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Temperature depeddence of the microwave surface resistance of YBCO thin films from microstrip resonator measurements
Physica C 175 ( 1991 ) 603-606 North-Holland
Temperature dependence of the microwave surface resistance of YBCO thin films from microstrip resonator measurements I.S. Gergis, P.H. Kobrin, J.T. Cheung, E.A. Sovero, C.L. Lastufka, D.S. Deakin and J. Lopez Rockwell International Science Center, Thousand Oaks, CA 91360, USA
Received 29 January 1991
The surface resistance of YBa2Cu3OT_x (YBCO) thin films were obtained from measuring the Q-factor of inverted microstrip resonators at 6-7 GHz over the temperature range of 16-80 K. The inverted microstrip which included a sapphire spacer between the YBCO line and a YBCO ground plane has lower dielectric loss than that of regular microstrips since sapphire has a much lower loss tangent than that of the film substrate. This enables the determination of Rs to a much higher sensitivity. We have examined good quality epitaxial YBCO films fabricated by several techniques; ion beam sputtering, pulsed-laser deposition, and off-axis magnetron sputtering. Most films have Tc's of 85-90 K and Jc of 0.5-2 × 106 A/cm 2at 77 K. The loaded Q-factors were 2500-4800 at 77K increasing up to 77 000 at 16 K, which, to our knowledge, is the highest Q measured for a high-Tomicrowave planar resonator. We have found that the surface resistances of the YBCO films of comparable Tc and Jc have similar values at relatively high temperatures (T> 70 K) even though these films were grown by different techniques. The surfaces resistance, scaled to 10 GHz was in the range 0.44-0.7 f~m at 77 K and as low as 37 ttfl at 16 K.
1. Introduction The use o f Cu-oxide high-To superconductors in m i c r o w a v e passive devices is emerging as a potentially useful a p p l i c a t i o n o f these materials. Epitaxial thin films o f YBa2Cu3OT_x a n d T I B a C a C u O with lower losses than that o f Cu at frequencies up to 80 G H z at 77 K have already been d e m o n s t r a t e d [ 1 3 ]. M e a s u r e m e n t o f the surface resistance provides an i m p o r t a n t p a r a m e t e r for predicting the performance o f devices in a d d i t i o n to u n d e r s t a n d i n g the fund a m e n t a l properties o f these materials. Several techniques have been used to measure Rs in thin films. These include resonant techniques such as cavities [ 1 ] with the H T S C film replacing part o f the wall o f the cavity, and transmission line resonators in microstrip [ 2 ], stripline [ 4 ], c o p l a n a r [ 5 ] line and parallel plate [ 6 ] configurations. A n o t h e r technique measures the m i c r o w a v e transmission [ 7 ] through the film to d e t e r m i n e the s u p e r c o n d u c t o r ' s complex conductivity. Most o f the resonant techniques are limited in sensitivity by losses other than due to the superconductor, such as o h m i c losses in the n o r m a l metal walls o f the resonant cavity or dielectric losses
in the substrate. D e t e r m i n a t i o n o f the surface resistance by the transmission technique is limited by the fact that once the complex conductivity becomes overwhelmingly reactive, measuring the real part becomes exceedingly difficult a n d an accurate measurement o f Rs is l i m i t e d to t e m p e r a t u r e s > 80 K for good quality Y B C O films [ 8 ]. We have devised a technique to extend the sensitivity o f surface resistance m e a s u r e m e n t using p l a n a r transmission line resonators by reducing the c o n t r i b u t i o n o f the dielectric losses in the resonator. We were able to measure loaded Q o f up 77 000 which to our knowledge is the highest Q r e p o r t e d for a p l a n a r high-To resonator at this frequency. The corresponding surface resistance was 37 ttfl.
