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Gap enhancement in aluminum tunnel junctions coupled to microstrip resonators
NC 3
Physica 108B (1981) 827-828 North-Holland Publishing Company
GAP ENHANCEMENT IN ALUMINUMTUNNEL JUNCTIONS COUPLEDTO MICROSTRIP RESONATORS L. B. Holdeman, James T. Hall, D. VanVgchten, and R. J. Soulen, Jr. National Bureau of Standards Washington, D. C. 20234 Irradiated (9.7 GHz) Al films show gap enhancement that agrees with Eliashberg's theory. We recently reported observation of microwave enhancement of superconductivity in Al tunnel junctions[l], thus confirming similar observations reported e a r l i e r by others[2]. The base electrode of our junction formed a 50-~ micros t r i p transmission l i n e along which microwaves could be propagated over a wide frequency range (O.l-18 GHz). Counterelectrodes in a crossedfilm geometry enabled the effects of the microwaves to be investigated via tunneling. In contrast to theoretical expectations, appreciable gap enhancementwas observed only from about l GHz to about 5 GHz; this was subsequently interpreted in terms of the resonance frequency of the tunnel junctions. The substrate used was a 1.27-mm-thick single-crystal BaF2 (Er=7.33), requiring a strip width of 1.47 mm for a charact e r i s t i c impedanceof 50~. This width W was the longest dimension of the junction, so that for electrodes of equal thickness d, the lowest resonance frequency v 0 of the junction is given by[3] : v0 = (c/2w) { c [ l + (2~/~) coth(d/~)]} - I / 2
(1)
where ~ and c are the thickness and r e l a t i v e dielectric constant of the tunnel barrier, c is the speed of l i g h t , and ~ is the superconducting penetration depth. Using the values d=200 nm, ~(0)=50 nm, ~=2.5 nm, and E=lO, the value of vo at T=O is calculated to be 5 GHz. This same value was determined experimentally from Fiske steps when the sample was cooled to 15 mK. Equation (1) assumes ~ is much smaller than the classical skin depth a, but ~ ~ ~ as T + Tc. A formula that is valid up to Tc can be obtained by replacing ~-2 by [~-2 + i(a/2)-2] in the calculations leading to Eq.(1). Using the experimental values for the r e s i s t i v i t y and RRR of our films to calculate a, the value of u0 is found to be 1.8 GHz at Tc, so that 1.8 GHz < ~0 ~ 5 GHz for T < T~. At a given T, radiation ~ouples to the junctlon over a frequency range determined in part by the junction Q. The junction resonance makes gap enhancementmore readily observable by amplifying the radiation in the part of the film being sampled by tunneling and by coupling the radiation to the counter electrode. The BCS dependenceof ~ on the energy gap A is given by = ~(O){[A/A(O)] tanh (A/2kBT)}-I/3
(2)
This functional dependencemay or may not be 0378-4363/81/0000-0000/$02.50
© North-Holland Publishing Company
valid in nonequilibrium situations, but i t is clear that the dependence of k on A w i l l make detailed comparison between theory and experiment quite d i f f i c u l t near a junction resonance.
Fig. l :
Doubleresonator device used in gap enhancement experiments.
In order to maintain the advantages of resonance while avoiding these complications, we have used junctions coupled to microstrip resonators for which the resonator frequency v R is insensitive to variations in k. The film configuration used (Fig. l ) was developed for voltage standards applications[4], and has been previously studied in great d e t a i l . In essence, the device comprises two "half-wavelength" microstrip resonators coupled by a section of high-impedance transmission l i n e which overlaps one of the resonators to form a tunnel junction. The width of the transmission l i n e coupling the resonators is 125um and the i n - l i n e dimension was 535um, so that v0 was quite different from ~R for temperatures near Tc. A disadvantage of this configuration for gap enhancement studies is that an additional potential drop can develop i f a portion of the film common to the current and voltage leads is driven normal. This does indeed occur at higher r f power levels, but the power level at which this f i r s t occurs (300~W for our sample) is easily determined. Figure 2(a) shows dV/dl vs V curves for sample 181V80-5 at different power levels for v=vR. The thickness of the base electrode (unshaded in Fig. l ) was 200 nm and the thickness of the counter electrode was 150 nm. Junction 181V80-6 (the control) c e r t i f i e d that the bath temperature did not change when 181V80-5 was irradiated. Figure 3 shows the power dependenceof 2AI, 2A2, AI+A2, and AI+A2+h~. The frequency of the 827
828
(a) SN4PLE
:~ 1 8 - I V - 8 0 - 5 Glass s u b s t r a t e v R = 9.745 GHz
INPUT PO&IER (.w)
/
I
I
I
I
i
.
