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f noise
Physica C 372–376 (2002) 233–236 www.elsevier.com/locate/physc
LTS slotted SQUIDs for reduction of 1=f noise pez, J. Flokstra, H. Rogalla E. Bartolome *, R. Lo Low Temperature Division, Department of Applied Physics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
Abstract We have developed Nb/Al dc SQUIDs with differently structured washers (including slots and/or holes, a moat surrounding the washer and a zipper slit) to study the reduction of 1=f noise owing to hopping of flux vortices, trapped in the SQUID body during the cool-down process. A gradual reduction of the 1=f noise (measured down to 0.2 Hz) was measured for SQUIDs with increasing number of slots. Holes proved to be less effective than slots in reducing the flicker noise. The 1=f noise of the SQUIDs with a moat and zipper slit was smaller than that of a bold SQUID, but the reduction of noise was on the average less significant than for the slotted SQUIDs. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: LTS SQUIDs; Reduction 1=f noise; Slots and holes; Moats
1. Introduction The reduction of 1=f noise of low critical temperature (LTS) dc SQUIDs is crucial in applications where the SQUID has to operate at very low frequencies (103 –1 Hz) (e.g. in the readout of a cryogenic current comparator [1], gravitation gradiometers or the relativity gyroscope experiment). Flicker noise arises from fluctuations in the critical current, and hopping of vortices, trapped in the SQUID washer during the cool-down process. The noise due to critical current fluctuations can be adequately suppressed by appropriate modulation schemes. The problem of vortex hopping in LTS SQUIDs is less severe than for HTS SQUIDs, because of the lower operation temperature and the
*
Corresponding author. Tel.: +31-53-489-3125; fax: +31-53489-1099. E-mail address: [email protected] (E. Bartolome).
possibility of shielding the device to a great extent from environmental noise. In spite of that, flux generated within the device itself can be trapped, move around and produce non-negligible excess noise [2,3]. A possible way of reducing this 1=f noise is preventing the penetration of vortices in the SQUID, by narrowing the width of the strips forming the washer. Based on this idea, slotted and/ or holed SQUID washers have been employed in HTS SQUIDs for use in ambient magnetic fields (50 lT) [4]. The application of slot and hole structures to LTS SQUIDs has not been studied yet. Alternatively, flux trapping can be prevented by patterning a ‘‘moat’’ around the superconducting device [5,6]. A different strategy to reduce flux hopping is to use the washer slit edge roughness to create strong pinning centers in the SQUID, where vortices can be tightly trapped and thus move around less [3]. We have developed Nb/Al dc SQUIDs with all these different structures to investigate the reduction of 1=f noise.
0921-4534/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 2 ) 0 0 6 7 8 - 0
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E. Bartolome et al. / Physica C 372–376 (2002) 233–236
2. Structured-washer SQUIDs The nine different washer configurations studied are shown in Fig. 1. The washer outer size (445 lm) and hole size (77 lm) were in all cases the same. The 4 4 lm2 area junctions were shunted by Rsh ¼ 2 X shunt resistors and the washer was shunted by a Rd ¼ 2 X damp resistor. A bold, non-structured SQUID was used as reference. Its washer inductance was calculated to be Lsq ¼ 189 pH. The designed flux-to-voltage transfer was 24 lV=U0 and the white noise level 1.5 lU0 =Hz1=2 . SQUIDs with an increasing number of slots, holes, or a combination of the slots and holes were designed, in a similar way as it was done in existing structured HTS SQUIDs [4,7]. In principle, slots can also be applied to LTS devices since the background theory is material independent. Indeed, consider a type II superconducting strip of width w and thickness t, such that t w, and t > 2k, cooled down in the presence of a magnetic
Fig. 1. Schematic of the nine SQUID washer designs investigated. The strips were w ¼ 4 lm wide (the minimum allowed in our photolithographic process) and the slots and holes size was 8 lm.