2. Experimental procedure The m e a s u r e d quality factor (QL) o f a resonator is d e t e r m i n e d by resonator losses in the superconductor and the dielectric substrate and loading by the input and output lines. This can be expressed in terms o f effective Q-factors as follows:
0921-4534/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)
604
LS. Gergis et al. / Surface resistances of YBCO thin films "tBCO Microslrlp Line
I / Q L = I / Q E + llQs + llQd,
Input/Output1,4~rost6p
where QE accounts for the loading, and Qs and Qd are the effective Qs due to the superconductor and dielectric losses, respectively. In a microstrip, the field, thus energy, concentrates mostly in the dielectric substrate and only a maximum QL, slightly higher than 1/(tan ~) can be obtained. Suitable substrate materials currently being used for growing high-To films such as LaAIO3 and MgO have dielectric loss tangents [9] (tanS) of the order of 10 -4. The dielectric losses can be substantially reduced using an inverted microstrip (fig. 1 ( a ) ) where a larger portion of the energy exists in the empty space between the ground plane and the conductor line. However, for substrates with high dielectric constants (~r is about 25 for LaAIO3 and 10 for MgO) a significant part of the energy still exists in the film substrate. By replacing the air space with sapphire (fig. 1 ( b ) ) , which has a very low loss tangent ( < 10-5) and a dielectric constant of about 10, a much larger fraction of the electromagnetic energy will propagate in the sapphire spacer resulting in a much higher Qa and thus higher sensitivity of the Rs measurement. Similar techniques [ 6,10 ] have been reported which also reduce the contribution of the dielectric losses of the substrate. We used the test configuration shown in fig. 2. The input and output lines are regular 50 ~ Au microstrips on 0.25 m m thick alumina substrates. The superconducting ground plane, prepared with Au metallization borders, contacts the Au ground planes of the input/output microstrips using pressure from beryllium-copper springs. Indium stripes, 50 microns thick, were placed between the contact surfaces to reduce the resistance. The resonator lines were defined lithographically, and were typically 6-
~
Microstrip~ S p a c e r IIIIIIlltllllltltllllllllllltll|lltlllllll
I
GroundPlane (a)
I
GroundPlane (b)
Fig. 1. Inverted microstrip with air space between the microstrip line and ground plane (a), and with sapphire spacer (b).
Sapphire Spacer
~ . ~
ll[llIllllllllllllllllllllllllllllllllrllidl[lllllllllllllllllllllllc~ ~+oH I~'~'%~'x'~x-%~\\~x"~\\"'~/
YBCOGroundPlane
Fig. 2. Schematic diagram of the experimental test configuration used for the measurement of S-parameters of YBCO inverted microstrip resonators. Table 1 Parameters of the YBCO films. Resonator#
#1
#2
Film thickness (nm) Linewidth (microns) Tc (K) Field penetration depth a t 0 K (nm) Jc, 7 7 K ( × 1 0 6 A / c m 2) (measured in similar films )
300 300 150 450 86 86 270 270
100 250 450 150 150 90 89 86 200 210 -
0.8
2
0.8
#3
#4
1.5
Ground plane
0.8
8 m m long, with various widths. The resonator substrate (0.5 m m thick) was placed, with the film side down, on the sapphire plate (0.25 m m thick) symmetrically between the ends of the input and output microstrips. The coupling between the resonator and the input/output lines can be adjusted by changing the size of the coupling gap. The test fixture housing was made of Au-plated Cu and included a cover to eliminate radiation losses. The loaded quality factor, QL, was determined from the primary resonance line width and Qo was calculated from QL and the transmission loss at resonance.
3. Experimental results We show here the results obtained on four resonators from films grown by three methods (ion beam sputtering, off-axis magnetron sputtering, and pulsedlase deposition) but with comparable Tc and Jc- Table 1 lists some of the relevant parameters of these films. Resonators 1, 3, and 4 were weakly coupled down to the lowest temperature and Qo was, thus, assumed to be the same as QL which are shown, as a function of temperature, in fig. 3 (a). Resonator 2 was strongly coupled at low temperatures as seen
LS. Gergis et al. / Surface resistances ofYBCO thin films
(a)
Q-factor
10 s
of
I
150 pun wide
I
resonators
I
I
I
I
0.676 for the 460 micron line. The intrinsic surface resistance R,o was then calculated by correcting for the finite thickness of the films using the equation
I
o#1 •
o #3 x #4
o
x
R~/R~o = c o t h ( d / 2 ) + ( d / 2 ) /sinh2( d / 2 ) ,
• x
O
104
a3
0
x
a O O
6
x
o x
~ x
1 0~ 10
I
I
I
I
I
20
30
40
50
60
Temperature Q-factor of
(b) 10 s
|
I
I
T 8O
90
(K)
a n d Insertion Resonator #2 I
I 70
Loss
I
I
I
Q0
35 ¥
30 25
104 o m
20
"7
0
15 1 03 10 IL
_
0 ..,I 0 ~
y,. ~
5 102 10
I
I
20
30
605
I
I
I
I
I
40
50
60
70
80
90
Temperature (K) Fig. 3. (a) Measured Q-factors of resonators 1,3 and 4 as a function of temperature. (b) Measured Q-factor, insertion loss (IL) and unloaded Q for resonator 2 as a function of temperature.
