cu30 7.£, by fitting their
d a ta to a quadratic frequency dependence for Rg.
obtained for Rg a t 58.6 GHz and 77 K.
A value of 102 mfl was
This value agrees very well with our
experimentally obtained value of 103 mfl a t the same tem perature.
approach was used for our film on LaGaOs.
An analogous
Using the d a ta reported by Cooke
et al.,9 for a YBa2Cu30 7.£ thin film deposited by magnetron sputtering on
L aG a03, an interpolation of Rg between their reported values measured a t 22, 86,
and 148 GHz and a t 70 K was performed.
The obtained Rg value of 106 mil at
58.6 GHz compares favorably, within experimental error, with our value of 116 mfl
at the same frequency and tem perature.
This result indicates th a t our value fits
well with the nearly quadratic dependence for Rg (Rg oc c«/n, n=2.06±0.14), as
reported in Ref.9.
The results obtained are also consistent w ith the behavior for
Rg expected for a Bardeen-Cooper-Schrieffer (BCS) superconductor.
The merits of
our power transmission technique for the determination of Rg are further supported
by the good agreement between the Rg values in table 4.1, and those obtained a t
77 K for the films on S rT i0 3 and L aG a0 3 (~28 and 39 mfl, respectively) when
scaled to 30.6 GHz using a quadratic frequency dependence for Rg. The Rg results
discussed above can also be found in reference 10.
In summary, we have measured the surface resistance of preferentially c-axis
oriented polycrystalline YBa2Cu30 7.£ superconducting laser-ablated thin films a t
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150
58.6 GHz via a TE013 cavity wall replacement method.
The values of Rg obtained
for the films on S rT i0 3 and L aG a0 3 at 77 K are less or equal to that of the
gold-plated cavity.
A comparison of the Rs values obtained for both films with
values for similar films measured by other researchers a t different frequencies shows
th a t our values are consistent with the frequency dependence for Rg observed in
classical superconductors and with the prediction of the BCS theory.
5.7
1.
References
Jackson, J. D.; Classical E lectrodynam ics, Sec. Ed., John Wiley and Sons, Inc.,
334-390 (1975).
2. Ramo, S.; Whinnery, J. R.; and Van Duzer, T.: F ields a n d W aves in
C om m unication E lectronics, John Wiley and Sons, Inc., 497 (1985).
3.
Ginzton, E. L.: M icrow ave M easu rem en ts, N fG raw Hill Book C o., (1957).
4.
Romanofsky, R. R.: A n a lytica l and E x p erim e n ta l P rocedures fo r D eterm in in g
P ropagation C haracteristics o f M illim eter- W a ve G allium A rse n id e M icro strip
Lines, NASA TP-2899 (1989).
5.
Smith, P. H.: Transm ission L in e C alculator, Electronics 12, 29-31 (1939).
6.
Smith, P. H.: An Im p ro ved Transm ission L in e C alculator, Electronics 17, ISO133, 318-325 (1944).
7.
Klein, N.; Muller, G.; Piel, H.; Roas, B.; Schultz, L.; Klein, U.; and Peiniger,
M.: M illim eter w ave surface resistance o f ep ita xia lly grow n Y B a 2C u 3O j ^
th in film s, Appl. Phys. Lett. 54, 757-759 (1989).
8.
Klein, N.; Muller, G.; Orbach, S.; Piel, H.; Chaloupka, H.; Roas, B.; Schultz,
L.; Klein, U.; and Peiniger, M.: M illim ete r w ave surface resistance and
London penetra tion d ep th o f Y B a2C u30 7mj thin film s, Physica C 162-164,
1549-1550 (1989).
9.
Cooke, D. W.; Gray, E. R.; Houlton, R. J.; Javadi, H. H. S.; Maez, M. A.;
Bennett, B. L.; Rusnak, B.; Meyer, E. A.; Arendt, P. N.; Beery, J. G.;
R eproduced w ith perm ission o f the copyright owner. F urth er reproduction prohibited w itho ut perm ission.
151
Brown, D. R.; Garzon, F. H.; Raistrick, I. D.; Rollet, A. D.; Bolmaro, B.;
Elliot, N. E.; Klein, N.; Muller, G.; Orbach, S.; Piel, H.; Josefowicz, J.Y.;
Rensch, D. B.; Drabeck, L.; and Gruner, G.: Surface resistance o f
Y B a 2C u30 7mj film s deposited on L a G a 0 3 su b stra tes, Physica C 162-164,
1537-1538 (1989).
10. M iranda, F. A.; Gordon, W. L.; Bhasin, K. B.; and W arner, J. D.:
M illim eter-w a re Surface R esistance o f Laser-ablated
Y B a 2C u30 7mj
Su p erco n d u ctin g F ilm s, Appl. Phys. Lett. 57, 1058-1060, (1990).
I
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Chapter 6
Conclusions
We have studied the microwave response of YBa^CujO^.g, Bi-based, and Tlbased HTS thin films.
We have measured the transm itted power as a function
of tem perature, incident power, and film thickness.
We found that the microwave
transmission properties are weakly dependent on tem perature in the normal state,
but change drastically upon transition to the superconducting state.
In particular,
the transmission decreases and there is a negative relative phase shift with respect
to the phase a t room tem perature when the sample is cooled through its transition
temperature.
The magnetic penetration depth for all films was determined from the surface
reactance of the films.
We found th at the smallest penetration depth values were
obtained for the Y B a jC u jO ^ films, whose values of A were consistent with the
best values reported by others so far.
We were able to verify experimentally the
intrinsic anisotropy of A for this HTS superconductor by measuring this param eter
in c-axis and predominantly a-axis oriented thin films.
As expected from the
intrinsic anisotropy of these HTS materials, the value of A for the a-axis oriented
film was larger than the values obtained for c-axis oriented films.
In fact, the
ratio of A for an a-axis oriented film to th at of c-axis oriented films agrees very
well with th at reported
superconductor.
by others
for single crystals of the
YBa2Cu30 7_£
We also observed th a t A increased with increasing film thickness,
which is consistent with the increase of the number of a-axis oriented grains and
152
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153
other structured and m aterial defects with increasing film thickness.
From the
thickness dependence of A we were able to determine, for the first time, an
intrinsic value of A for the YBa2Cu30 7.^ superconductor.
This value is consistent
with th at expected from measurements of A in single crystals by other techniques.
The A values for the Bi-based films and Tl-based films were larger than those
obtained for the YBa2Cu30 7_j films, and for the Tl-based films the calculated A
values were larger than the best reported values to date.
We have seen that
these large values may be associated with the poor grain connectivity exhibited by
these films.
Values for A were also determined from the measured <?2.
It was
found th a t the values of A calculated in this manner were larger than those
obtained from Xg.
The microwave complex conductivity was determined in both the normal and
the superconducting state.
The largest values for the conductivity in the normal
state were obtained for the YBa2Cu30 7.£.
For the three types of HTS films we
observed th a t both <r1 and <r2 increased upon transition to the superconducting
state.
This implies th at the tem perature dependence of <?l deviates from the
predictions of the two-fluid model.
In addition, we found th at the tem perature
dependence of <r1 is not consistent with th at expected from the M attis-Bardeen
equations, and the BCS theory.
YBa2Cu30 7.£ thin films.
The largest values for <r2 were measured for the
We found th at for the Bi-based and Tl-based films we
were able to measure <rl for all measurable tem peratures below T“ w, while for
most of the YBa2Cu30 7.^ films we were unable to measure ffj for tem peratures
far below T™w.
r
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154
We have calculated the surface resistance Rg for the three types of HTS films
studied.
We found th at for high quality Y B a ^ C ^ O ^ thin films the Rg values
a t 77 K compared fairly well with those reported by other researchers for similar
films and were equal or smaller than th at for copper a t the same frequency and
tem perature.
However, for the Bi-based and Tl-based films the calculated Rg
values were larger than those of YBa^CujO^^ thin films and of copper for all the
tem peratures considered in this study.
We have also fabricated a cylindrical
copper cavity to measure Rg. The measured Rg values for YBa2Cu30 7_£ thin films
on S rT i0 3 and L aG a03 are in good agreement with Rg values reported by others
using resonant cavity
techniques and with those obtained using our power
transmission measurement technique, if a quadratic frequency dependence for Rg is
assumed.
O ur analysis suggests that, among those studied, the laser ablated and dc offaxis magnetron sputtered Y B a g C u jO ^ thin films are the most promising for
microwave
applications.
However,
we
believe
th a t
improvements
in
the
superconducting properties of Bi-based and Tl-based HTS thin films could be
achieved by using ”in-situ” deposition techniques.
In our case, the fabrication of
both the Bi-based and the Tl-based films included a post-deposition heat treatm ent.
We have observed th at Y B a jC u jO ^ thin films preparation processes which include
a post-deposition annealing, such as sequential evaporation, yield films which are
of lower quality than those deposited by "in-situ” techniques such as laser
ablation.
r
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155
The merits of our experimental technique have been tested against widely
accepted characterization techniques, such as resonant cavity measurements.
The
consistency of the Rg values measured using both techniques supports the validity
of our method.
The strength of our technique is th a t it allows the calculation of
several transport param eters, such as A, a , and Rs, from one single measurement,
an a ttrib u te rarely found in any of the other probing techniques actually employed
in HTS films research.
The versatility of our technique rests not only in yielding
values for A, a*, and Rg in good agreement w ith those obtained by other
techniques, but also in being sensitive to the intrinsic anisotropy of these materials,
as evidenced by the results for A of YBa2Cu30 7.g thin films.
As further research, it will be useful to investigate the behavior of the
param eters studied in this thesis using the power transmission technique when an
external magnetic field greater than Hct is applied.
Such a study would provide
information on how the field magnitude and orientation could limit the use of
HTS thin films for microwave applications.
r
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Appendix A
Thin Film Deposition Techniques
A .l Pulsed Excimer Laser Ablation
A major problem in the fabrication of high-Tc
using conventional deposition
superconducting thin films
techniques such as electron beam evaporation,
sputtering, etc., is the accurate control of the stoichiometry of the multicomponents
vapors.
In addition, the ” in-situ” deposition requires background pressures of
oxygen too high to be compatible with conventional deposition techniques.
A
technique th at has proven to be useful for the deposition of HTS thin films is the
one known as pulsed laser deposition (PLD) technique.1,2’3 In this technique, laser
pulses (KrF, ArF excimer lasers, or a Nd-YAG laser, among most commonly used)
are fired onto a stoichiometric target of the HTS m aterial to be deposited.
This
result in a plasma ’’plume” of ejected m aterial from the target which condense
onto a substrate mounted onto a heated holder.
The main advantage of this
technique is th at the laser-produced ” plume” is stoichiometric in composition.4
The laser ablated YBa3Cu30 7.£ thin films considered in this thesis were
deposited by Mr. Joseph D. W arner, et al.5,6’7 a t the NASA-Lewis
Center, Cleveland, Ohio.
Research
A schematic of the set-up is shown in figure A.I.
For
the deposition of the HTS thin films the substrates most frequently used were
double-sided polished LaA103 (100), MgO (100), and Zr0 90Y010O2 (100).
Less
156
F
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157
VACUUM CHAMBER
LASER BEAM
P o , = 170 MILLITGRR
HTS
TARGET
>>$
i|i« illiii
PLASMA
HEATED SAMPLE
(750 °C)
Figure A.1:
Laser ablation technique.
frequently, SrTiO j (100) and L aG a03 (100) substrates were used, particularly to
deposit films which were intended for measurements of surface resistance (Rs) using
resonant cavity techniques (see chapter 5).
In general, the area of the films deposited by this technique was 1 cm2,
although larger Dims were also deposited.
In order to remove any grease and
other impurities th a t could have adhered to the substrates due to handling and
cutting to the appropriate deposition size, each substrate was cleansed w ith acetone
and methanol before being glued with silver paint to the stainless steel sample
holding stage.
The target surface was sanded flat between each deposition, in an
attem pt to reduce the particulates on the film surface.8 The substrate was then
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158
placed in the vacuum chamber which was evacuated
to 4xl0'6 torr or less, using
a liquid nitrogen cold trapped diffusion pump, and wanned to 700°C within 30
minutes.
A continuous flow of oxygen of ~19 cubic centimeters per minute a t
standard tem perature and pressure (19 Seem), was then introduced into the
chamber, and the substrate was heated to
the appropriate tem perature for
deposition of approximately 755° C, using resistive heating.
When the substrate
has reached thermal equilibrium a t 755°C, the film deposition is commenced.
During this process, the oxygen pressure was 170 m torr, the wavelength of the
KrF excimer laser was 248 nm, the laser fluence was approximately 2.0 J/c m 2 per
pulse, the pulse duration was 20 to 30 ns, and the pulse rate was of 2 pulses per
second.