field Ba perpendicular to the strip. At temperatures 6 Tc , at which the freeze-out of vortices and antivortices occurs, the two-dimensional screening length KðT Þ ¼ 2k2 ðT Þ=t is much larger than the typical strip width w, because the penetration depth of the film k ! 1 at Tc . Note that this holds both for HTS as for LTS strips. Then, the dynamics of a vortex is dominated by its kinetic energy, and not by screening effects. The Gibbs energy of the vortex, at a position x (0 < x < w) inside the strip can be described by [8]: GðxÞ ¼
px 4p U20 2w sin ln l0 8p2 K pn w 4p U0 Ba xðw xÞ; l0 4pK
ð1Þ
where n is the coherence length; and l0 , the permeability of the vacuum. The first term is the kinetic self-energy of the vortex. The second term represents the energy involved when the field Ba penetrates locally in the superconducting strip. From the analysis of this function (Fig. 2) one can see that if Ba > Bc1 ð2U0 =pw2 Þ lnð2w=pnÞ, vortices will inevitably remain trapped at the center of the strip, while if Ba < BT ¼ pU0 =4w2 (threshold
Fig. 2. Gibbs free energy (reduced with respect to U20 =2pKl0 ) as a function of the position x of the vortex in the strip, of width e.g. w ¼ 4 lm.
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field), vortices will be expelled from the strip (provided there are not strong pinning sites). We fabricated also a SQUID with a washer moat, which should prevent the entrance of vortices. It has been shown that the threshold field for complete vortex shielding strongly depends on the configuration, size and gap of the moat. Long, continuous moats seem to be more effective than broken moats [6]. We patterned a continuous 4 lm width moat at 8 lm form the edge of the washer. Finally, we included a SQUID with a zipperlike slit to favorise the strong pinning of vortices at the rough edge of the slit. For all the SQUIDs the flux was applied via a one-turn feedback coil surrounding the washer. An input coil, covering the whole washer, was only implemented for the 1=2 slotted SQUID.
3. Measurements The measured I–V and V–U characteristics of the nine SQUIDs were very similar. The critical current was I0 20 lA and the shunt resistor Rsh 2 X. The I–V curves showed some resonances, which were independent of the washer geometry. The feedback mutual inductance Mfb increased proportionally to the amount of available open area close to the central hole (up to a 30% increase for the all slotted SQUID with respect to the bold Mfb ¼ 140 pH). Noise measurements down to 0.2 Hz were performed with the SQUIDs shielded by a Nb and a room temperature l-metal cans, and readout with ‘‘Oxford Instruments’’ electronics. A conventional bias reversal scheme was used to get rid of the 1=f noise owing to DI0 fluctuations. Each SQUID was cooled down at least five times. In each thermal cycling, the local field might be different, and thus the probability of flux entry vary a little. Noise results are summarized in Fig. 3. The noise spectrum of the bold SQUID showed a white level 7 lU0 =Hz1=2 (the electronics noise limit for SQUIDs with a transfer <60 lV=U0 ) and a corner frequency at 4 Hz. Despite the shielding, the flux-hopping 1=f noise is large, as can be concluded from the large variations of the noise at
Fig. 3. Measured flux noise at 0.2 Hz for (above) the slotted SQUIDs and (below) alternative designs.
0.2 Hz for different cool downs. The strip width is such (184 lm), that vortices will penetrate even if the local field is as small as 0.05 lT. A reduction of the low-frequency noise is measured as the number of slots increases. The improvement when the solid inner half of the washer was replaced by slots is larger than when also the outermost half of the washer was slotted, because moving vortices couple more noise the closer they are with respect to the central hole. The noise of the 1=2 slotted SQUID with input coil is smaller than that of the SQUID without it. We believe that the coil is partially shielding the washer, thus reducing the area where vortices can enter. The holed SQUIDs seem less effective than the slotted ones in expelling vortices, a result also found in [4]. The completely holed SQUID is less noisy than the 1=2 slotted/ holed one. The SQUID with a moat had an average noise 36 lU0 =Hz1=2 (at 0.2 Hz) smaller than the bold SQUID, but the spread was comparable. The ‘‘zipper-slit’’ SQUID showed a smaller average noise (37 lU0 =Hz1=2 at 0.2 Hz)
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and spread than the bold one, probably thanks to the combined effect of having a smaller trapping area and the pinning of vortices at the slit. However the method is less effective than the slots in reducing the average flicker noise.
Acknowledgements
4. Conclusions
References
We have shown that slotted and holed washers can be used to reduce the 1=f noise due to flux hopping in LTS SQUIDs. Noise measurements at different constant fields should be done in the future to determine the threshold field for expulsion of vortices. The average reduction of noise attained using slots was larger than the one reached using alternative moat and zipper-slit structures.