where 2 is the field penetration depth and d is the film thickness. We used the penetration depth data obtained, on similar films, from 60 GHz transmission measurements [ 7 ]. We then scaled Rso to 10 GHz assuming it to be proportional to the square of the frequency and the results are plotted in fig. 4.. The above results show that the surface resistance of the YBCO films that we examined had similar values at relatively high temperatures ( T > 70 K) even though these films were grown by different techniques. The 77 K surface resistance scaled to 10 GHz were 0.44-0.70 mf~ which is at least a factor of 20 lower than that of Cu under the same conditions. The results also show that the measurement technique described above is capable of measuring R~ as low as 37 ~.f2. The results indicate that the surface resistance did not decrease as rapidly as would be expected from the BCS theory, where R, is proportional to e - a / k T . We also compared our results with what is predicted by the two fluid model Rs = o92/Zo22o3a, ( T / T c ) 4 / 2 ( 1 - ( T / T c ) 4) 3/4,
where o, is the normal conductivity just above Tc (assumed 10- 4 f~- ~c m - ~ and 2 o is the penetration
from the transmission loss date in fig. 3(b). Q0 was extracted from these data and is also plotted in fig. 3 ( b ) . In all cases Q-factors much higher than l / (tan J) o f LaAlO3 ( l 0 - 4 ) were o b t a i n e d . T h e highcst Q ( 7 7 0 0 0 ) was o b t a i n e d for resonator 1 at 16 K,
which, as shown below, also corresponds to the lowest Rs. The surface resistance (Rs) was calculated assuming that losses are only in the superconductors, i.e. neglecting dielectric losses. We used the Wheeler method [ 11 ] to correct for the nonuniform current distribution across the stripline width. The ratio, between the surface resistance thus calculated and one obtained neglecting losses in the ground plane and assuming uniform current distribution in the microstrip line, is 0.74 for the 160 microns lines and
Rs i
• c x D
Scaled
i
to
i
10
GHz
I
i
I
#1 #2 #3 #4
A
o
x
E
2-FLUID
O
x 0
O
0.1
I
X
X
X × D
g
g
~"
I
I
I
40
50
60
OQ
w ...."
0.01
0
I
I
20
30
I./' 70
80
90
Temperature (K) Fig. 4. Surface resistances of resonators 1, 2, 3 and 4 scaled to l0 GHz as a function of temperature. Also shown is the theoretical R, using the two-fluid model (small dots).
606
LS. Gergis et al. /Surface resistances of YBCO thin films
depth at 0 K (assumed 150 nm). The results, plotted in fig. 4, show that the measured Rs is considerably higher, at all temperatures, than what is predicted by this phenomenological model.
References [ 1 ] N. Klein, G. Muller, H. Piel, B. Roas, L. Schultz, U. Klein and M. Peiniger, Appl. Phys. Lett. 54 (1989) 757. [ 2 ] D. Kolokitis et al., J. Electronic Mater. 19 (1990) 117. [3]R.B. Hammond, G.V. Negrete, M.S. Schmidt, M.J. Moskowitz, M.M. Eddy, D.D. Strother and D.L. Skoglund, Tech Digest IEEE Microwave Symposium 2 (1990) 867.
[4] D.E. Oates and A.C. Anderson, SPIE vol. 1187, Processing of Films for High-To Superconducting Electronics, 1989, pp. 326-337. [ 5 ] A.A. Valenzuela and P. Russer, Appl. Phys. Len. 55 ( 1989 ) 1029. [6] W. Ho, P.J. Hood, W.F. Hall, P. Kobrin, A.B. Harker and R.E. DeWames, Phys. Rev. B 38 (1988) 7029. [7] P.H. Kobrin, J.T. Cheung, W.W. Ho, N. Glass, J. Lopez, I.S. Gergis, R.E. DeWames, W.F. Hall, presented at the Third Int. Symp. on Superconductivity, Sendai, Japan, 6-9 November, 1990. [ 8 ] R.W. Simon et al., Appl. Phys. Len. 53 (1988) 2677. [9]L.A. Hornak, M. Hatamian, S.K. Tewksbury, E.G. Burkhardt, R.E. Howard, P.M. Mankiewich, B.L. Straughn and C.D. Brandle. J. Appl. Phys. 66 5066. [ 10] T.B. Taber, Rev. Sc. Instrum. 61 (1990) 2200. [ 11 ] H.A. Wheeler, IEEE trans, on Microwave Theory and Tech., MTT-25, 1977, p. 631.