The deposition was performed w ith a stoichiometric YBa2Cu30 7.£ target
a t least 95% the theoretical density (~6.4 g/cm 3).9
Throughout the deposition
process, the sample and the target were kept a t a distance of 7.5 cm, while the
laser beam was scanned back and forth a t 1 cm /m in across the target to preserve
stoichiometry.
The film deposition rate was generally 100 A per minute.
To
monitor the tem perature of the sample, a type-K thermocouple welded to the
stainless steel stage, was used.
The distance between the tip of the thermocouple
and the sample was approximately 5 millimeters.
At the end of the deposition process, the oxygen pressure was raised to 1 atm ,
and the tem perature was lowered slowly (usually a t a rate of 2°C/m in) to 450°C;
the sample was typically kept a t this tem perature for two hours, in order to
optimize its oxygen content.
r
Afterwards, the sample was cooled slowly to 40°C
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159
or less before it was removed from the chamber.
Thin films of YBa2Cu30 7.£ with
o
thicknesses ranging from 800 to 12 000 A were obtained using this technique.
The laser ablated Tl-Ba-Ca-Cu-O thin films used in this work were deposited
by Dr. Ned J. Ianno, et al.10 a t the University of Nebraska-Lincoln, Lincoln,
Nebraska.
The deposition was performed at a substrate tem perature of 200° C
and an ambient oxygen pressure of 170 m torr.
The laser wavelength was 248 nm,
and the laser fluence on the target was 1.0 J /c m 2.
The target was a composite
of Tl-Ba-Ca-Cu-O made by sintering a mixture of T120 3, CaO, BaO, and CuO
with a metal cation ratio of 2-2-2-3.
Upon completion of the deposition, 250 torr
of oxygen was bled into the chamber, the substrate heater was turned off, and the
sample was allowed to cool to room tem perature before removal.
description of the deposition technique is given in Ref. 10.
A more detailed
The as-deposited films
were not superconducting, and a post annealing step was required.
The annealing
process was similar to th at used by other researchers.11
A.2
Sequential Evaporation
The deposition of YBa2Cu30 7.£ superconducting thin films using a multi-layer
sequential evaporation technique was first reported by B. Y. Tsaur, et al..12 In
this technique the multi-layer film is made by electron beam evaporation of
alternate layers of either Cu, Ba, find Y, or Cu, BaF2, and Y.
layer stack is repeated to give a total of 12 to 18 layers.
The basic three
This technique allows
the deposition of films with little spatial variation of stoichiometry across the
k
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160
substrate as all components of the films are evaporated from the same point in
space.
The stoichiometry of the films is easily adjusted by controlling the
thickness of the individually deposited layers.
However, this deposition technique
requires post-deposition annealing of the film in order to atta in the superconducting
phase.
The sequentially evaporated films (~1.0 /tm thick) used in this study were
deposited on MgO substrates a t the Ohio State University by Dr. G. Valeo, et
al.13,14
The depositions were done with a background vacuum of approximately
5x l0 '7 Torr.
and Cu.
The multi-layer film was formed from the evaporation of Y, BaF2,
The BaF2 was used rather than Ba because BaF2 is less reactive.
The
basic three layer stack was repeated four times for a total of twelve layers.
Afterwards, a post-deposition annealing of the samples was carried out a t 850 °C
for 0.5 hr.
During the annealing a t 850 °C the sample was exposed to ultra high
purity oxygen which has been bubbled a t room tem perature water.
vapor hydrolyzed the BaF2 to form BaO and HF.
remaining of the annealing process.
at a rate of -2 °C /m inute.
The water
Dry oxygen was used for the
The tem perature was then ramped to 450 °C
The samples were held a t 450 °C for 6 hr and then
the tem perature was ramped to room tem perature a t -2 °C /m inute.
A schematic
representation of the as deposited multi-layer structure of the film and the
superconducting film after annealing is shown in figure A.2.
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161
■BaF,
■Y
*Cu
& 3& B i& 88i8& 883Z £450333
ANNEAL IN
OXYGEN
Figure A.2:
SUBSTRATE
Schematic representation of the as deposited multi-layer
structure of the film (left), and the superconducting film after annealing on
the right; (taken from Ref. 14).
A.3
Co-evaporation
In this
deposition
process the evaporation of the
primary or primitive,
components is performed a t the same time, having a separate source for each
element (metal or fluoride sources).
Since the evaporated amount of each of the
primary components is monitored by three independent thickness monitors (usually
small pieces of quartz, properly localized), this method offer the advantage of very
good control and flexibility in the final composition of the sample.
In general, the oxygen pressure during the deposition is approximately 10*5 to
10*
torr, the deposition rate is 1 to 10 A per second, and the substrate is
maintained a t room tem perature.
Since the high-Tc superconducting phase is
formed a t tem peratures well above room tem perature, a post-deposition annealing
is required when films are deposited using this technique (i.e., this is an Bex-situ”
deposition technique).
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162
Co-evaporation from Y, BaF2, and Cu sources, followed by oxygen annealing,
has become one of the most common methods of making YBa2Cu30 7.£ high-Tc
thin films.15' 18 Y, Cu, and BaF2 are evaporated from three separate sources,
forming
a
non-hydroscopic
amorphous
film
of approximately
correct
metal
stoichiometry, but with the lim itation of containing BaF2 and being oxygen
deficient.
Therefore, an ”ex-situ” oxygen annealing is generally required, in which
the fluorine is replaced by oxygen which is necessary for the crystalline phases to
grow.
Bi-Sr-Ca-Cu-0 superconducting thin films, deposited using this technique by Dr.
T. S. Kalkur, et al.,19 of the University of Colorado a t Colorado Springs, are part
of the films analyzed in this thesis.
in figure A.3.
A schematic of the deposition set-up is shown
In this process, bismuth was evaporated using an electron beam,
and copper was evaporated from a tungsten boat. Calcium and strontium fluorides
were evaporated together in one tungsten boat since their melting and evaporation
tem peratures are very close.
The melting and evaporation tem peratures are 1473
and 2489°C for SrF2, and 1423 and 2500 °C for C aF2.20
The mixing ratio of
fluorides in the boat is made to equal the composition of Sr and Ca in the final
film.
The composition of the deposited film was monitored by three independent
quartz thickness monitors.
Before the film deposition, the vacuum system was
pumped down to a pressure of less than 10'6 torr.
Oxygen was leaked into the
system through a nozzle near the substrate holder.
The chamber pressure in the
system during the deposition process was maintained around 5xl0*5 torr.
During
I
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163
VACUUM CHAMBER
EVAPORATOR
THICKNESS
MONITORS
1
SUBSTRATE
HOLDER
E-BEAM
EVAPORATOR
FOR Bi
VACUUM PUMP
Figure A.3:
OXYGEN
LEAK VALVE
Co-evaporation set-up for Bi, CaF2 + SrF2 and Cu.
•
*
evaporation, the copper was evaporated a t a rate of 0.8±0.1 A per second,
bismuth a t 1.2±0.3 A per second and the Sr and Ca fluorides a t 3.2±0.5 A per
second.
The average thickness of the deposited films was 5200 A (800 A of Cu,
1200 A of Bi, and 3200 A of the fluorides).
The films were deposited on LaA103
and MgO substrates.
Finally, the as-deposited Bi-Sr-Ca-Cu-0 films were annealed in a furnace,
following a two-step procedure.
r
The first step of the annealing was done a t 725°C
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164
in wet oxygen for about 30 to 60 minutes.
This step was performed to
decompose the fluorides, so th at the fluorine will react with the H20 molecules
forming volatile hydrogen fluoride gas (HF).
The second annealing step was
carried out to form the superconducting phase.
This step was performed a t 850°C
for about 5 to 15 minutes.
Afterwards the sample was allow to cool down slowly
(~2° C/m in) to room tem perature, before removing it from the deposition system.
A. 4 dc Magnetron Sputtering
Thin films of YBa2Cu30 7_£ deposited by Dr. John Talvacchio, et al.21 of the
Westinghouse Electric Corporation, Pittsburgh PA., using an *in-situ” off-axis dc
magnetron sputtering geometry, were also analyzed in this study.
The deposition
was carried out at high Ar gas pressures (150 m torr) in order to enhance the
collision frequency of sputtered atoms thereby making the deposition process more
efficient.
This also minimizes the resputtering of the growing film due to negative
oxygen ions because the ions lose a considerable am ount of its energy due to
inelastic collisions.
A small oxygen pressure (20 m torr) is also used to keep
negative ions effects small.
During deposition, the substrate was held with silver
paste to a stainless steel block heated to achieve substrates tem peratures of 650°C.
A target with a composition ratio Y:Ba:Cu=l:2:3 was used for each deposition.
Generally, the deposition rate was 200 A /hr, and the sputtering power was 45 W
dc.
I
A more detailed description of this deposition technique is given in Ref. 21.
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165
A.5
rf Magnetron Sputtering
Another deposition technique which has evolved from the need to overcome
problems associated with high tem perature deposition methods such as poor surface
morphologies, cracking, film-substrate interdiffusions, lim itations of choices of
substrates
materials,
and
the
incompatibility
of
these
temperatures
1 1 4 1% A A f
O A 4
semiconductor devices technology, ’
with
is rf magnetron sputtering. ’ ’
In this
technique, a composite oxide powdered target is spread on a metal plate (usually
copper) which acts as the cathode of the sputtering chamber.
A power supply
generates an rf input power (~100 to 300 W) which drives the sputtering gas ions
(generally any of the following combinations; Ar(80%) + 0 2 (20%),23 Ar(70%) +
O2(30%),24 Ar(90%) + 0 2 (10%),25 or even pure Ar) toward the powdered oxide
target.
When the sputtering gas ions reach the target, target atoms are sputtered
out of the target and driven toward the substrate.
All the deposition process is
carried out a t sputtering gas pressures of approximately 3xl0'2 to 8xl0‘2 torr.25
During deposition the substrates are kept a t temperatures between 650 to 700°C.
The growth race of the Sims depends upon the rf power used for a particular
deposition, but commonly is within 24 to 70 A/m in.
An ”in-situ” annealing in
an 0 2 atmosphere is usually required in order to improve the value of T c for the
Sims.
A Tl-Ba-Ca-Cu-O superconducting thin film deposited by this technique a t the
University of Cincinnati by Dr. G. Subramanyam, et al.26 was also analyzed in
this study.
A. schematic of the deposition sei~up is shown in figure A.4.
Briefly,
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166
SUBSTRATE
0
O
REDUCED
P R EU
SRE
S U R E -^ /
I
2
T
r TARGET
ATOMS
THIN FILM
> O
0
0
\
.
0 /-ARGON
/ IONS
o - I
M/ \ i /
"
POWDERED
TARGET
/
^-TARGET
ELECTRODE
^. -POWER
SUPPLY
Figure A.4: rf magnetron sputtering deposition system.
a target powder of Tl2Ca2Ba2Cu3Ox (with an excess of 10% TI20 3 to compensate
for T1 loss during the sintering and annealing process) was spread on an 8 inches
copper plate which is the cathode, and pressed to obtain a uniform surface.
The
sputtering process was carried out in a pure Ar atmosphere with the following
r
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167
sputtering parameters; rf power of 250-300 W, chamber pressure of 5 m torr, an
At flow of 31.5 Seem, and a deposition rate of approximately 30-50 A per minute.
The resultant films were in general between 0.5 and 1.0 p m thick.
The post
deposition processing of the film consisted of a sintering in air and an annealing
in an oxygen atmosphere.
The sintering in air was carried out a t 850°C for 15
minutes to establish the superconducting phase.
Afterwards, an oxygen annealing
was performed to improve the film’s grain boundaries, and thus improve its
superconducting properties.
The oxygen annealing was performed
with an oxygen
flow of 500 Seem.
A. 6
References
1.
Dijkkamp, D.; Venkatesan, T.; Wu, X. D.; Shaheen, S. A.; Jisrawi, N.; MinLee, Y. H.; McLean, W. L.; and Croft, M.: P reparation o f Y-B a-C u
O xide Su perconductor T hin F ilm s U sing P u lsed L aser E vaporation F rom
High T c B u lk M aterial, Appl. Phys. Lett. 51, 619-621 (1987).
2.
Roas, B.; Schultz, L.; and Endres, G.: E p ita x ia l G ro w th o f Y B a 2C u30 7mX Thin
F ilm s b y a L aser E vaporation Process, Appl. Phys. Lett. 53, 1557-1559
(1989).
3.
Inam, A.; Hedge, M. S.; Wu,
F.; Chase, E. W.; Chang,
A s-d ep o sited High T c and
T em peratures, Appl. Phys.
4.
Venkatesan, T.; Wu, X. D.; Inam, A.; and W achtman, J. B.: O bservation o f
T w o D istin c t C om p onents D uring P ulsed L aser D eposition o f High T c
Supercond ucting F ilm s, Appl. Phys. Lett. 52, 1193-1195 (1988).