[1] K. Harvey, Rev. Sci. Instrum. 43 (1972) 1626. [2] J. Gail et al., Appl. Phys. Lett. 73 (1998) 2663. [3] M. Huber et al., IEEE Trans. Appl. Supercond. 7 (1997) 2882. [4] E. Dantsker et al., Appl. Phys. Lett. 70 (1997) 2037. [5] M. Jeffery et al., Appl. Phys. Lett. 67 (1995) 1769. [6] K. Suzuki et al., IEEE Trans. Appl. Supercond. 11 (2001) 238. [7] A. Jansman et al., IEEE Trans. Appl. Supercond. 9 (1999) 3290. [8] J.R. Clem, Phys. Rev. Lett. B. 43 (1991) 7837, and personal communication.
The authors would like to thank J.R. Clem for discussions. This work was funded by the STW organization, The Netherlands.
LTS slotted SQUIDs for reduction of 1=f noise pez, J. Flokstra, H. Rogalla E. Bartolome *, R. Lo Low Temperature Division, Department of Applied Physics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
Abstract We have developed Nb/Al dc SQUIDs with differently structured washers (including slots and/or holes, a moat surrounding the washer and a zipper slit) to study the reduction of 1=f noise owing to hopping of flux vortices, trapped in the SQUID body during the cool-down process. A gradual reduction of the 1=f noise (measured down to 0.2 Hz) was measured for SQUIDs with increasing number of slots. Holes proved to be less effective than slots in reducing the flicker noise. The 1=f noise of the SQUIDs with a moat and zipper slit was smaller than that of a bold SQUID, but the reduction of noise was on the average less significant than for the slotted SQUIDs. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: LTS SQUIDs; Reduction 1=f noise; Slots and holes; Moats
1. Introduction The reduction of 1=f noise of low critical temperature (LTS) dc SQUIDs is crucial in applications where the SQUID has to operate at very low frequencies (103 –1 Hz) (e.g. in the readout of a cryogenic current comparator [1], gravitation gradiometers or the relativity gyroscope experiment). Flicker noise arises from fluctuations in the critical current, and hopping of vortices, trapped in the SQUID washer during the cool-down process. The noise due to critical current fluctuations can be adequately suppressed by appropriate modulation schemes. The problem of vortex hopping in LTS SQUIDs is less severe than for HTS SQUIDs, because of the lower operation temperature and the
*
Corresponding author. Tel.: +31-53-489-3125; fax: +31-53489-1099. E-mail address: [email protected] (E. Bartolome).
possibility of shielding the device to a great extent from environmental noise. In spite of that, flux generated within the device itself can be trapped, move around and produce non-negligible excess noise [2,3]. A possible way of reducing this 1=f noise is preventing the penetration of vortices in the SQUID, by narrowing the width of the strips forming the washer. Based on this idea, slotted and/ or holed SQUID washers have been employed in HTS SQUIDs for use in ambient magnetic fields (50 lT) [4]. The application of slot and hole structures to LTS SQUIDs has not been studied yet. Alternatively, flux trapping can be prevented by patterning a ‘‘moat’’ around the superconducting device [5,6]. A different strategy to reduce flux hopping is to use the washer slit edge roughness to create strong pinning centers in the SQUID, where vortices can be tightly trapped and thus move around less [3]. We have developed Nb/Al dc SQUIDs with all these different structures to investigate the reduction of 1=f noise.
0921-4534/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 2 ) 0 0 6 7 8 - 0
234
E. Bartolome et al. / Physica C 372–376 (2002) 233–236
2. Structured-washer SQUIDs The nine different washer configurations studied are shown in Fig. 1. The washer outer size (445 lm) and hole size (77 lm) were in all cases the same. The 4 4 lm2 area junctions were shunted by Rsh ¼ 2 X shunt resistors and the washer was shunted by a Rd ¼ 2 X damp resistor. A bold, non-structured SQUID was used as reference. Its washer inductance was calculated to be Lsq ¼ 189 pH. The designed flux-to-voltage transfer was 24 lV=U0 and the white noise level 1.5 lU0 =Hz1=2 . SQUIDs with an increasing number of slots, holes, or a combination of the slots and holes were designed, in a similar way as it was done in existing structured HTS SQUIDs [4,7]. In principle, slots can also be applied to LTS devices since the background theory is material independent. Indeed, consider a type II superconducting strip of width w and thickness t, such that t w, and t > 2k, cooled down in the presence of a magnetic
Fig. 1. Schematic of the nine SQUID washer designs investigated. The strips were w ¼ 4 lm wide (the minimum allowed in our photolithographic process) and the slots and holes size was 8 lm.