Temperature dependence of the microwave surface resistance of YBCO thin films from microstrip resonator measurements I.S. Gergis, P.H. Kobrin, J.T. Cheung, E.A. Sovero, C.L. Lastufka, D.S. Deakin and J. Lopez Rockwell International Science Center, Thousand Oaks, CA 91360, USA
Received 29 January 1991
The surface resistance of YBa2Cu3OT_x (YBCO) thin films were obtained from measuring the Q-factor of inverted microstrip resonators at 6-7 GHz over the temperature range of 16-80 K. The inverted microstrip which included a sapphire spacer between the YBCO line and a YBCO ground plane has lower dielectric loss than that of regular microstrips since sapphire has a much lower loss tangent than that of the film substrate. This enables the determination of Rs to a much higher sensitivity. We have examined good quality epitaxial YBCO films fabricated by several techniques; ion beam sputtering, pulsed-laser deposition, and off-axis magnetron sputtering. Most films have Tc's of 85-90 K and Jc of 0.5-2 × 106 A/cm 2at 77 K. The loaded Q-factors were 2500-4800 at 77K increasing up to 77 000 at 16 K, which, to our knowledge, is the highest Q measured for a high-Tomicrowave planar resonator. We have found that the surface resistances of the YBCO films of comparable Tc and Jc have similar values at relatively high temperatures (T> 70 K) even though these films were grown by different techniques. The surfaces resistance, scaled to 10 GHz was in the range 0.44-0.7 f~m at 77 K and as low as 37 ttfl at 16 K.
1. Introduction The use o f Cu-oxide high-To superconductors in m i c r o w a v e passive devices is emerging as a potentially useful a p p l i c a t i o n o f these materials. Epitaxial thin films o f YBa2Cu3OT_x a n d T I B a C a C u O with lower losses than that o f Cu at frequencies up to 80 G H z at 77 K have already been d e m o n s t r a t e d [ 1 3 ]. M e a s u r e m e n t o f the surface resistance provides an i m p o r t a n t p a r a m e t e r for predicting the performance o f devices in a d d i t i o n to u n d e r s t a n d i n g the fund a m e n t a l properties o f these materials. Several techniques have been used to measure Rs in thin films. These include resonant techniques such as cavities [ 1 ] with the H T S C film replacing part o f the wall o f the cavity, and transmission line resonators in microstrip [ 2 ], stripline [ 4 ], c o p l a n a r [ 5 ] line and parallel plate [ 6 ] configurations. A n o t h e r technique measures the m i c r o w a v e transmission [ 7 ] through the film to d e t e r m i n e the s u p e r c o n d u c t o r ' s complex conductivity. Most o f the resonant techniques are limited in sensitivity by losses other than due to the superconductor, such as o h m i c losses in the n o r m a l metal walls o f the resonant cavity or dielectric losses
in the substrate. D e t e r m i n a t i o n o f the surface resistance by the transmission technique is limited by the fact that once the complex conductivity becomes overwhelmingly reactive, measuring the real part becomes exceedingly difficult a n d an accurate measurement o f Rs is l i m i t e d to t e m p e r a t u r e s > 80 K for good quality Y B C O films [ 8 ]. We have devised a technique to extend the sensitivity o f surface resistance m e a s u r e m e n t using p l a n a r transmission line resonators by reducing the c o n t r i b u t i o n o f the dielectric losses in the resonator. We were able to measure loaded Q o f up 77 000 which to our knowledge is the highest Q r e p o r t e d for a p l a n a r high-To resonator at this frequency. The corresponding surface resistance was 37 ttfl.
