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Cooling below 1K a long Josephson junction in the voltage state
PflYSICA
Physica B 194-196 (1994) 33-34 North-Holland
COOLING BELOW 1K A LONG JOSEPHSON JUNCTION IN THE VOLTAGE STATE L. Baselgia-Stahel, O.G. Symko, and D. J. Zheng Department of Physics, University of Utah, Salt Lake City, Utah 84112 A long Josephson junction was cooled inside the mixing chamber of a dilution refrigerator for studies of macroscopic quantum tunneling. As the junction was biased at a voltage state the heat generated was dissipated by a specially designed sample holder in contact with the dilute mixture. 1. INTRODUCTION An interesting application of a Josephson junction is to the study of Macroscopic Quantum Tunneling (1). This usually requires temperatures below 1K where the junction crosses over from a thermally activated region to the quantum mechanical regime. We have shown (2) that a long Josephson junction is well-suited for such studies and we have investigated tunneling between a double-well potential as created when the junction is biased in a magnetic field at Fiske steps. We have measured in such junctions incoherent tunneling between a double well down to - 15 mK. This system provides also an opportunity to investigate macroscopic coherent tunneling. When a long junction is biased in the non-zero voltage state cooling to the 10 mK range becomes difficult. Results are presented here on this problem.
phase. The circulating 3He helps to maintain a fixed temperature near the junction; also any stray heat influxes are minimized in such an arrangement. In the presence of heat production in the junction, the Kapitza boundary resistance (3) between the junction and the dilute 3He will limit the ultimate temperature of the junction. Even though the junction has over 100 times the surface area of a regular junction, a typical power input of 3x10 -s watts to the junction will cause an enormous temperature difference at the interface with the liquid. The junction, on a boron doped silicon wafer, was mounted on a fiber glass sample holder with patterned copper lines for electrical connections. It was shielded by a brass cup anchored to the fiber glass plate and in contact with the dilute 3He in the mixing chamber, Fig. 1. 3 4
2. EXPERIMENTAL DETAILS In order not to be affected by the temperature dependence of the junction critical current and related parameters when studying macroscopic quantum tunneling, we have used long Josephson junctions with NbN electrodes and MgO barrier, the critical temperature being ~ 17K. Dimensions of the junctions presented here are 100 pm long and 6 pm wide and they have critical current densities of - 1 0 0 - 1,000 A/cm2. They were fabricated by reactive magnetron sputtering onto a silicon substrate, (6ram x 6ram). Each NbN electrode is
3,000 ~, thick. In order to optimize the cooling of the junction, we keep it inside the mixing chamber, in the dilute
-
~,~,
~ ......
y///////~ Fig 1:
Sample holder with long Joseph junction inside mixing chamber
Temperatures were measured by a CMN thermometer with SQUID readout. The refrigerator was first cooled to the lowest temperature, - 15 mK, and then measurements of the tunneling rate were taken at fixed temperature steps as the mixing chamber was heated by an internal heater. It took
0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0921-4526(93)E0590-D
~. He Hedilute / mixture ~.-BrassCap ~'Junction ~"Silicon plate / z-Fibergrass // holder
34
2 1/2 hours to establish equilibrium at each temperature point. The results of the switching rates between 2 adjacent Fiske steps as a function of temperature are shown in Fig. 2. i.e. the jump rate back and forth between the 2 levels; they follow a power law, characteristic of incoherent tunneling in this temperature regime. 4
.-.10
~ 2 ~10 c-
glO 0.01
0.1 T (K)
Fig. 2: Temperature dependence of tunneling rate between 2 adjacent Fiske steps. 3. DISCUSSION The tunneling rate follows the expected behavior down to the lowest temperature data point. There appears to be no obvious manifestation of losing thermal contact with the mixing chamber at the lowest temperature reached. To verify that selfheating is not causing problems here, we have analyzed our system using available data on Kapitza resistance and thermal conductivity. A model, shown in Fig. 3, is used to analyze the heat flow. It is a series of thermal resistances R between the NbN junction and the dilute 3He bath with contacts at NbN to Si, Si to fiber glass (Fg) and to brass, fiber glass to helium, brass to helium, and N-bN to helium.