X. D.; Venkatesan, T.; England, P.; Miceli, P.
C. C.; Tarascon, J. M.; and W achtman, J. B.:
J c S u p erconducting T h in F ilm s M a d e a t L o w
Lett. 53, 908-910 (1988).
5. W arner, J. D.; Meola, J. E.; and Jenkins, K. E.: S tu d y o f D eposition o f
Y B a2C u30 j mg on C ubic Zirconia, Superconductivity and Applications, Plenum
Publishing Corporation, 163-167 (1990).
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.
168
6.
W arner, J. D.; Bhasin, K. B.; and M iranda, F. A.: D ependence o f th e C ritical
T em p era tu re o f Laser A b la te d Y B a 2C u30 7_£ T bin F ilm s on L a A 1 0 3
S u b stra te G row th Technique, Supercond. Sci. Technol. 3, 437-439 (1990).
7.
W arner, J. D.; Bhasin, K. B.; Varaljay, N. C.; Bohman, D. Y.; and Chorey,
C. M.; G row th and P a tte rn in g o f L aser A b la te d Superco n d u ctin g
YBa2Cu30 7mj F ilm s on LaA103 S u b stra tes, NASA TM-102436 (1990).
8.
Chang, C. C.; Wu, X. D.; Ramesh, R.; Xi, X. X.; Ravi,T. S.; Venkatesan,
T.; Hwang, D. M.; Muenchausen, R. E.; Foltyn, S.; and Nogar, N. S.:
Origin of Surface Roughness for C-axis O riented Y -B a-C u-O S u p ercon ducting
F ilm s, Appl. Phys. Lett. 57, 1814-1816 (1990).
9.
Bell, A. M. T.: C alculated x-ra y P ow der D iffraction P a tte rn s, a n d Theoretical
D ensities fo r P hases E ncountered in In vestig a tio n s
of
Y -B a-C u-O
Superconductors, Supercond. Sci. Technol. 3, 55-61 (1990).
10. Ianno, N. J.; Liou, S. H.; Woollam, J. A.; Thompson, D.; and Johs, B.:
P u lsed
Laser D eposition o f Tl-B a-C a-C u-O F ilm s a t 532 and 248
N anom eters, subm itted to J. of M at. Res. (1990).
11. Lee, W. Y.; Lee, V. Y.; Salem, J.; Huang, T. C.; Savoy, R.; Bullock, D. C.;
and Parkin, S. S. P.: Superco nducting T l-C a -B a -C u -0 T h in F ilm s W ith
Zero R esistance a t T em pera tu res o f u p to 120 K , Appl. Phys. Lett. 53,
329-331 (1988).
12.
Tsaur, B. Y.; Dilorio, M. S.; and Strauss,
A. J.: P reparation o f
Supercond ucting Y B a2C u3Ox T hin F ilm s b y O xygen A n n ea lin g o f M u ltila y er
M e ta ls F ilm s, Appl. Phys. Lett. 51, 858-860 (1987).
13. Valeo, G. J.; Rohrer, N. J.; W arner, J. D.; and Bhasin, K. B.: S eq u en tia lly
E vaporated T h in Y -B a-C u-O Superconductor F ilm s: C om position and
Processing E ffects, American Institute of Physics, Proceedings no. 182, 147152 (1989).
14. Valeo, G. J.; Rohrer, N. J.; Warner, J. D.; and Bhasin, K. B.: Sequen tia lly
E va p o ra ted T h in Y -B a-C u-O S u p erco n d u ctin g F ilm s on M icrow ave
S ubstrates, Proceedings of the DOD Workshop on High Temperature
Superconductivity, Huntsville, Al, Gaciac IIT Research Institute, 197-203
(1989).
15. Mankiewich, P. M.; Scoefield, J. H.; Skocpol, W. J.; Howard, R. E.; Dayen,
A. H.; and Good, E.: R eproducible T echnique fo r F abrication o f T hin F ilm s
o f High T ransition T em p era tu re Superconductors, Appl. Phys. Lett. 51,
1753-1755 (1987).
R eproduced w ith perm ission o f the copyright owner. F urther reproduction prohibited w ith o u t perm ission.
169
16. Chan, S. W.; Bagley, B. G.; Greene, L. H.; Giroud, M.; Feldman, W. L.;
Jenken, K. R.; and Wilkins, B. J.: E ffect o f th e P ost-D eposition Processing
Ambient on the Preparation o f Superconducting Y B a 2C u30 7_x C oevaporated
T hin F ilm s U sing a B a F 2 Source, Appl. Phys. Lett. 53, 1443-1445 (1988).
17. Phillips, J. R.; Mayer, J. W.; M artin, J. A.; and Nastasi, M.: Vapor-deposited
Superconducting Y B a 2C u30 7^ Lines: E ffe ct o f T hickness a nd W id th on
Morphology, Appl. Phys. Lett. 56, 1374-1376 (1990).
18. Gijs, M. A. M.; and Jansen, R. J. E., M icrow ave R esponse o f Y B a C u O Thinfilm D a yem B ridges, Appl. Phys. Lett. 56, 1484-1486 (1990).
19. Kalkur, T. S.; Kwor, R.; Jernigan, S.; and Smith, R.: C o-evaporated Bi-Sr-CaC u-O xide S u p erco n d u ctin g F ilm s and T h eir P a ttern in g , presented a t the
Conf. Sci. Technol. Thin Films Supercond., Colorado Springs, CO., Nov. 1418, (1988).
20. W east, R. C., ed.: C R C H andbook o f C h e m istry a nd P hysics, 69th edition,
CRC Press, Inc. (1988-1989).
21. Talvacchio, J.; Gavaler, J. R.; Forrester, M. G.; and Braggins: to appear in
Science and Technology o f T hin F ilm s Superconductors II, eds. R. D.
McConnell and S. A. Wolf, Plenum Publishing Corporation (1990).
22. Venkatesan, T.; Chang, C. C.; Dijkkamp, D.; Ogale, S. B.; Chase, E. W.;
Farrow, L. A.; Hwang, D. W.; Miceli, P. F.; Schwarz, S. A.; Tarascon, J.
M ; Wu, X. D.; and Inam, A.: S u b stra te E ffec ts on th e P roperties o f Y-BaC u-O Sup ercond ucting F ilm s P repared b y L aser D eposition, J. Appl. Phys.
63, 4591 (1988).
23.
Adachi; H.; Hurochi, K.; Setsune, K.; Kitabatake, M.; and Wasa, K.: L o w
T em p era tu re Process fo r th e P reparation o f H igh T c Su p erco n d u ctin g T hin
film s, Appl. Phys. Lett. 51, 2263-2265 (1987).
24.
Mizuno, K.; Higashino, K.;
Setsune K.; and Wasa,K.:
F abrication o f Thinfilm -ty p e Josephson Ju n ctio n s Using a Bi-Sr- Ca- Cu- O /B i-S r- Cu- O /B i-S r- Car
C u -0 S tru ctu re,” Appl. Phys. Lett. 56, 1469-1471 (1990).
25. Takano, S.; Hayashi, N.; Okuda, S.; and Hitotsuyanagi: Y 1B a 2Cu30 7m^ Thin
F ilm s G row n b y R F M a gnetron S p u tterin g , Physica C 162-164, 1535-1536
(1989).
26. Subramanyam, G.; Radpour, F.; and Kapoor, V. J.: F abrication o f Tl-Ca-BaC u -0 Superconducting T hin F ilm s on L a A lO s S u b strates, Appl. Phys. Lett.
56, 1799-1801 (1990).
r
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Appendix B
Other Sample Characterizations
B .l dc Resistance Versus Temperature
Measurements
To determine the resistive transition tem perature (T^c) of the thin films
analyzed in this study, a four-point probe measuring technique was used.
Figure
B .l shows a schematic of this configuration, implemented by Mr. Joseph D.
Warner of the NASA Lewis Research Center a t Cleveland, Ohio.
A constant
current is passed through the outer leads and the voltage is measured between the
~ 3 mm
GOLD
N FILM
SUBSTRATE
Figure B .l: Four-point probe measurement set-up.
170
I
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171
inner two leads.
In order to cancel the contribution of any thermal voltage, two
measurements are performed with the current reversed between the measurements.
The resistance is then determined from the average of these measurements.
Note
that the contact resistance is not measured in this technique since the amount of
current th at flows in the voltage leads is negligible.
The criteria for the
determination of T^° was the resistivity decreasing below the noise level of 10*8
fl-cm.
During the actual measurements a current of approximately 100 micro­
amperes (or a current density of 2 to 10 A /cm 2) is passed through the sample.
The contacts between all the leads and the films were made by wire bonding 1
by 2 mils gold ribbons directly
to the sample.
leads was usually between 3 to 6 mm.
The spacing between the voltage
All the measurements were started a t
room tem perature, and subsequent measurements taken while cooling the film using
a Janis’ closed-cycle He gas refrigerator.
As the tem perature neared the transition
tem perature, the tem perature decrement size was reduced to obtain more data in
this region.
Typical tem perature decrement sizes were,
120 K < T < 300 K
A T = 20
K
95 K < T < 120 K
A T = 5.0 K
80 K < T < 95 K
AT = 0.2 K
The precision and accuracy of the tem perature measurements were within ± 0 . 1
and ± 0.5 K, respectively.
Values of the T^c for some of the films analyzed in
this study are given in tables B .l and B.2 at the end of this appendix.
ir
!t
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172
B.2
X-ray Diffraction Analysis
The films were also analyzed by X-ray diffraction.
The X-ray diffraction
measurements were performed by Mr. Ralph Garlick, of the NASA Lewis Research
Center.
This analysis was performed using a Scintag Diffractometer with an
energy dispersive detector which perm its minor im purity phase determination in
thin films.
The d ata was taken using Cu-Ka^ radiation (wavelength of 1.54 A).
This analysis provided information about the crystal orientation of the films (for
example, c-axis perpendicular or parallel to the surface of the substrate), and the
type of crystal structure (i.e., orthorhombic, tetragonal, etc.).
of the films was determined using X-ray rocking curves.
The mosaic spread
Values for the X-ray
rocking curves full width a t half maximum (FWHM) for these films are given in
tables B .l and B.2 at the end of this appendix.
B.3
Surface Morphology Analysis
The surface morphology of the films was studied by Scanning Electron
Microscopy (SEM).
Scanning electron micrographs of the films, a t magnifications
ranging from 500 to 40,000 times normal size, were taken by Mr. Nicholas
Varaljay and Ms. Donna Bohman of the NASA Lewis Research Center using an
ISI DS-130 Scanning Electron Microscope.
All the pictures were taken with the
surface of the film perpendicular to the incident electron beam.
hIt
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173
B.4
The
Film Thickness
thickness
(d)
of each
Glm was
measured
with
a
Dektak
surface
profilometer over steps etched a t the corner of the Glm using undiluted phosphoric
acid (H3P 0 4).
T o perform the etching the corner of the Glm was dipped in the
acid for a tim e interval of 5 to 10 seconds, then rinsed with 200 proof ethanol
to sharpen the steps.
These measurements were performed by Mr. Nicholas
Varaljay and Ms. Donna Bohman of the NASA Lewis Research Center.
For the
thinnest laser ablated Glms the thickness was determined by scaling from the
deposition rate.
The thicknesses of the Glms used in this study are given in
tables B .l and B.2.
k
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174
TABLE B.1: MATERIAL PARAM ETERS OF YBa,Cu30 7. ; THIN FILMS
SUBS.
D.M.
d (A)
T * (K )
1
LaAlOj
L.A.
4900
88.3
0.84
2
YSZ
OAMS
800
91
0.96
3
LaAlOg
L.A.
2400
90.6
0.86
4
LaAlOj
L.A.
1769
87.3
0.90
5
LaAlOj
L.A.
828
85.2
0.74
6
LaAlOj
L.A.
1762
55.5
0.68*
7
MgO
OAMS
1000
87.2
0.76
8
L aG a03
L.A.
4000
88.0
0.80
9
LaA103
L.A.
1000
86.2
0.51
10
MgO
L.A.
3500
87.5
1.08
11
LaA103
OAMS
2600
87.5
0.62
12
LaA103
L.A.
2665
82
-
13
LaA103
L.A.
2655
86.3
-
14
LaA l03
L.A.
4000
84.2
1.04
SAMPLE
FW HM (DEG)
SUBS. = Substrate
D.M. = Deposition method
L.A. = Laser Ablated
OAMS = Off-axis Magnetron Sputtered
FW HM = Full width a t half maximum for the (005) X-ray diffraction peak of
YBa2Cu30 7.^; * using the (003) X-ray diffraction peak.
!
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175
T able B.2: M A T E R IA L PA R A M E T E R S O F Bi AND Tl-B A SED T H IN FILM S
SAMPLE
SUBS.
D.M.
d (A)
T f (K)
FWHM (DEG)
Bi # 1
LaAIOg
C.E.
5000
80
----
Bi # 2
MgO
C.E.
5000
80
-----
Bi # 3
MgO
C.E.