RNN = 4
o
q
I00
80
-
A :)
W
60
40
"
•
I
Fig. 3:
i
8 -
t
r
INPUT POWER TOSNIPLE
?O
1
I
~
I
I
-
-
0
~
--
I
°"
2
Fig. 4: -------
•
I
103x 6 6 -
# 18-IV-80-6 G]ass substrat~ 1 = 9.590 GHz
r
ouo
I
Energy gaps as a function of power. I
290
I
I
I00 200 INPUTMICROWAVEPOWER(~W)
0
(b) CONTROL
Al/Al oxide/Al Glass Substrate
_ ~.~
j.~-m
;
Comparison of data with Eliashberg's theory.
The agreement between theory and experiments is quite satisfactory. This work was supported in part by NASA through GO #H-27908B.
i -100
v(Iv)
I 100
Fig. 2: dV/dl vs V curves for the sample and control. applied radiation is greater than the pairbreaking frequency 2A2/h in the film with the lower Tc. (At s l i g h t l y higher T, a2 decreases, and A2 increases at s l i g h t l y lower T.) In Fig. 4 we have plotted the quantity[5] ~=O.106(kBTc )-2 {A2(T,P) - A2(T,O)} as a function of power for comparison with theory. The solid curve is 6E=l/4(%/y r) (h~/kBTc) G(al/hv) with ~JYr=O.025 at P=I90~W.
REFERENCES [ I ] Hall, J.T., Holdeman, L.B., and Soulen, R.J. Jr., Phys. Rev. Lett. 45 (1980) l O l l - l O l 4 . [2] Kommers, T. and Clarke, J., Phys. Rev. Lett. 38 (1977) I091-I094. [3] Swihart, J.C., J. Appl. Phys.32(1961) 461. [4] Holdeman, L.B., Field, B.F., Toots, J., and Chang, C.C., in Deaver, B.S.Jr., Falco, C.M., Harris, J.H., and Wolf, S.A. (eds) Future Trends in Superconductive Electronics (AIP, New York, 1978) 182-186. [5] Mooij, J.E., in Nonequilibrium Superconduct i v i t y , Phonons, and Kapitza Boundaries, Proceedings of the NATOAdvanced Study I n s t i t u t e (1980) to be published.
Physica 108B (1981) 827-828 North-Holland Publishing Company
GAP ENHANCEMENT IN ALUMINUMTUNNEL JUNCTIONS COUPLEDTO MICROSTRIP RESONATORS L. B. Holdeman, James T. Hall, D. VanVgchten, and R. J. Soulen, Jr. National Bureau of Standards Washington, D. C. 20234 Irradiated (9.7 GHz) Al films show gap enhancement that agrees with Eliashberg's theory. We recently reported observation of microwave enhancement of superconductivity in Al tunnel junctions[l], thus confirming similar observations reported e a r l i e r by others[2]. The base electrode of our junction formed a 50-~ micros t r i p transmission l i n e along which microwaves could be propagated over a wide frequency range (O.l-18 GHz). Counterelectrodes in a crossedfilm geometry enabled the effects of the microwaves to be investigated via tunneling. In contrast to theoretical expectations, appreciable gap enhancementwas observed only from about l GHz to about 5 GHz; this was subsequently interpreted in terms of the resonance frequency of the tunnel junctions. The substrate used was a 1.27-mm-thick single-crystal BaF2 (Er=7.33), requiring a strip width of 1.47 mm for a charact e r i s t i c impedanceof 50~. This width W was the longest dimension of the junction, so that for electrodes of equal thickness d, the lowest resonance frequency v 0 of the junction is given by[3] : v0 = (c/2w) { c [ l + (2~/~) coth(d/~)]} - I / 2
(1)
where ~ and c are the thickness and r e l a t i v e dielectric constant of the tunnel barrier, c is the speed of l i g h t , and ~ is the superconducting penetration depth. Using the values d=200 nm, ~(0)=50 nm, ~=2.5 nm, and E=lO, the value of vo at T=O is calculated to be 5 GHz. This same value was determined experimentally from Fiske steps when the sample was cooled to 15 mK. Equation (1) assumes ~ is much smaller than the classical skin depth a, but ~ ~ ~ as T + Tc. A formula that is valid up to Tc can be obtained by replacing ~-2 by [~-2 + i(a/2)-2] in the calculations leading to Eq.(1). Using the experimental values for the r e s i s t i v i t y and RRR of our films to calculate a, the value of u0 is found to be 1.8 GHz at Tc, so that 1.8 GHz < ~0 ~ 5 GHz for T < T~. At a given T, radiation ~ouples to the junctlon over a frequency range determined in part by the junction Q. The junction resonance makes gap enhancementmore readily observable by amplifying the radiation in the part of the film being sampled by tunneling and by coupling the radiation to the counter electrode. The BCS dependenceof ~ on the energy gap A is given by = ~(O){[A/A(O)] tanh (A/2kBT)}-I/3
(2)
This functional dependencemay or may not be 0378-4363/81/0000-0000/$02.50
© North-Holland Publishing Company
valid in nonequilibrium situations, but i t is clear that the dependence of k on A w i l l make detailed comparison between theory and experiment quite d i f f i c u l t near a junction resonance.