~j'Heat "4
/1
RNbN,He
R SI,He
I.~RI R NbN,SI
He
I,Fg RFg,He ,Br R Br,He
Vt
Fig. 3: Model for heat flow fromjunction to dilute 3He in mixing chamber
For heat production at a rate of 3xl0"SW (when the junction is biased at a Fiske step at 100/t volts for a bias current of 3x10 -4 amps), a Kapitza resistivity (4) of approximately 5x10"3K4m2W-I between the junction electrodes and the dilute 3He causes a AT of - 140 mK at the lowest temperature achieved in the mixing chamber. Therefore the cooling of the junction must take place through the silicon substrate via the fiberglass and brass cap, both in contact with the dilute phase. Recent studies (5) of the thermal resistance at interfaces of selected metals and silicon substrate, compute a thermal resistivity of - 10"3K4m2W"l using the acoustic mismatch model and the diffuse mismatch model. This depends on the quality of the interface. As our silicon wafer was plasma etched with argon just before the NbN deposition, a good bond is expected to be formed between the two. For an area of contact of 10"sin2, the junction will reach a temperature of 30ink when the mixing chamber is at 15inK. Since the silicon - fiberglass contact area is 5x10"Sm2, that of the fiberglass - dilute 3He is 2x103m 2, and the brass to helium is 6.7x10-4m2, the silicon substrate is close to the temperature of the mixing chamber. With all the uncertainties of the thermal resistance values, the junction temperature is calculated to be ~ 25 nil(. The thermal contact may also rely on surface defects on the silicon substrate produced during the various plasma etching steps of the junction fabrication. A combination of large junction in contact with large surface areas ensures that it cools to temperatures close to that of the mixing chamber in the presence of heat generation in the junction. This is substantiated by the temperature dependence of the switching rate down to the lowest temperature of 20 mK as shown in Fig. 2. This ~ c h was supported by U.S. Air Force grant # AFOSR-89-O149. 4. R E F E R E N C E S 1. R.F. Voss and R.A. Webb, Phys. Rev. Lett. 47, 265 (1981). 2. L. Baselgia Stahel and O.G. Symko, Phys. Lett. A. 166, 399 (1992). 3. W.A. Little, Can. J. Phys. 37, 334 (1959). 4. G. Frossati, J. Low Temp. Phys.87,595 (1992). 5. E.T. Swartz and R.O. Pohi, Appl. Phys. Lett. 51, 2200 (1987).
Physica B 194-196 (1994) 33-34 North-Holland
COOLING BELOW 1K A LONG JOSEPHSON JUNCTION IN THE VOLTAGE STATE L. Baselgia-Stahel, O.G. Symko, and D. J. Zheng Department of Physics, University of Utah, Salt Lake City, Utah 84112 A long Josephson junction was cooled inside the mixing chamber of a dilution refrigerator for studies of macroscopic quantum tunneling. As the junction was biased at a voltage state the heat generated was dissipated by a specially designed sample holder in contact with the dilute mixture. 1. INTRODUCTION An interesting application of a Josephson junction is to the study of Macroscopic Quantum Tunneling (1). This usually requires temperatures below 1K where the junction crosses over from a thermally activated region to the quantum mechanical regime. We have shown (2) that a long Josephson junction is well-suited for such studies and we have investigated tunneling between a double-well potential as created when the junction is biased in a magnetic field at Fiske steps. We have measured in such junctions incoherent tunneling between a double well down to - 15 mK. This system provides also an opportunity to investigate macroscopic coherent tunneling. When a long junction is biased in the non-zero voltage state cooling to the 10 mK range becomes difficult. Results are presented here on this problem.
phase. The circulating 3He helps to maintain a fixed temperature near the junction; also any stray heat influxes are minimized in such an arrangement. In the presence of heat production in the junction, the Kapitza boundary resistance (3) between the junction and the dilute 3He will limit the ultimate temperature of the junction. Even though the junction has over 100 times the surface area of a regular junction, a typical power input of 3x10 -s watts to the junction will cause an enormous temperature difference at the interface with the liquid. The junction, on a boron doped silicon wafer, was mounted on a fiber glass sample holder with patterned copper lines for electrical connections. It was shielded by a brass cup anchored to the fiber glass plate and in contact with the dilute 3He in the mixing chamber, Fig. 1. 3 4
2. EXPERIMENTAL DETAILS In order not to be affected by the temperature dependence of the junction critical current and related parameters when studying macroscopic quantum tunneling, we have used long Josephson junctions with NbN electrodes and MgO barrier, the critical temperature being ~ 17K. Dimensions of the junctions presented here are 100 pm long and 6 pm wide and they have critical current densities of - 1 0 0 - 1,000 A/cm2. They were fabricated by reactive magnetron sputtering onto a silicon substrate, (6ram x 6ram). Each NbN electrode is
3,000 ~, thick. In order to optimize the cooling of the junction, we keep it inside the mixing chamber, in the dilute
-
~,~,
~ ......