3000
78.6
1.06
Bi # 4
LaAlOg
C.E.
3000
79.2
1.26
T1 # 1
LaA103
L.A.
5000
101.8
1.62
T1 # 2
LaA103
L.A.
4000
99.8
1.78
T1 # 3
MgO
L.A.
5000
83
----
T1 # 4
LaA103
RFMS
5000
83
----
SUBS. = Substrate
D.M.
= Deposition Method
C.E.
= Co-evaporation
L.A.
= Laser Ablation
RFMS
FW HM
= rf M agnetron Sputtering
= Full width a t half maximum; for the (0012) X-ray diffraction peak of
the Bi-Sr-Ca-Cu-O films, and for the (0016) X-ray diffraction peak of the Tl-BaCa-Cu-0 films.
at
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Appendix C
Dielectric Substrates For HTS Thin
Films
C .l Microwave Substrates
The use of high-Tc superconductors for microwave applications is subject to the
availability of substrates with low and thermally stable dielectric constant, low
losses, and w ith a good lattice m atch with the new superconducting oxides.
The
deposition of HTS thin films onto S rT i0 3 substrates have produced high quality
films mainly because of the excellent lattice match between the S rT i0 3 and the
superconducting copper oxides.
This excellent lattice m atch has resulted in the
best critical current values so far, with J c > 1 x 106 A /cm 2 a t 77 K and zero
magnetic field for currents on the a-b plane,1 and values an order of magnitude
lower for currents along the c-axis.2
Nevertheless, its microwave applications are
iimited because of the large and strongly tem perature dependent relative dielectric
constant of approximately 300 a t room tem perature and over a 1000 a t 77 K,3’4
and its large loss tangent a t microwave frequencies,5 which result in a degradation
of the microwave transmission properties.
MgO, with a dielectric constant of 9.8 and a loss tangent of approximately
A
I? 7
10* at room tem perature, ’ is a convenient substrate for microwave applications.
However, it has a large lattice mismatch with the new superconducting oxides
176
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177
which makes epitaxial film growth more difficult.
The lack of a good epitaxial
m atch
detrim ental
between
film
and
substrate
could
be
superconducting transport properties of the film.
to
the
overall
The same applies for the YSZ,
with dielectric constant of 27 and a loss tangent 10*3 a t room tem perature,8 but
with a considerable lattice mismatch with the HTS.
The newly developed LaA103 substrate overcomes the lim itations that hamper
the SrTiO j and the MgO substrates.
constant of 22 a t
This substrate has a relative
room tem perature,9 changing less than
tem perature range of interest in this study.
dielectric
10% within
the
It also has a loss tangent of 10'4 at
room tem perature and approximately 10'5 a t 77 K,10 and an excellent lattice
m atch w ith the high-Tc superconductors.
The aforementioned properties make the
LaA103 substrate very appropriate for operation a t microwave frequencies.
The properties of the L aG a03 substrates are very similar to those of LaA103.
It has a dielectric constant of 25 a t room tem perature,8 and a good lattice match
w ith the new high-Tc superconductors.
Table C .l summarizes some of the most
relevant properties of the substrates considered in this study.
¥
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE C.1: MICROWAVE SUBSTRATES FOR HTS THIN FILMS
M aterial
S tru c tu re
(298 K)
D ielectric
C o n sta n t,t r
M gO
Cubic
9.8
3.0 x 10'4
4.178
a= 11.0%
c=12.8%
Sm all area, good for "in -situ ”
film grow th, reacts w ith 0 {
L aA I0 3
Pseudocubic
22
5.8 x 10'4
3.792
a = 0.7%
c— 2.6%
L arge area, tw inning, very
high quality films
L aG a03
O rthorhom bic
25
1.8 x 10,-3
3.902
a = 2.1%
c = 0.2%
L arge area, phase tran sitio n s
a t 140 and 400 °C m ay cause
surface roughness (steps)
S rT iO ,
Cubic
3.0 x 10'*
6.0 x 10*
3.905
a = 2.2%
c = 0.3%
Sm all area, high q u ality films
YSZ
C ubic
5.4 x 10'3
3.648
a = 4.6%
c = 6.3%
L arge a rea su b strates
-300 300 K
-1900 80 K
-18000 4.2 K
27
Loss T an g en t
(298 K)
L attice Size
(A)
L attice M ism atch
Rem arks
—J
00
179
C.2 Tc Dependence on LaA103 Substrate Growth
Technique
High-temperature superconducting
LaA103
(HTS)
thin
films have been grown on
substrates because of its good lattice m atch with the YBa2Cu30 7_£
superconductor and
its possible suitability
devices.10 Since the surface quality
for the fabrication of microwave
of the substrate
is very
im portant in
determining the quality of the HTS film to be deposited, knowledge of the possible
changes th a t the substrate’s surface can undergo during HTS film growth becomes
indispensable.
For L aG a03, Miyazawa has shown th a t their surface roughened
during the thermal cycling of growing YBa2Cu30 7.£ thin films.11 Since the LaA103
substrate is isomorphic with LaGaOj and undergoes a second-order phase transition
around 400 °C, one might expect th at its surface would roughen as well.
It is
well known th a t for m etal-substrate interfaces, the substrate’s surface roughness
increases the microwave losses.12 Therefore, we considered it worthwhile to see if
this
same
effect
in
the
YBa2Cu30 7.^— LaA103
interface
would
cause
any
degradation of the superconducting properties of the film.
At present, there are two different methods by which commercially available
single crystals of LaA103 are prepared.
Czochralski
methods.
These are the flame fusion and the
The method of substrate
preparation could possibly
determine the extent of surface roughening during therm al cycling of the substrate.
M otivated by this possibility, LaA103 substrates (~ 500 fim thick) made by the
above mentioned methods were subjected to the same thermal cycling conditions
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180
they would have to undergo during the growth of YBa2Cu30 7. j thin films by laser
ablation (see appendix A).
To determine the effect of surface roughening on the
critical tem perature of the superconducting thin films, films of YBa2Cu30 7.£ were
grown on each type of substrate, with identical growth conditions, by laser
ablation.
The surface roughness of the substrate made by the Czochralski method
(hereinafter called Czochralski substrate) and of the one made by flame fusion
(hereinafter called flame fusion substrate) was compared before and after annealing.
The roughness was measured by a profilometer and calculated by taking the root
mean square deviation of the distribution of data points from a smooth curve
fitted through the profilometer’3 data.
piecewise
continuous,
second-order
For measurements before the annealing, a
function
was
fitted
to
the
data;
measurements after the annealing, a straight line was fitted to the data.
for
Both
substrates were annealed together a t a tem perature of 750 °C for 1 hr w ith a slow
cool to room tem perature in an oxygen atmosphere.
As can be seen from figure C .l, both substrates roughened after the a n n e a lin g
although the Czochralski substrate roughened considerably more.
For the flame
fusion substrate the average surface roughness before the annealing was ~100 A
and after annealing it was ~ 530
A.
On the other hand, for the Czochralski
substrate the average surface roughness before the annealing was ~ 130 A and
after annealing an order of magnitude greater, ~ 1490 A.
t
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181
3000
2000
r- Before annealing
1000
-1000
5
After annealing
-2000
cn
in
<
e0 -3000
®
3000
3
03
2000
-
500
1000
1500
After annealing
2000
^ —
1000
-1000
'-B e fo re
annealing
-2000
-3000
0
500
1000
1500
2000
Scanning length (jim)
Figure C .l: Surface roughness of LaA103 as measured with a profilometer
before
and
after
annealing
for
(a)
flame
fusion
substrate
and
(b)
Czochralski substrate.
Thin films of YBa2Cu30 7.^ (~ 6000 A thick) were grown on the two
substrates by laser ablation.
The T^c of the film made on the flame fusion
substrate was 89.8 K and exhibited a narrow transition region ( ~ 0.6 K), while
the film made on the Czochralski substrate had a T^c of 85.9 K, a broad
transition region ( ~ 4 K), with a different tail, as can be seen from the inset of
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182
1.2
1
1
1
1
1
1
T
Flame fusion method
Czochralski method
1.0x10
T arrcw fam rt (K)
86
88
90
92
94
96
98
100
Temperature (K)
Figure C.2: Plots of relative resistance versus tem perature for YBa2Cu30 7.£
films on (100) LaA103 made by flame fusion and by the Czochralski
method.
figure C.2.
Since two different roughening behaviors were observed in LaA103
substrates made by the fiame fusion and the Czocnraiski method, we believe th at
the roughening is not due to the intrinsic properties of LaA103.
The relatively
large post-anneal roughening observed for the Czochralski substrate could have been
caused by relief of stress created during the growth process or during the sawing
or polishing of the substrate.
Thus, we have shown th at there is roughening of the surface of LaA103 when
subjected to an annealing process similar to the one th at the substrate undergoes
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183
during the deposition of YBa2Cu30 7.^ thin films by laser ablation.
The surface
roughening was larger for the substrate made by the Czochralski method than for
the one made by flame fusion.
The roughening of the surface of the Game fusion
substrate had no noticeable effect on the T^c of the Glm on it, as compared with
similar films on S rT i0 3.
However, we believe th at the 4 K decrease in T f for
the film deposited on the Czochralski substrate may be a direct consequence of the
enormous surface roughening developed by the substrate during the therm al cycling
involved in the deposition process.
Therefore, a careful testing of LaA103
substrates m ust be performed before the deposition of HTS films by laser ablation
to determine if the surface roughens as a result of the heating and cooling cycle
involved in the deposition method.
The results of this analysis are summarized
in reference 13.
C.3
h
References
1.
Klein, N.; Muller, G.; Piel, H.; Roas, B.; Schultz, L.; Klein, U.; and Peiniger,
M.: M illim ete r Wave Surface R esistance o f E p ita x ia lly own Y B a3C u30 7mX
T hin F ilm s, Appl. Phys. Lett. 54, 757-759 (1989).
2.
W orthington, T. K.; Gallagher, W. J.; and Dinger, T. R.:A n iso tro p ic N a tu re
o f H ighrT em perature S u p erco n d u ctiv ity in Single-C rystal Y l B a 2C u30 7 x ,
Phys. Rev. Lett. 59, 1160-1163 (1987).
3.
Samara, G. A.; and Giardini, A. A.: Pressure D ependence o f th e D ielectric
C o n sta n t o f Strontium Titanife, Phys. Rev. 140, A954-A957 (1965).
4.
Weaver, H. E.: D ielectric P roperties o f Single Crysteds o f S r T i0 3 a t
T em p eratures, Phys. Chem. Solids 11, 274-277 (1959).
5.
Harvey, A. F.: M icrow ave E ngineering, Academic Press, 253-254 (1963).
Low
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.
184
6.
M iranda, F. A.; Gordon, W. L; Heinen, V. O.; Ebihara, B. T.; and Bhasin,
K. B.: M ea su rem en ts o f C o m plex P e r m ittiv ity o f M icrow ave S u b stra te s in
th e 2 0 to 300 K T em perature R ange F rom 26.5 to 40.0 G H z, Advances in
Cryogenic Engineering 35, Plenum Publishing Corporation, 1593-1599 (1990).
7.
Von Hippel, A. R.: D ielectric M aterials a n d A p p lications, (The M IT Press,
Cambridge, MA, 1954).
8.
Sandstrom, R. L.; Giess, E. A.; Gallagher, W. J., Segmuller, A.; Cooper, E.
I., Chisholm, M. F.; G upta, A; Shinde, S.; and Laibowitz, R. B.:
L a n th a n u m
G allate
Su b stra tes
for
E p ita xia l
H igh-tem perature
S u p erco n d u ctin g T h in F ilm s, Appl. Phys. Lett. 53, 1874-1876 (1988).
9.
M iranda, F. A.; Gordon, W. L.; Bhasin, K. B.; Ebihara, B. T.; Heinen, V.
O.; and Chorey, C. M.: C o m plex P e r m ittiv ity o f L a n th a n u m A lu m in a te in
the 20 to 300 K T em perature R ange F rom 26.5 to 40.0 G H z, Microwave
Opt. Tech. Lett. 3, 11-13 (1990).
10. Simon, R. W.; P la tt, C. E.; Lee, G. S.; Daly, K. P.; Wire, M. S.; Luine, J.
A.; and Urbanik, M: Low -loss S u b stra te fo r E p ita xia l G row th o f Hightem p era tu re Superconductor T h in F ilm s, Appl. Phys. Lett. 53, 2677-2679
(1988).
11. Miyazawa, S.: Surface R ough ening A ssociated W ith ~ 140 °C Transition o f a
L a G a O j S u b stra te For H igh T c S uperconducting F ilm s, Appl. Phys. Lett.
55, 2230-2232 (1989).
12. Bhasin, K. B.; W arner, J. D.; Liu, D. C.; and Romanofsky, R. R.: Interfacial
R o u g h n ess in H igh F requency M icroelectronics Interconnections a n d
P ackaging, J. Vac. Sci. Technol. A3, 778-781 (1985).