2. Experimental procedure The m e a s u r e d quality factor (QL) o f a resonator is d e t e r m i n e d by resonator losses in the superconductor and the dielectric substrate and loading by the input and output lines. This can be expressed in terms o f effective Q-factors as follows:
0921-4534/91/$03.50 © 1991 - Elsevier Science Publishers B.V. (North-Holland)
604
LS. Gergis et al. / Surface resistances of YBCO thin films "tBCO Microslrlp Line
I / Q L = I / Q E + llQs + llQd,
Input/Output1,4~rost6p
where QE accounts for the loading, and Qs and Qd are the effective Qs due to the superconductor and dielectric losses, respectively. In a microstrip, the field, thus energy, concentrates mostly in the dielectric substrate and only a maximum QL, slightly higher than 1/(tan ~) can be obtained. Suitable substrate materials currently being used for growing high-To films such as LaAIO3 and MgO have dielectric loss tangents [9] (tanS) of the order of 10 -4. The dielectric losses can be substantially reduced using an inverted microstrip (fig. 1 ( a ) ) where a larger portion of the energy exists in the empty space between the ground plane and the conductor line. However, for substrates with high dielectric constants (~r is about 25 for LaAIO3 and 10 for MgO) a significant part of the energy still exists in the film substrate. By replacing the air space with sapphire (fig. 1 ( b ) ) , which has a very low loss tangent ( < 10-5) and a dielectric constant of about 10, a much larger fraction of the electromagnetic energy will propagate in the sapphire spacer resulting in a much higher Qa and thus higher sensitivity of the Rs measurement. Similar techniques [ 6,10 ] have been reported which also reduce the contribution of the dielectric losses of the substrate. We used the test configuration shown in fig. 2. The input and output lines are regular 50 ~ Au microstrips on 0.25 m m thick alumina substrates. The superconducting ground plane, prepared with Au metallization borders, contacts the Au ground planes of the input/output microstrips using pressure from beryllium-copper springs. Indium stripes, 50 microns thick, were placed between the contact surfaces to reduce the resistance. The resonator lines were defined lithographically, and were typically 6-
~
Microstrip~ S p a c e r IIIIIIlltllllltltllllllllllltll|lltlllllll
I
GroundPlane (a)
I
GroundPlane (b)
Fig. 1. Inverted microstrip with air space between the microstrip line and ground plane (a), and with sapphire spacer (b).
Sapphire Spacer
~ . ~
ll[llIllllllllllllllllllllllllllllllllrllidl[lllllllllllllllllllllllc~ ~+oH I~'~'%~'x'~x-%~\\~x"~\\"'~/
YBCOGroundPlane
Fig. 2. Schematic diagram of the experimental test configuration used for the measurement of S-parameters of YBCO inverted microstrip resonators. Table 1 Parameters of the YBCO films. Resonator#
#1
#2
Film thickness (nm) Linewidth (microns) Tc (K) Field penetration depth a t 0 K (nm) Jc, 7 7 K ( × 1 0 6 A / c m 2) (measured in similar films )
300 300 150 450 86 86 270 270
100 250 450 150 150 90 89 86 200 210 -
0.8
2
0.8
#3
#4
1.5
Ground plane
0.8
8 m m long, with various widths. The resonator substrate (0.5 m m thick) was placed, with the film side down, on the sapphire plate (0.25 m m thick) symmetrically between the ends of the input and output microstrips. The coupling between the resonator and the input/output lines can be adjusted by changing the size of the coupling gap. The test fixture housing was made of Au-plated Cu and included a cover to eliminate radiation losses. The loaded quality factor, QL, was determined from the primary resonance line width and Qo was calculated from QL and the transmission loss at resonance.
3. Experimental results We show here the results obtained on four resonators from films grown by three methods (ion beam sputtering, off-axis magnetron sputtering, and pulsedlase deposition) but with comparable Tc and Jc- Table 1 lists some of the relevant parameters of these films. Resonators 1, 3, and 4 were weakly coupled down to the lowest temperature and Qo was, thus, assumed to be the same as QL which are shown, as a function of temperature, in fig. 3 (a). Resonator 2 was strongly coupled at low temperatures as seen
LS. Gergis et al. / Surface resistances ofYBCO thin films
(a)
Q-factor
10 s
of
I
150 pun wide
I
resonators
I
I
I
I
0.676 for the 460 micron line. The intrinsic surface resistance R,o was then calculated by correcting for the finite thickness of the films using the equation
I
o#1 •
o #3 x #4
o
x
R~/R~o = c o t h ( d / 2 ) + ( d / 2 ) /sinh2( d / 2 ) ,
• x
O
104
a3
0
x
a O O
6
x
o x
~ x
1 0~ 10
I
I
I
I
I
20
30
40
50
60
Temperature Q-factor of
(b) 10 s
|
I
I
T 8O
90
(K)
a n d Insertion Resonator #2 I
I 70
Loss
I
I
I
Q0
35 ¥
30 25
104 o m
20
"7
0
15 1 03 10 IL
_
0 ..,I 0 ~
y,. ~
5 102 10
I
I
20
30
605
I
I
I
I
I
40
50
60
70
80
90
Temperature (K) Fig. 3. (a) Measured Q-factors of resonators 1,3 and 4 as a function of temperature. (b) Measured Q-factor, insertion loss (IL) and unloaded Q for resonator 2 as a function of temperature.