y///////~ Fig 1:
Sample holder with long Joseph junction inside mixing chamber
Temperatures were measured by a CMN thermometer with SQUID readout. The refrigerator was first cooled to the lowest temperature, - 15 mK, and then measurements of the tunneling rate were taken at fixed temperature steps as the mixing chamber was heated by an internal heater. It took
0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0921-4526(93)E0590-D
~. He Hedilute / mixture ~.-BrassCap ~'Junction ~"Silicon plate / z-Fibergrass // holder
34
2 1/2 hours to establish equilibrium at each temperature point. The results of the switching rates between 2 adjacent Fiske steps as a function of temperature are shown in Fig. 2. i.e. the jump rate back and forth between the 2 levels; they follow a power law, characteristic of incoherent tunneling in this temperature regime. 4
.-.10
~ 2 ~10 c-
glO 0.01
0.1 T (K)
Fig. 2: Temperature dependence of tunneling rate between 2 adjacent Fiske steps. 3. DISCUSSION The tunneling rate follows the expected behavior down to the lowest temperature data point. There appears to be no obvious manifestation of losing thermal contact with the mixing chamber at the lowest temperature reached. To verify that selfheating is not causing problems here, we have analyzed our system using available data on Kapitza resistance and thermal conductivity. A model, shown in Fig. 3, is used to analyze the heat flow. It is a series of thermal resistances R between the NbN junction and the dilute 3He bath with contacts at NbN to Si, Si to fiber glass (Fg) and to brass, fiber glass to helium, brass to helium, and N-bN to helium.
~j'Heat "4
/1
RNbN,He
R SI,He
I.~RI R NbN,SI
He
I,Fg RFg,He ,Br R Br,He
Vt
Fig. 3: Model for heat flow fromjunction to dilute 3He in mixing chamber
For heat production at a rate of 3xl0"SW (when the junction is biased at a Fiske step at 100/t volts for a bias current of 3x10 -4 amps), a Kapitza resistivity (4) of approximately 5x10"3K4m2W-I between the junction electrodes and the dilute 3He causes a AT of - 140 mK at the lowest temperature achieved in the mixing chamber. Therefore the cooling of the junction must take place through the silicon substrate via the fiberglass and brass cap, both in contact with the dilute phase. Recent studies (5) of the thermal resistance at interfaces of selected metals and silicon substrate, compute a thermal resistivity of - 10"3K4m2W"l using the acoustic mismatch model and the diffuse mismatch model. This depends on the quality of the interface. As our silicon wafer was plasma etched with argon just before the NbN deposition, a good bond is expected to be formed between the two. For an area of contact of 10"sin2, the junction will reach a temperature of 30ink when the mixing chamber is at 15inK. Since the silicon - fiberglass contact area is 5x10"Sm2, that of the fiberglass - dilute 3He is 2x103m 2, and the brass to helium is 6.7x10-4m2, the silicon substrate is close to the temperature of the mixing chamber. With all the uncertainties of the thermal resistance values, the junction temperature is calculated to be ~ 25 nil(. The thermal contact may also rely on surface defects on the silicon substrate produced during the various plasma etching steps of the junction fabrication. A combination of large junction in contact with large surface areas ensures that it cools to temperatures close to that of the mixing chamber in the presence of heat generation in the junction. This is substantiated by the temperature dependence of the switching rate down to the lowest temperature of 20 mK as shown in Fig. 2. This ~ c h was supported by U.S. Air Force grant # AFOSR-89-O149. 4. R E F E R E N C E S 1. R.F. Voss and R.A. Webb, Phys. Rev. Lett. 47, 265 (1981). 2. L. Baselgia Stahel and O.G. Symko, Phys. Lett. A. 166, 399 (1992). 3. W.A. Little, Can. J. Phys. 37, 334 (1959). 4. G. Frossati, J. Low Temp. Phys.87,595 (1992). 5. E.T. Swartz and R.O. Pohi, Appl. Phys. Lett. 51, 2200 (1987).