13. W arner, J. D.; Bhasin, K. B.; and M iranda, F. A.: D ependence o f th e C ritical
T em p era tu re o f Laser-ablated Y B a 2C u30 7_g T hin F ilm s on L a A 1 0 3
S u b stra te G row th Technique, Supercond. Sci. Technol. 3, 437-439 (1990).
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w ith o u t perm ission.
Appendix D
Evaluation of the Gap Parameter
The tem perature dependence of the gap param eter A(T) can be determine by
solving numerically the following expression,1'2
(D .l)
(N(O)V)"1 = /{j^tanh [%0(£2 + A 2) * ]( £ 2 + A 2) ',yid f
where, in the BCS theory, N(0) is the density of states a t the Fermi level, V is
the interaction potential, hv is the cutoff energy 3 Vy^, = -V for kstates <
and Vkk> = 0 for k states > hi/, ^ = l/k g T , and
hv
is the single particle
energy relative to the Fermi energy.
Before equation (D .l) can be solve for A, one must know N(0)V and h v .
To
determine N(0)V and hv one can use the following equation,1,2
kBT c =
where dc = l / k BT™w.
1/ ^ c =
l - l S h v e t '1^
(D.2)
0^
The procedure to determine N(0)V and hv simultaneously
is given below.
1. Using the measured value of T^IW we determined £c.
2. To determine hv and N(0)V, we assumed a trial value for hv, and using
equation (D.2) calculate a value for N(0)V.
This value is then used in
185
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186
equation (D .l) to calculate A.
We continued to vary hi/ and calculate N(0)V
until the calculated A in equation (D .l) is < 5 x 10'6 eV.
This will give
a good approximation to A (T“ w)=0, and for hi/ and N(0)V.
3. Finally, using the values of hi/ and N(0)V, which satisfy the condition
A (T“ W) < 5 x 10*6 eV, in equation (D .l), and allowing T to change, we
determined how A varies with T.
The obtained values for A(T) (~ 5.4 x 10*3 eV a t T /T c = 0.95) were consistent
w ith values reported by others (~ 5.6 x 10"3 eV a t T /T c = 0.95)3 assuming a
BCS-type gap for the YBa2Cu30 7 (j superconductor.
References
1.
Bardeen, J.; Cooper, L. N.; and Schrieffer, J. R.: T h eo ry o f Su p erco n d u ctivity,
Phys. Rev. 108, 1175-1204 (1957).
2.
Tinkham , M.: Intro d u ctio n to S u p erco n d u ctivity, 34 (Krieger, M alabar, FL,
1985).
3.
G ittlem an, J. I.; and M atey, J. R.: M o d elin g th e M icrow ave P roperties o f th e
Y B a 2Cu30 7 x Superconductors, J. Appl. Phys. 65, 688-691 (1989).
i
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.
Literature Cited
Chapter 1
1. Bardeen, J.; Cooper, L. N.; and Schrieffer, J. R.: T h e o ry o f Sup erco n d u ctivity,
Phys. Rev. 108, 1175-1204 (1957).
2. Onnes, H. K.: T he R esistan ce o f P u re M ercu ry a t H elium Tem peratures.
F u rth er E xp erim e n ts W ith L iq u id H elium , Leiden Commun. 120b, 657-658
(1911); D isappearance o f th e E lectrical R esista n ce o f M ercu ry a t H elium
Tem peratures, Leiden Commun. 122b, 657-658 (1911).
3.
File, J.; and Mills, R. G.: O bservation o f P ersistent Current
Superco nducting Solenoid, Phys. Rev. Lett. 10, 93-96 (1963).
4.
Meissner, W.; and Ochsenfeld, R.: E in n euer E ffe k t bei
Supraleitfahigkeit, Naturwissenschaften 21, 787-788 (1933).
5.
Bednorz, J. G.; and Mueller K. A.: P ossible H ig h -T c S u p erc o n d u ctiv ity in th e
B a-L a-C u-O S y ste m , Z. Physics B 64, 189-193 (1986).
6.
Wu, M. K.; Ashburn, J. R.; Torng, C. J.; Hor, P. H.; Meng, R. L.; Gao, L.;
Huang, Z. J.; Wang, Y. Q.; and Chu, C. W.: S u p e rc o n d u ctiv ity a t 93 K
in a N e w M ixed-P hase Y -B a -C u -0 C om pound S y ste m a t A m b ie n t Pressure,
Phys. Rev. Lett. 58, 908-910 (1987).
7.
Sheng, Z. Z.; and Hermann, A. M.: B u lk S u p erco n d u c tivity a t 120 K in the
T I-C a /B a -C u -O S yste m , Nature 332, 138-139 (1988).
8.
Glover, R. E.; and Tinkham, M.: C o n d u c tiv ity o f Supercondu cting F ilm s fo r
P h o to n Energies B etw een 0.3 and 40 K T C, Phys. Rev. 108, 243-256 (1957).
9.
Rugheimer, N. M.; Lehoczky, A.; and Briscoe, C. V.: M icrow ave Transm issionand-R eflection-C oefficient R a tio s o f T h in S uperco nducting T h in F ilm s, Phys.
Rev. 154, 414-421 (1967).
10.
in
E in tr itt
a
der
Lehoczky, S. L.; and Briscoe, C. V.: F lu ctu a tio n E ffe cts in th e ac
C o n d u c tiv ity o f T hin Superconducting L ea d F ilm s a t M icrow ave
Frequencies, Phys. Rev. B 11, 3938-3951 (1971).
11. M attis, D. C.; and Bardeen, J.: T h eo ry o f T h e A n o m a lo u s Skin E ffect in
N orm al and Superconducting M etals, Phys. Rev. I l l , 412-417 (1958).
187
r
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.
188
12. Sridhar, S: M icrow ave R esponse o f T h in F ilm Superconductors, J. Appl. Phys.
63, 159-166 (1988).
13. Tarascon, J. M.; Greene, L. H.; McKinnon, W. R.; and Hull, G. W.;
S u p e rc o n d u c tiv ity a t 90 K in a M u ltip h a se O xide o f Y -B a-C u, Phys. Rev.
B 35, 7115-7117 (1987).
14. G rant, P. M.; Beyers, R. B.; Gngler, E. M.-, Lim, G.; Parkin, S.S.P.; Ramirez,
M. L.; Lee, V. Y.; Nazzal, A.; Vazquez, J. E.; and Savoy, R. J.:
S u p e rc o n d u c tiv ity A b o v e 90 K in the C om pound Y B a 2C u3Ox : Stru ctu ra l,
T ra n sp o rt, a n d M a g n etic P roperties, Phys. Rev. B 35, 7242-7244 (1987).
15. Greedan, J. E.; O’Reilly, A. H.; and Stager, C. V.: O xygen O rdering in the
C ry sta l S tru c tu re o f th e 93-K Superconductor Y B a 2Cu30 7 U sing P ow der
N e u tro n D iffraction a t 298 a n d 79.5 K , Phys. Rev. B 35, 8770-8773 (1987).
16. Tarascon, J. M.; McKinnon, W. R.; Greene, L. H.; Hull, G. W.; and Vogel,
E. M.: O xygen and R are-earth D oping o f th e 90-K S u percon ducting
P e ro v sk ite Y B a 2C u30 7-x, Phys. Rev. B 36, 226-234 (1987).
17. Cava, R. J.; Batlogg, B.; Chen, C. H.; Rietman, E. A.; Zahurak, S. M.; and
W erder, D.: Single-phase 60-K B u lk Superconductor in A nnealed
B a 2 Y C u 30 7mj (0.3 < 6 < 0.4) W ith C orrelated O xygen Vacancies in the
C u-O C hains, Phys. Rev. B. 36, 5719-5722 (1987).
18. Maeda, H.; Tanaka, Y.; Fukutomi, M.; and Asano, T.: A N ew H ig b -T c O xide
Superco nductor W ith o u t a R a re E a rth E lem en t, Jpn. J. Appl. Phys. 27,
L209-L210 (1988).
19. Hanzen, R. M.; Prew itt, C. T.; Angel, R. J.; Ross, N. L.; Finger, L. W.;
Hadidiacos, C. G.; Veblen, D. R.; Heaney, P. J.; Hor, P. H.; Meng, R. L.;
Sun, Y. Y.; Wang, Y. Q.; Xue, Y. Y.; Huang, Z. J.; Gao, L.; Bechtold,
J.; and Chu, C. W.: S u p erc o n d u c tivity in th e H igh-T c B i-Sr-C a-C u-O
S y stem : P hase Id entifica tion , Phys. Rev. Lett. 60, 1174-1177 (1988).
20. Subramanian, M. A.; Torardi, C. C.; Calabrese, J. C.; Gopalaskrishnan, J.;
Morrissey, K. J.; Askew, T. R.; Flippen, R. B.; Chowdhry, U.; and Sleight,
A. W.: A N e w H igb-T em pera tu re Superconductor: B i ^ r ^ x Cax C u2Og+^
Science 239, 1015-1017 (1988).
21. Herman, F.; Kasowski, R. V.; and Hsu, W. Y.: Electronic S tru ctu re o f
B ijS rjC a C u jO g h ig b -T c Superconductors, Phys. Rev. B 38, 204-207 (1988).
22. M attheiss, L. F.; and Hamann, D. R.: E lectronic B a n d P roperties o f
C a S r jB ijC u P g , Phys. Rev. B 38, 5012-5015 (1988).
I
R eproduced w ith perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
189
23. Green, S. M.; Mei, Y.; Manzi, A. E.; Luo, H. L.; Ramesh, R.; and Thomas,
G.: E ffects o f C o m po sitio nal
V ariations on
th e P roperties o f
Superco n d u ctin g (B iJ t b ) ^ r 2Ca2C u30 ^ , J. Appl. Phys. 66, (1989).
24. Ramesh, R.; Green, S. M.; Mei, Y.; Manzi, A. E.; and Luo, H. L.:
M icro stru ctu re-p ro p erty
C orrelations
in
th e
B i(P b)-Sr-C arC urO
Superconducting S y ste m , J. Appl. Phys. 66, 1265-1272 (1989).
25. Parkin, S. S. P.; Lee, V. Y.; Engler, E. M.; Nazzal, A. I.; Huang, T. C.;
Gorman, G.; Savoy, R.; and Beyers, R.: B u lk S u p e rc o n d u c tiv ity a t 125 K
in T l2C a2B a3C u3Ox, Phys. Rev. Lett. 60, 2539-2542 (1988).
26. Wu, P. T.; Liu, R. S.; Liang, J. M.; Lee, W. H.; and Chang, L.: S ynthesis,
T ransp ort, M a g n etiza tio n a n d S tru ctu ra l C haracterizations o f T l-C a-B a-C u-O
Specim ens w ith T 0= 123 K and T 0juet= 155 K , Physica C 156, 109-112
(1988).
27. Ihara, H.; Sugise, R.; Hirabayashi, M.*, Terada, N.; Jo, M.; Hayashi, K.;
Negishi, A.; Tokumoto, M.; Kimura, Y.; and Shimomura, T.: A N ew HighT c T lB a 2Ca3C u4O n Superconductor w ith T c > 120 K , Nature 334, 510-511
(1988).
28. Torardi, C. C.; Subramanian, M. A.; Calabrese, J. C.; Gopalakrishnan, J.;
Morrissey, K. J.; Askew, T. R.; Flippen, R. B.; Chowdhry, U; and Sleight,
A. W.: C rysta l S tru c tu re o f T l ^ a j C a j C u f l ^ g , a 125 K Superconductor,
Science 240, 631-634 (1988).
29. Hazen, R. M.; Finger, L. W.; Angel, R. J.; Prew itt, C. T.; Ross, N. L.;
Hadidiacos, C. G.; Heaney, P. J.; Veblen, D. R.; Sheng, Z. Z.; El Ali, A.;
and Hermann, A. M.: 100-K S uperconducting P hases in th e T l-C a-B a-C u-O
S y ste m , Phys. Rev. Lett. 60, 1657-1660 (1988).
30. Ginley, D. S.; Morosin, B.; Baughman, R. J.; Schirber, E. L., and Kwak, J.
F.: G row th o f C rystals an d E ffects o f O xygen A n n e a lin g in th e Bi-Ca-SrC u-O a nd Tl-C arBarC u-O Superconductor S y stem s, J. Cryst. Growth 91,
466-470 (1988).
31. Ianno, N. (Private communication).
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w ith o u t perm ission.
190
Chapter 2
1.
Glover III, R. E.; and Tinkham, M.: C o n d u c tiv ity o f S u p erco n d u ctin g F ilm s
for P h o to n Energies B etw een 0.3 and 40 K g T c, Phys. Rev. 108, 243-256
(1957).
2.
Sridhar, S: M icrow ave R esponse o f T b in -F ilm Su perconductors, J. Appl. Phys.
63, 159-166, (1988).
3.