where 2 is the field penetration depth and d is the film thickness. We used the penetration depth data obtained, on similar films, from 60 GHz transmission measurements [ 7 ]. We then scaled Rso to 10 GHz assuming it to be proportional to the square of the frequency and the results are plotted in fig. 4.. The above results show that the surface resistance of the YBCO films that we examined had similar values at relatively high temperatures ( T > 70 K) even though these films were grown by different techniques. The 77 K surface resistance scaled to 10 GHz were 0.44-0.70 mf~ which is at least a factor of 20 lower than that of Cu under the same conditions. The results also show that the measurement technique described above is capable of measuring R~ as low as 37 ~.f2. The results indicate that the surface resistance did not decrease as rapidly as would be expected from the BCS theory, where R, is proportional to e - a / k T . We also compared our results with what is predicted by the two fluid model Rs = o92/Zo22o3a, ( T / T c ) 4 / 2 ( 1 - ( T / T c ) 4) 3/4,
where o, is the normal conductivity just above Tc (assumed 10- 4 f~- ~c m - ~ and 2 o is the penetration
from the transmission loss date in fig. 3(b). Q0 was extracted from these data and is also plotted in fig. 3 ( b ) . In all cases Q-factors much higher than l / (tan J) o f LaAlO3 ( l 0 - 4 ) were o b t a i n e d . T h e highcst Q ( 7 7 0 0 0 ) was o b t a i n e d for resonator 1 at 16 K,
which, as shown below, also corresponds to the lowest Rs. The surface resistance (Rs) was calculated assuming that losses are only in the superconductors, i.e. neglecting dielectric losses. We used the Wheeler method [ 11 ] to correct for the nonuniform current distribution across the stripline width. The ratio, between the surface resistance thus calculated and one obtained neglecting losses in the ground plane and assuming uniform current distribution in the microstrip line, is 0.74 for the 160 microns lines and
Rs i
• c x D
Scaled
i
to
i
10
GHz
I
i
I
#1 #2 #3 #4
A
o
x
E
2-FLUID
O
x 0
O
0.1
I
X
X
X × D
g
g
~"
I
I
I
40
50
60
OQ
w ...."
0.01
0
I
I
20
30
I./' 70
80
90
Temperature (K) Fig. 4. Surface resistances of resonators 1, 2, 3 and 4 scaled to l0 GHz as a function of temperature. Also shown is the theoretical R, using the two-fluid model (small dots).
606
LS. Gergis et al. /Surface resistances of YBCO thin films
depth at 0 K (assumed 150 nm). The results, plotted in fig. 4, show that the measured Rs is considerably higher, at all temperatures, than what is predicted by this phenomenological model.
References [ 1 ] N. Klein, G. Muller, H. Piel, B. Roas, L. Schultz, U. Klein and M. Peiniger, Appl. Phys. Lett. 54 (1989) 757. [ 2 ] D. Kolokitis et al., J. Electronic Mater. 19 (1990) 117. [3]R.B. Hammond, G.V. Negrete, M.S. Schmidt, M.J. Moskowitz, M.M. Eddy, D.D. Strother and D.L. Skoglund, Tech Digest IEEE Microwave Symposium 2 (1990) 867.
[4] D.E. Oates and A.C. Anderson, SPIE vol. 1187, Processing of Films for High-To Superconducting Electronics, 1989, pp. 326-337. [ 5 ] A.A. Valenzuela and P. Russer, Appl. Phys. Len. 55 ( 1989 ) 1029. [6] W. Ho, P.J. Hood, W.F. Hall, P. Kobrin, A.B. Harker and R.E. DeWames, Phys. Rev. B 38 (1988) 7029. [7] P.H. Kobrin, J.T. Cheung, W.W. Ho, N. Glass, J. Lopez, I.S. Gergis, R.E. DeWames, W.F. Hall, presented at the Third Int. Symp. on Superconductivity, Sendai, Japan, 6-9 November, 1990. [ 8 ] R.W. Simon et al., Appl. Phys. Len. 53 (1988) 2677. [9]L.A. Hornak, M. Hatamian, S.K. Tewksbury, E.G. Burkhardt, R.E. Howard, P.M. Mankiewich, B.L. Straughn and C.D. Brandle. J. Appl. Phys. 66 5066. [ 10] T.B. Taber, Rev. Sc. Instrum. 61 (1990) 2200. [ 11 ] H.A. Wheeler, IEEE trans, on Microwave Theory and Tech., MTT-25, 1977, p. 631.