Fig. l :
Doubleresonator device used in gap enhancement experiments.
In order to maintain the advantages of resonance while avoiding these complications, we have used junctions coupled to microstrip resonators for which the resonator frequency v R is insensitive to variations in k. The film configuration used (Fig. l ) was developed for voltage standards applications[4], and has been previously studied in great d e t a i l . In essence, the device comprises two "half-wavelength" microstrip resonators coupled by a section of high-impedance transmission l i n e which overlaps one of the resonators to form a tunnel junction. The width of the transmission l i n e coupling the resonators is 125um and the i n - l i n e dimension was 535um, so that v0 was quite different from ~R for temperatures near Tc. A disadvantage of this configuration for gap enhancement studies is that an additional potential drop can develop i f a portion of the film common to the current and voltage leads is driven normal. This does indeed occur at higher r f power levels, but the power level at which this f i r s t occurs (300~W for our sample) is easily determined. Figure 2(a) shows dV/dl vs V curves for sample 181V80-5 at different power levels for v=vR. The thickness of the base electrode (unshaded in Fig. l ) was 200 nm and the thickness of the counter electrode was 150 nm. Junction 181V80-6 (the control) c e r t i f i e d that the bath temperature did not change when 181V80-5 was irradiated. Figure 3 shows the power dependenceof 2AI, 2A2, AI+A2, and AI+A2+h~. The frequency of the 827
828
(a) SN4PLE
:~ 1 8 - I V - 8 0 - 5 Glass s u b s t r a t e v R = 9.745 GHz
INPUT PO&IER (.w)
/
I
I
I
I
i
.
RNN = 4
o
q
I00
80
-
A :)
W
60
40
"
•
I
Fig. 3:
i
8 -
t
r
INPUT POWER TOSNIPLE
?O
1
I
~
I
I
-
-
0
~
--
I
°"
2
Fig. 4: -------
•
I
103x 6 6 -
# 18-IV-80-6 G]ass substrat~ 1 = 9.590 GHz
r
ouo
I
Energy gaps as a function of power. I
290
I
I
I00 200 INPUTMICROWAVEPOWER(~W)
0
(b) CONTROL
Al/Al oxide/Al Glass Substrate
_ ~.~
j.~-m
;
Comparison of data with Eliashberg's theory.
The agreement between theory and experiments is quite satisfactory. This work was supported in part by NASA through GO #H-27908B.
i -100
v(Iv)
I 100
Fig. 2: dV/dl vs V curves for the sample and control. applied radiation is greater than the pairbreaking frequency 2A2/h in the film with the lower Tc. (At s l i g h t l y higher T, a2 decreases, and A2 increases at s l i g h t l y lower T.) In Fig. 4 we have plotted the quantity[5] ~=O.106(kBTc )-2 {A2(T,P) - A2(T,O)} as a function of power for comparison with theory. The solid curve is 6E=l/4(%/y r) (h~/kBTc) G(al/hv) with ~JYr=O.025 at P=I90~W.
REFERENCES [ I ] Hall, J.T., Holdeman, L.B., and Soulen, R.J. Jr., Phys. Rev. Lett. 45 (1980) l O l l - l O l 4 . [2] Kommers, T. and Clarke, J., Phys. Rev. Lett. 38 (1977) I091-I094. [3] Swihart, J.C., J. Appl. Phys.32(1961) 461. [4] Holdeman, L.B., Field, B.F., Toots, J., and Chang, C.C., in Deaver, B.S.Jr., Falco, C.M., Harris, J.H., and Wolf, S.A. (eds) Future Trends in Superconductive Electronics (AIP, New York, 1978) 182-186. [5] Mooij, J.E., in Nonequilibrium Superconduct i v i t y , Phonons, and Kapitza Boundaries, Proceedings of the NATOAdvanced Study I n s t i t u t e (1980) to be published.