Gorter, J. C.; and Casimir, H. B. G.: T h e th erm o d yn a m ics
S uperconducting S ta te, Physik. Z. 35, 963-966 (1934).
4.
Bardeen, J.; Cooper, L. N.; and Schrieffer, J. R.: T h e o ry o f S u p erco n d u ctivity,
Phys. Rev. 108, 1175-1204 (1957).
o f th e
5. M attis, D. C.; and Bardeen, J.: T h eo ry o f th e A n o m a lo u s S kin E ffec t in
N orm al a n d Superconducting M etals, Phys. Rev. I l l , 412-417 (1958).
6.
Hinken, J. H.: Superconductor Electronics: F u n d a m e n ta ls a n d M icrow ave
A pplica tion s, 23 (Springer-Verlag, New York, 1989)-.
7. Sridhar, S.: M icrow ave D yn a m ics o f Q uasi particles a n d C ritical F ields in
Superconducting F ilm s, Ph.D. thesis, California Institute of Technology,
(1983).
8.
Halbritter, J.: C om parison B etw een M easured a n d C alculated R F Losses in th e
Superconducting S ta te, Z. Physik 238, 466-476 (1970).
9.
Jackson, J. D.: Classical E lectrodynam ics, Sec. Ed., 296 (John Wiley and Sons,
Inc., New York, 1975).
10. Gittlem an, J. I.; and Rosemblum, B.: M icrow ave P roperties o f Superconductors,
IEEE Proc. 52, 1138-1147 (1964).
Chapter 3
1.
Lehoczky, S. L.; and Briscoe, C. V.: F lu ctu a tio n E ffects in th e ac
C o n d u c tiv ity o f thin S u p ercondu cting L ea d F ilm s a t M icrow ave Frequencies,
Phys. Rev. B 11, 3938-3951 (1971).
r
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.
191
2. Rugheimer, N. M.; Lehoczky, A.; and Briscoe, C. V.: M icrow ave Transm issionand-reflection-coeflicient R a tio s o f Thin Superco n d u ctin g films., Phys. Rev.
154, 414-421 (1967).
3. Venkatesan, T.; Wu, X. D.; D utta, B.; Inam, A.; Hedge, M. S.; Hwang, D.
M.; Chang, C. C.; Nazar, L.; and Wikens, B.: H igh-T em perature
S u p e rc o n d u c tiv ity in U ltrathin F ilm s o f Y B a 2Cu30 7mX, Appl. Phys. Lett. 54,
581-583 (1989).
4. Hewlett Packard: M illim eter-w ave V ector M ea su re m en ts U sing th e H P 8510A
N e tw o rk A nalyzer: P ro d u ct N o te no. 8510-1, 10 (1984).
5. M iranda, F. A.; Gordon, W. L; Heinen, V. O.; Ebihara, B. T.; and Bhasin,
K. B.: M ea su rem en ts o f C om plex P e r m ittiv ity o f M icrow ave S u b stra tes in
th e 20 to 300 K T em p era tu re R ange F rom 26.5 to 40.0 G H z, Advances in
Cryogenic Engineering 35, Plenum Publishing Corporation, 1593-1599 (1990).
6. M iranda, F. A.; Gordon, W. L.; Bhasin, K. B.; Ebihara, B. T.; Heinen, V.
O.; and Chorey, C. M.: C om plex P e r m ittiv ity o f L a n th a n u m A lu m in a te in
th e 20 to 300 K T em p era tu re R a n g e F rom 26.5 to 40.0 G H z, Microwave
Opt. Tech. Lett. 3, 11-13 (1990).
Chapter 4
1.
Talvacchio, J.; and Wagner, G. R.: H ig h -T c F ilm D evelo p m en t fo r Electronic
A p p lica tio n s, in Superconductivity Applications for Infrared and Microwave
Devices, SPIE Proc. 1292, 2-12 (1990).
2.
Harshmann, D. R.; Schneemeyer, L. F.; Waszczak, J. V.; Aeppli, G.; Cava,
R. J.; Batlogg, B.; Rupp, L. W.; Ansaldo, E. J.; and Williams, D. LI.:
M a g n etic P enetratio n D ep th in S in gle-C rystal Y B a 2C u30 7^ Phys. Rev. B
39, 851-854 (1989).
3.
Krusin-Elbaum, L.; Greene, R. L.; Holtzberg, F.; Malozemoff, A. P.; and
Yeshurun, Y.: Direct Measurement o f th e T em p era tu re-D ep en d en t M agnetic
P en etra tio n D epth in Y -B a-C u-O C rystals, Phys. Rev. Lett. 62, 217-220
(1989).
4. Klein, N.; Muller, G.; Piel, H.; Roas, B.; Schultz, L.; Klein, U.; and Peiniger,
M.: M illim ete r W ave Surface R esistance o f E p ita x ia lly G row n Y B a 2Cu30 7_g
T hin F ilm s, Appl. Phys. Lett. 54, 757-759 (1989).
R eproduced with perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
192
5.
Qiu, X. G.; Cui, C. G.; Zhang, Y. Z.; Li, S. L.; Zhao, Y. Y.; Xu, P.; and
Li, L.: C ritical C urrent M easu rem ents in Y B a 2C u3O r_x T hin F ilm G rown
L aA 103 su b stra te , J. Appl. Phys. 68, 884-886 (1990).
6.
Miranda, F. A.; Gordon, W. L.; Bhasin, K. B.; Heinen, V. O.; W arner, J. D.;
and Valeo, G. J.: M illim eter W ave Transm ission S tu d ie s o f Y B a 2C u30 7 ^
Thin F ilm s in the 26.5 to 40.0 G H z F requency R ange, Superconductivity
and Applications, Plenum Press, 735-748 (1990).
7. Sridhar, S.: M icrow ave D ynam ics o f Q uasi particles a n d C ritical F ields in
Superconducting F ilm s, Ph.D. Thesis, California Institute of Technology,
(1983).
8.
Anlage, S.; Sze, H.; Snortland, H. J.; Tahara, S.; Langley, B.; Eom, C. B.;
and M. R. Beasley: M easurem en ts o f th e M ag netic P enetratio n D epth in
Y B a 2C u30 7 j T hin F ilm s b y the M icrostrip R eso n a to r Technique, Appl.
Phys. L e tt.' 54, 2710-2712 (1989).
9.
England, P.; Venkatesan, T.; Wu, X. D.; Inam, A.; Hedge, M. S.; Cheeks, T.
L.;
and
Craighead,
H.
G.:
Intrinsic
S uperconductor/N orm alM eta l/S u p erco n d u cto r-like W eak L in k s in Y B a 2C u30 7 x T hin F ilm s, Appl.
Phys. Lett. 53, 2336-2338 (1988).
10. Dubson, M. A.; Herbert, S. T.; Calabrese, J. J.; Harris, D. C.; P atton, B. R.;
Garland, J. C.: N on-O hm ic D issipative R egim e in the Superconducting
Transition o f P olycrystalline Y 1B a2C u3Ot , Phys. Rev. Lett. 60, 1061-1064
(1988).
11. Nichols, C. S.; Shiren, N. S.; Laibowitz, R. B.; and Kazyaka, T. G.:
M icrow ave S tu d ies Through F ilm s o f Y B a 2C u30 7mg, Phys. Rev. B 38,
11970-11973 (1988).
12. Blazey, K. W., Muller, K. A.; Bednorz, J. G.; Belinger, W.; Amoretti, G.;
Buluggiu, E.; Vera, A.; and M atacotta, F. C.: Low -F ield M icrow ave
A b sorption in th e Superconducting C opper O xides, Phys. Rev. B 36, 72417243 (1987).
13.
Wu, D. H.; Shiftman, C. A.; and Sridhar, S.: F ield Variation o f the
P enetration D epth in Ceram ic Y j B a ^ U j O ^ Phys. Rev. B 38, 9311-9314
(1988).
14. Golosovsky, M.; Davidov, D.; Rettori, C.; and Stern A.: M a g n etic Field
M odulation E ffects on the M icrow ave Transm ission T hrough Su perconducting
T h in F ilm s o f Y-B a-C u-O , Phys. Rev. B 40, 9299-9302 (1989).
I
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.
193
15. Bardeen, J.; Ginsberg, D. M.; and Salamon, M. B.: E xcito a ic S u p erco n d u ctivity
in L a yer S tru ctu res, Novel Superconductivity, eds. S. A. Wolf, and V.
Kreain, Plenum Press, 333-339 (1987).
16. Ramesh, R.; Chang, C. C.; Ravi, T. S.; Hwang, D. M.; Inam, A.; Xi, X. X.;
Li, Q.; Wu, X. D.; and Venkatesan, T.: S tru c tu ra l P erfection o f Y-Ba-C uO T hin F ilm s C ontrolled b y th e G row th M echanism , Appl. Phys. Lett. 57,
1064-1066 (1990).
17. Phillips, J. M.; Siegal, M. P.; Perry, C. L.; and M arshall, J. H.: C om parison
o f B a2 Y C u30 7mg F ilm s on N d G a 0 3 a n d L a A lO j, to be published in IEEE
Trans, on Magnetics (1991).
18. Shah, S. I.; and Carcia, P. F.: S u p erc o n d u ctiv ity and R e sp u tte rin g E ffects in
R f S p u tte re d Y B a 2C u30 7mX T hin F ilm s, Appl. Phys. Lett. 51, 2146-2148
(1987).
19. Migliuolo, M.; Belan, R. M.; and Brewer, J. A.: A b sen ce o f N ega tive Ions
E ffects D u rin g O n -A xis Single T arget S p u tte r D epositions o f Y-Ba- C u-O
Thin F ilm s on Si(100), Appl. Phys. Lett. 56, 2572-2574 (1990).
20. Venkatesan, T.: Private Communication.
21. Talvacchio, J.: Private Communication.
22. Chorey, C. M.; Bhasin, K. B.; Warner, J. D.; Josefowicz, J. Y.; Rensch, D.
B.; and Nieh, C. W.: A n E xp erim en ta l S tu d y o f H igh T c Supercondu cting
M icrostrip T ransm ission L in es a t 35 G H z a n d th e E ffect o f F ilm
M orphology, Presented a t the ” 1990 Applied Superconductivity Conference” ,
sponsored by the Institute of Electrical and Electronics Engineers, Aspen,
Colorado, September 24-28, 1990.
23. Drabeck, L.; Carini, J. P.; Gruner, G.; Hylton, T.; Char, K.; and Beasley, M.
R.: P ow er-law T em perature D ependence o f th e E lectro d yn a m ic P roperties
in O riented Y B a 2C u30 Jmg a n d Y2B a4C ugO 16mg F ilm s, Phys. Rev. B 39,785788 (1989).
24.
Chi, H.; Nagi, A. D. S.: M a g n etic P enetration D ep th
Superconductors, Phys. Rev. B 40, 7361-7363 (1989).
of
H ig h -T c
25. Schilling, A.; Hulliger, F.; and O tt, H. R.: M ea su rem en t o f the London
P enetration D ep th on Y B a2C u 4Og and Y B a 2C u30 7 P olycrystals, Physica C
168, 272-278 (1990).
R eproduced w ith perm ission o f the copyright owner. F urth er reproduction prohibited w itho ut perm ission.
194
26. Kobrin, P. H.; Ho, W.; Hall, W. F.; Hood, P.J.; Gergis, I. S.; and Harker, A.
B.: M illim eterw a ve C o m p lex C o n d u c tiv ity o f som e E p ita x ia l Y B a 2Cu30 7,g
F ilm s, Phys. Rev. B 42, 6259-6263 (1990).
27. Drabeck, L.; Gruner, G.; Chang, J. J.; Inam, A.; Wu, X. D.; Nazar, L.;
Venkatesan, T.; Scalapino, D. J.: M illim eter-w a ve Surface Im pedance o f
Y B 2C u3O t_6 T h in F ilm s, Phys. Rev. B 40, 7350-7353 (1989).
28. Klein, N.; Muller, G.; Orbach, S.; Piel, H.; Chaloupka, H. Roas, B.; Schultz,
L.; Klein, U.; and Peiniger, M.: M illim e te r W ave Surface R esistance and
L ondon P enetration D ep th o f YBa~C u?O r x T h in F ilm s, Physica C 162-164,
1549-1550 (1989).
* 3 "
29. Hylton, T. L.; Beasley, M . R.; Kapitulnik, A.; Carini, J. P.; Drabeck, L.; and
Gruner, G.: Surface Im pedance S tu d ie s o f th e High- Tc O xide
Superconductors, IEEE Trans, on Magnetics 25, 810-813 (1989).
30. Klein, N.; Chaloupka, H.; Muller, G.; Orbach, S.; Piel, H.; Roas, B.; Schultz,
L.; Klein, U.; and Peiniger, M.: T h e E ffe ctiv e M icrow ave Surface Im pedance
o f Highr T c T hin F ilm s, J. Appl. Phys. 67, 6940-6945 (1990).
31. Piel, H.; and Muller, G.: T h e M icrow ave Surface Im pedance o f H ig h -T c
Superconductors, presented a t the ” 1990 Applied Superconductivity
Conference” , sponsored by the IEEE, Aspen, Colorado, September 24-28,
1990; Also to be published in the IEEE Trans, on Magn. (1991).
32. M attis, D. C.; and Bardeen, J.: T h eo ry o f th e Anomalous Skin E ffect in
N orm al a n d S u p erconductin g M etals, Phys. Rev. I l l , 412-417 (1958).
33. Tinkham, M.: Intro d u ctio n to S u p erco n d u ctivity, (Krieger, M alabar, FL, 1985).
34. Bardeen, J.; Cooper, L. N.; and Schrieffer, J. R.: T h e o ry o f S u p erco n d u ctivity,
Phys. Rev. 108, 1175-1204 (1957).
35. Hebei, L. C.; and Slichter, C. P.: N uclear S pin R elaxa tion in N orm al and
Superco n d u ctin g A lu m in u m , Phys. Rev. 107, 901 (1957); 113, 1504-1519
(1959).
36. W arren, W. W.; W alstedt, R. E.; Brennert, G. F.; Espinosa, G. P.; and
Rameika, J. P.: E vidence fo r T w o P airing Energies from N uclear SpinL a ttic e R ela xa tio n in S u p erconducting B a2 Y C u 30 7 g Phys. Rev. Lett. 59,
1860-1863 (1987).
r
R eproduced w ith perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
195
37. Ho, W.; Hood, P. J.; Hall, W. F.; Kobrin, P.; Harker, A. B.; and DeWames,
R. E.: M illim eter-w a ve C o m plex C o n d u c tiv ity M ea su rem en ts o f B i-C a-Sr-C uO S u percon ducting T h in F ilm s, Phys. Rev. B 38, 7029-7032 (1988).
38. Bhasin, K. B.; W arner, J. D.; Chorey, C. M.; Ebihara, B. T.; Romanofsky,
R. R.; Heinen, V. O.; M iranda, F. A.; and Gordon, W. L.: M icrow ave
C o n d u c tiv ity o f Laser A b la te d Y B a 2C u30 7mg Superco n d u ctin g T h in F ilm s
and Its R elation to M icrostrip Transm ission L in e Perform ance, NASA CP
10043 , 78-81 (1990).
39. Bhasin, K. B.; W arner, J. D.; Romanofsky, R. R.; Heinen, V. O.; Chorey, C.
M.; Kong, K. S.; Lee, H. Y.; and Itoh, T.: P erform ance a n d M o d elin g o f
Su p ercond ucting R in g R esonators a t M illim eter-w ave Frequencies, IEEE
MTT-S International Microwave Symposium Digest 1, 269-272 (1990).
40. Hu, Q.; and Richards, P. L.: Design A n a ly sis o f a High T c Superco n d u ctin g
M icrobolom eter, Appl. Phys. Lett. 55, 2444-2446 (1989).
41.
Newman, N; Char, K.; Garrison, S. M.; Barton, R. W.; Taber, R. C.; Eom,
C. B.; Geballe, T. H.; and Wilkens, B.: Y B a 2C u30 %g Sup ercond ucting
F ilm s w ith L o w M icrow ave Surface R esistance O ver Large A reas, Appl.
Phys. Lett. 57, 520-522 (1990).
42. Sridhar, S.: Microwave R esponse o f T h in F ilm Superconductors, J. Appl. Phys.
63, 159-166 (1988).
43. Larson, D. C.: P hysics o f T h in F ilm s, 6, 83 (1971).
44. Carini, J. P.; Awasthi, A. M.; Beyermann, W.; Gruner, G.; Hylton, T.; Char,
K.; Beasley, M. R.; and Kapitulnik, A.: M illim eter-w a ve Surface R esistance
M ea su rem en ts in H ighly O riented Y B a 2Cu30 7 g T hin F ilm s, Phys. Rev. B.
37, 9726-9729 (1988).
45. Sridhar, S.; and Kennedy, W.: N ovel T echnique to M easure th e M icrow ave
R esponse o f High T c Superconductors B etw een 4.2 a n d 200 K , Rev. Sci.
Instrum. 59, 531-536 (1988).
46. Bhasin, K. B.; Warner, J. D.; M iranda, F. A.; Gordon, W. L.; and Newman,
H. S.: D eterm ination o f Surface R esista nce a n d M a g n etic P en etration D epth
o f Superconducting Y B a 2Cu30 7mg Thin F ilm s b y M icrow ave P ow er
Transm ission M easurem ents, to be published in IEEE Trans, on Magnetics
(1991), and NASA TM-103616 (1990).
f
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.
196
47. Maeda, H; Tanaka, Y; Fukutomi, M.; and Asano, T.: A N e w H ig h -T c O xide
S uperconductor W ith o u t a R are E a rth E lem en t, Jpn. J. Appl. Phys. 27,
L209-L210, (1988).
48. Valeo, G. J; Rohrer, N. J.; W arner, J. D.; and Bhasin, K. B.: S eq u en tia lly
E vaporated T h in Y -B a-C u-O S u p ercon ductor Film s: C om position and
Processing E ffects, American Institute of Physics, Proceedings no. 182, 147152 (1989).
49. Kalkur, T. S.; Kwor, R.; Jernigan, S.; and Smith, R.: C oevaporated Bi-Sr-CaCu O xide S uperconducting F ilm s an d T heir P a ttern in g , presented a t the
Conf. Sci. Technol. Thin Films Supercond., Colorado Springs, CO, 14-18
November (1988).
50. Balestrino, G.; Foglietti, V.; Marinelli, M.; Milani, E.; Paoletti, A.; and Paroli,
P.: T ransport C ritical C urrent D e n sity in E p ita xia l B i2S r2C a1C u2°8 + x
Film s: E ffects O f the S u b stra te T w inning, Appl. Phys. Lett. 57, 2359-2361
(1990).
51. M iranda, F. A.; Bhasin, K. B.; Heinen, V. O.; Kwor, R.; and Kalkur, T. S.:
M icrow ave co n d u c tiv ity o f su percon ducting B i-Sr-C a-C u-O th in S im s in the
26.5 to 40.0 G H z frequency range, Physica C 168, 91-98 (1990).
52. Ashcroft, N. W.; and Mermin, N. D.: Solid S ta te P hysics, Holt, Rinehart and
Winston, 8 (1976).
53. Torardi, C. C.; Subramanian, M. A.; Calabrese, J. C.; Gopalakrishnan, J.;
Morrissey, K. J.; Askew, T. R.; Flippen, R. B.; Chowdhry, U.; and Sleight,
A. W.: C rysta l S tru ctu re o f T l ^ a 2Ca2C u2O 10, a 125 K Superconductor,
Science 240, 631-634 (1988).
54. Hylton, T. L.; Kapitulnik, A.; Beasley, M. R.; Carini, J. P.; Drabeck, L.; and
Gruner, G.: W ea kly C oupled G rain M o d el o f H igh-frequency Losses in H igh
T c Superconducting T h in F ilm s, Appl. Phys. Lett. 53, 1343-1345 (1988).
55. Muhlschlegel, B.: D ie Therm odynam ischen F u n ktio n en des Supraleiters, Z. Phys.
155, 313-327 (1959).
56. Lichti, R. L.; Chan, K. C. B.; Cooke, D. W.; and Boekema, C.: C oupling
S tre n g th s and F lu x P in n in g in O xide Superconductors, Appl. Phys. Lett.
54, 2361-2363 (1989).
57. Ianno, N. J.: P ulsed L aser D eposition o f Tl-C a-B a-C u-O film s a t 248 n m ,
Presented a t the 2nd Conf. on the Science and Technology of Thin Films
Superconductors, Denver, Co. March 29- April 1, 1990.
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.
197
58. Olson, W. L.; Eddy, M. M.; James, T. W.; Hammond, R. B.; Gruner, G; and
Drabeck, L.: P reparation o f Superconducting Tl-C arBarC u T h in F ilm s b y
C hem ical D eposition, Appl. Phys. Lett. 55, 188*190, (1989).
59. Chang, L. D.; Moskowitz, M. J.; Hammond, R. B.; Eddy, M. M.; Olson, W.
L.; Casavant, D. D.; Smith E. J.; and Robinson, M.: M icrow ave Surface
R esistance in Tl-based Superconductin g T hin F ilm s, Appl. Phys. Lett. 55,
1357-1359 (1989).
Chapter 5
1. Jackson, J. D.; Classical E lectrodynam ics, Sec. Ed., John Wiley and Sons, Inc.,
334-390 (1975).
2. Ramo, S.; Whinnery, J. R.; and Van Duzer, T.: F ields an d W aves in
C om m unication Electronics, John Wiley and Sons, Inc., 497 (1985).
3.
Ginzton, E. L.: A licrow ave M easurem ents, M°Graw Hill Book Co., (1957).
4.
Romanofsky, R. R.: A n a ly tic a l a nd E xp erim en ta l Procedures fo r D eterm in in g
P ropagation C haracteristics o f M illim eter- W ave G allium A rsen id e M icrostrip
L ines, NASA TP-2899 (1989).
5.
Smith, P. H.: T ransm ission L ine C alculator, Electronics 12, 29-31 (1939).
6.
Smith, P. H.: A n Im p ro ved Transm ission L in e C alculator, Electronics 17, ISO133, 318-325 (1944).
7.
Klein, N.; Muller, G.; Piel, H.; Roas, B.; Schultz, L.; Klein, U.; and Peiniger,
M.: M illim e te r w ave surface resistance o f e p ita xia lly grow n Y B a 2C u30 7mg
thin film s, Appl. Phys. Lett. 54, 757-759 (1989).
8.
Klein, N.; Muller, G.; Orbach, S.*, Piel, H.; Chaloupka, H.; Roas, B.; Schultz,
L.; Klein, U.; and Peiniger, M.: M illim eter w ave surface resistance and
London pen etration d ep th o f Y B a2C u 30 7^ th in film s, Physica C 162-164,
1549-1550 (1989).
9.
Cooke, D. W.; Gray, E. R.; Houlton, R. J.; Javadi, H. H. S.; Maez, M. A.;
Bennett, B. L.; Rusnak, B.; Meyer, E. A.; Arendt, P. N.; Beery, J. G.;
Brown, D. R.; Garzon, F. H.; Raistrick, I. D.; Rollet, A. D.; Bolmaro, B.;
Elliot, N. E.; Klein, N.; Muller, G.; Orbach, S.; Piel, H.; Josefowicz, J.Y.;
Rensch, D. B.; Drabeck, L.; and Gruner, G.: Surface resistance o f
R eproduced w ith perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
198
Y B a 2C u 30 7 g d im s deposited on L aG aO s su b stra tes, Physica C 162-164,
1537-1538 (1989).
10. M iranda, F. A.; Gordon, W. L.; Bhasin, K. B.; and W arner, J. D.:
M illim eter-w a ve
Surface R esistance o f L aser-ablated
Y B a 2C u30 7wg
S u p erconductin g F ilm s, Appl. Phys. Lett. 57, 1058-1060 (1990).
Appendix A
1.
Dijkkamp, D.; Venkatesan, T.; Wu, X. D.; Shaheen, S. A.; Jisrawi, N.; MinLee, Y. H.; McLean, W. L.; and Croft, M.: P reparation o f Y-B a-C u
O xide Superco nductor T hin F ilm s Using P ulsed L aser E va p o ra tio n F rom
High T c B u lk M aterial, Appl. Phys. Lett. 51, 619-621 (1987).
2.
Roas, B.; Schultz, L.; and Endres, G.: E p ita x ia l G row th o f Y B a 2C u30 7mX T hin
F ilm s b y a Laser E vaporatio n Process, Appl. Phys. Lett. 53, 1557-1559
(1989).
3. Inam, A.; Hedge, M. S.; Wu,
F.; Chase, E. W.; Chang,
A s-d ep o sited H igh T c a n d
T em p eratures, Appl. Phys.
X. D.; Venkatesan, T.; England, P.; Miceli, P.
C. C.; Tarascon, J. M.; and W achtman, J. B.:
J c Superconducting T hin F ilm s M ad e a t L o w
Lett. 53, 908-910 (1988).
4. Venkatesan, T.; Wu, X. D.; Inam, A.; and W achtman, J. B.: O bservation o f
T w o D istin c t C o m p o n en ts D uring P ulsed L aser D eposition o f H igh T c
Su p ercond ucting F ilm s, Appl. Phys. Lett. 52, 1193-1195 (1988).
5.
W arner, J. D.; Meola, J. E.; and Jenkins, K. E.: S tu d y o f D eposition o f
Y B a 2C u30 %$ on C ubic Zirconia, Superconductivity and Applications, Plenum
Publishing Corporation, 163-167 (1990).
6. W arner, J. D.; Bhasin, K. B.; and M iranda, F. A.: D ependence o f th e C ritical
T em p era tu re o f Laser A b la te d Y B a 2C u30 7 g T h in F ilm s on L a A 1 0 3
S u b stra te G row th Technique, Supercond. Sci. Technol. 3, 437-439 (1990).
7.
W arner, i . D.; Bhasin, K. B.; Varaljay, N. C.; Bohman, D. Y.; and Chorey,
C. M.;
G row th a n d P a tte rn in g o f Laser A b la te d Superconducting
Y B a2C u30 % s F ilm s on L a A 1 0 3 S u b strates, NASA TM-102436 (1990).
8. Chang, C. C.; Wu, X. D.; Ramesh, R.; Xi, X. X.; Ravi, T. S.; Venkatesan,
T.: Hwang, D. M.; Muenchausen, R. E.; Foltyn, S.; and Nogar, N. S.:
Origin of Surface Roughness for C-axis O riented Y-B arC u-O S uperconducting
F ilm s, Appl. Phys. Lett. 57, 1814-1816 (1990).
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.
199
9.
Bell, A. M. T.: C alculated x -ra y P ow der D iffraction P a tte rn s, and Theoretical
D en sities fo r P hases E ncountered in In vestig a tio n s o f Y-B a-C urO
Superconductors, Supercond. Sci. Technol. 3, 55-61 (1990).
10. Ianno, N. J.; Liou, S. H.; Woollam, J. A.; Thompson, D.; and Johs, B.:
P u lsed L aser D eposition o f TI-B a-C a-C u-O F ilm s a t 532 a n d 248
N ano m eters, subm itted to J. of M at. Res. (1990).
11. Lee, W. Y.; Lee, V. Y.; Salem, J.; Huang, T. C.; Savoy, R.; Bullock, D. C.;
and Parkin, S. S. P.: Superconducting T l-C a -B a -C u -0 T h in F ilm s W ith
Zero R esistance a t T em peratures o f up to 120 K , Appl. Phys. Lett. 53,
329-331 (1988).
12.
Tsaur, B. Y.; Dilorio, M. S.; and Strauss, A. J.: P reparation o f
S u p erco n d u ctin g Y B a 2C u3Ox T hin F ilm s b y O xygen A n n ea lin g o f M u ltila ye r
M e ta ls F ilins, Appl. Phys. Lett. 51, 858-860 (1987).
13. Valeo, G. J.; Rohrer, N. J.; W arner, J. D.; and Bhasin, K. B.: S eq u en tia lly
E v a p o ra te d T h in Y -B a-C u-O S uperconductor Film s: C om position and
P rocessing E ffects, American Institute of Physics, Proceedings no. 182, 147152 (1989).
14. Valeo, G. J.; Rohrer, N. J.; Warner, J. D.; and Bhasin, K. B.: Sequen tia lly
E va p o ra ted T h in Y -B a-C u-O S uperconducting F ilm s on M icrow ave
S u b stra tes, Proceedings of the DOD Workshop on High Tem perature
Superconductivity, Huntsville, Al, Gaciac IIT Research Institute, 197-203
(1989).
15. Mankiewich, P. M.; Scoefield, J. H.; Skocpol, W. J.; Howard, R. E.; Dayen,
A. H.; and Good, E.: R eproducible Technique fo r F abrication o f T hin F ilm s
o f H igh T ran sition T em p era tu re Superconductors, Appl. Phys. Lett. 51,
1753-1755 (1987).
16. Chan, S. W.; Bagley, B. G.; Greene, L. H.; Giroud, M.; Feldman, W. L.;
Jenken, K. R.; and Wilkins, B. J.: E ffect o f th e P ost-D eposition Processing
A m b ie n t on th e P reparation o f Superconducting Y B a2C u30 7 x C oevaporated
T h in F ilm s U sing a B a F 2 Source, Appl. Phys. Lett. 53, 1443-1445 (1988).
17. Phillips, J. R.; Mayer, J. W.; M artin, J. A.; and Nastasi, M.: V apor-deposited
S u p erco n d u ctin g Y B a 2C u30 7_ j Lines. E ffect o f T hickness a n d W id th on
Morphology, Appl. Phys. Lett. 56, 1374-1376 (1990).
18. Gijs, M. A. M.; and Jansen, R. J. E., M icrow ave
R esponse o f Y B a C u O Thinfilm D a yem B ridges, Appl. Phys. Lett. 56, 1484-1486 (1990).
i
R eproduced w ith perm ission o f the copyright owner. Further reproduction prohibited w itho ut perm ission.
200
19. Kalkur, T. S.; Kwor, R.; Jornigan, S.; and Smith, R.: C o-evaporated B i-S r-C a
C u-O xide S u percon ducting F ilm s a n d T heir P a tte rn in g , presented a t the
Conf. Sci. Technol. Thin Films Supercond., Colorado Springs, CO., Nov. 1418, (1988).
20. W east, R. C., ed.: C R C H andbook o f C h e m istry a nd P h ysics, 69th edition,
CRC Press, Inc. (1988-1989).
21. Talvacchio, J.; Gavaler, J. R.; Forrester, M. G.; and Braggins: to appear in
Science and Technology o f T hin F ilm s Superconductors II, eds. R. D.
McConnell and S. A. Wolf, Plenum Publishing Corporation (1990).
22. Venkatesan, T.; Chang, C. C.; Dijkkamp, D.; Ogale, S. B.; Chase, E. W.;
Farrow, L. A.; Hwang, D. W.; Miceli, P. F.; Schwarz, S. A.; Tarascon, J.
M.; Wu, X. D.; and Inam, A.: S u b stra te E ffec ts on th e P roperties o f Y - B a
C u-O S uperco nducting F ilm s P repared b y Laser D eposition, J. Appl. Phys.
63, 4591 (1988).
23. Adachi, H.; Hurochi, K.; Setsune, K.; Kitabatake, M.; and W asa, K.: L o w
T em perature Process for th e P reparation o f High T c S u p ercon ducting T hin
film s, Appl. Phys. Lett. 51, 2263-2265 (1987).
24. Mizuno, K.; Higashino, K.; Setsune K.; and Wasa, K.: F abrication o f Thinfilm -ty p e Josepbson Ju n ctio n s Using a B i-S r-Ca-C u -O /B i-S r-C u -O /B i-S r-C a
C u-O S tru c tu re,” Appl. Phys. Lett. 56, 1469-1471 (1990).
25. Takano, S.; Hayashi, N.; Okuda, S.; and Hitotsuyanagi: Y 1B a 2C u30 7mj Thin
F ilm s G rown b y R F M agnetron S p u tterin g , Physica C 162-164, 1535-1536
(1989).
26. Subramanyam, G.; Radpour, F.; and Kapoor, V. J.: Fabrication of T l-C a -B a
C u-O Supercondu cting T hin F ilm s on L a A 1 0 3 S u b stra tes, Appl. Phys. Lett.
56, 1799-1801 (1990).
Appendix C
1.
Klein, N.; Muller, G.; Piel, H.; Roas, B.; Schultz, L.; Klein, U.; and Peiniger,
M.: M illim eter Wave Surface R esistance o f E p ita x ia lly ow n Y B a 2C u30 7_x
T hin F ilm s, Appl. Phys. Lett. 54, 757-759 (1989).
f
R eproduced w ith perm ission o f the copyright owner. F urther reproduction prohibited w ith o u t perm ission.
201
2.
W orthington, T. K.; Gallagher, W. J.; and Dinger, T. R.: A n iso tro p ic N a tu re
o f H ig h -T em p era tu re S u p erc o n d u c tivity in Single-C rystal Y j B a ^ C u j O ^ ,
Phys. Rev. Lett. 59, 1160-1163 (1987).
3.
Samara, G. A.; and Giardini, A. A.: P ressure D ependence o f th e D ielectric
C o n sta n t o f S tro n tiu m T ita n ite, Phys. Rev. 140, A954-A957 (1965).
4.
Weaver, H. E.: D ielectric P roperties o f Single C rysta ls o f S r T iO j a t L o w
T em p era tu res, Phys. Chem. Solids 11, 274-277 (1959).
5.
Harvey, A. F.: M icrow ave E ngineering, Academic Press, 253-254 (1963).
6.
M iranda, F. A.; Gordon, W. L; Heinen, V. O.; Ebihara, B. T.; and Bhasin,
K. B.: M ea su rem en ts o f C o m plex P e r m ittiv ity o f M icrow ave S u b stra tes in
th e 20 to 300 K T em p era tu re R a n g e F ro m 26.5 to 40.0 G H z, Advances in
Cryogenic Engineering 35, Plenum Publishing Corporation, 1593-1599 (1990).
7.
Von Hippel, A. R.: D ielectric M aterials a n d A p p lications, (The M IT Press,
Cambridge, MA, 1954).
8.
Sandstrom, R. L.; Giess, E. A.; Gallagher, W. J., Segmuller, A.; Cooper, E.
I., Chisholm, M. F.; G upta, A; Shinde, S.; and Laibowitz, R. B.:
L a n th a n u m
G allate
S u b stra te s
fo r
E p ita x ia l
H igh-tem perature
S uperconducting T h in F ilm s, Appl. Phys. Lett. 53, 1874-1876 (1988).
9.
M iranda, F. A.; Gordon, W. L.; Bhasin, K. B.; Ebihara, B. T.; Heinen, V.
O.; and Chorey, C. M.: C o m p lex P e r m ittiv ity o f L a n th a n u m A lu m in a te in
th e 20 to 300 K T em p era tu re R a n g e F ro m 26.5 to 40.0 G H z, Microwave
Opt. Tech. Lett. 3, 11-13 (1990).
10. Simon, R. W.; P latt, C. E.; Lee, G. S.; Daly, K. P.; Wire, M. S.; Luine, J.
A.; and Urbanik, M: L ow -loss S u b stra te fo r E p ita xia l G row th o f Hightem p era tu re Superconductor T hin F ilm s, Appl. Phys. Lett. 53, 2677-2679
(1988).
11. Miyazawa, S.: Surface R ou g h en in g A sso cia ted W ith ~ 140 °C T ransition o f a
L a G a 0 3 S u b stra te For High T c S u p erconducting F ilm s, Appl. Phys. Lett.
55, 2230-2232 (1989).
12. Bhasin, K. B.; W arner, J. D.; Liu, D. C.; and Romanofsky, R. R.: Interfacial
R oughn ess in H igh F requency M icroelectronics Interconnections and
Packaging, J. Vac. Sci. Technol. A3, 778-781 (1985).
i
R eproduced w ith perm ission o f the copyright owner. F urth er reproduction prohibited w itho ut perm ission.
2 02
13. Warner, J. D.; Bhasin, K. B.; and M iranda, F. A.: D ependence o f th e C ritical
T em p era tu re o f L aser-ablated Y B a 2C u30 7^ T hin F ilm s on L a A 1 0 3
S u b stra te G row th Technique, Supercond. Sci. Technol. 3, 437-439 (1990).
Appendix D
1.
Bardeen, J.; Cooper, L. N.; and Schrieffer, J. R.: T h eo ry o f S u p erco n d u ctivity,
Phys. Rev. 108, 1175-1204 (1957).
2.
Tinkham, M.: Intro d u ctio n to S u p erco n d u ctivity, 34 (Krieger, M alabar, FL,
1985).
3.
Gittlem an, J. I.; and M atey, J. R.: M o d elin g th e M icrow ave P ro perties o f the
Y B a 2C u30 ^ x Superconductors, J. Appl. Phys. 65, 688-691 (1989).
h
R eproduced w ith perm ission o f the copyright owner. F urther reproduction prohibited w itho ut perm ission.
6S-3737
REV. 10/89
C entral R esearch & D evelopm ent
Experimental Station
P.O. Box 80228
Wilmington. Delaware 19880-0228
April 10,1991
Felix Miranda
NASA Lewis Research Center
Bldg. 77, Stop 77-5
Cleveland, OH 44135
Dear Sir.
This letter is to inform you that the authors of the paper, "Crystal Structure
ofTl2B a2C a 2 C u 3 0 io , a 125 K Superconductor", which was published in the journal
Science in 1988, hereby give you permission, consistent with the policies of the journal, to
use any or all of the illustrations appearing in this paper in your thesis.
Yours sincerely,
ft. «.
—
Richard B. Flippen
jf
203
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F urth er reproduction prohibited w itho ut perm ission.
204
April 0, 1991
From :
D r. L . H . Greene
Subject:
Authorization for use of Copyright material.
I give my permission to Mr. Felix A. Miranda to use Fig. 1, of the paper "Oxygen
and rare-earth doping of the 90-K superconducting perovskite YBa] Cu30 7.)|1,) by J. M.
Tarascon, W. R, Mckinnon, L. H. Greene, G. W. Hull, and E. M. Vogel, published in Phys.
Rev. B 36, .226-234, (1987), for his Ph.D. thesis.
I am aware that University Microfilms
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