field Ba perpendicular to the strip. At temperatures 6 Tc , at which the freeze-out of vortices and antivortices occurs, the two-dimensional screening length KðT Þ ¼ 2k2 ðT Þ=t is much larger than the typical strip width w, because the penetration depth of the film k ! 1 at Tc . Note that this holds both for HTS as for LTS strips. Then, the dynamics of a vortex is dominated by its kinetic energy, and not by screening effects. The Gibbs energy of the vortex, at a position x (0 < x < w) inside the strip can be described by [8]: GðxÞ ¼
px 4p U20 2w sin ln l0 8p2 K pn w 4p U0 Ba xðw xÞ; l0 4pK
ð1Þ
where n is the coherence length; and l0 , the permeability of the vacuum. The first term is the kinetic self-energy of the vortex. The second term represents the energy involved when the field Ba penetrates locally in the superconducting strip. From the analysis of this function (Fig. 2) one can see that if Ba > Bc1 ð2U0 =pw2 Þ lnð2w=pnÞ, vortices will inevitably remain trapped at the center of the strip, while if Ba < BT ¼ pU0 =4w2 (threshold
Fig. 2. Gibbs free energy (reduced with respect to U20 =2pKl0 ) as a function of the position x of the vortex in the strip, of width e.g. w ¼ 4 lm.
E. Bartolome et al. / Physica C 372–376 (2002) 233–236
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field), vortices will be expelled from the strip (provided there are not strong pinning sites). We fabricated also a SQUID with a washer moat, which should prevent the entrance of vortices. It has been shown that the threshold field for complete vortex shielding strongly depends on the configuration, size and gap of the moat. Long, continuous moats seem to be more effective than broken moats [6]. We patterned a continuous 4 lm width moat at 8 lm form the edge of the washer. Finally, we included a SQUID with a zipperlike slit to favorise the strong pinning of vortices at the rough edge of the slit. For all the SQUIDs the flux was applied via a one-turn feedback coil surrounding the washer. An input coil, covering the whole washer, was only implemented for the 1=2 slotted SQUID.
3. Measurements The measured I–V and V–U characteristics of the nine SQUIDs were very similar. The critical current was I0 20 lA and the shunt resistor Rsh 2 X. The I–V curves showed some resonances, which were independent of the washer geometry. The feedback mutual inductance Mfb increased proportionally to the amount of available open area close to the central hole (up to a 30% increase for the all slotted SQUID with respect to the bold Mfb ¼ 140 pH). Noise measurements down to 0.2 Hz were performed with the SQUIDs shielded by a Nb and a room temperature l-metal cans, and readout with ‘‘Oxford Instruments’’ electronics. A conventional bias reversal scheme was used to get rid of the 1=f noise owing to DI0 fluctuations. Each SQUID was cooled down at least five times. In each thermal cycling, the local field might be different, and thus the probability of flux entry vary a little. Noise results are summarized in Fig. 3. The noise spectrum of the bold SQUID showed a white level 7 lU0 =Hz1=2 (the electronics noise limit for SQUIDs with a transfer <60 lV=U0 ) and a corner frequency at 4 Hz. Despite the shielding, the flux-hopping 1=f noise is large, as can be concluded from the large variations of the noise at
Fig. 3. Measured flux noise at 0.2 Hz for (above) the slotted SQUIDs and (below) alternative designs.
0.2 Hz for different cool downs. The strip width is such (184 lm), that vortices will penetrate even if the local field is as small as 0.05 lT. A reduction of the low-frequency noise is measured as the number of slots increases. The improvement when the solid inner half of the washer was replaced by slots is larger than when also the outermost half of the washer was slotted, because moving vortices couple more noise the closer they are with respect to the central hole. The noise of the 1=2 slotted SQUID with input coil is smaller than that of the SQUID without it. We believe that the coil is partially shielding the washer, thus reducing the area where vortices can enter. The holed SQUIDs seem less effective than the slotted ones in expelling vortices, a result also found in [4]. The completely holed SQUID is less noisy than the 1=2 slotted/ holed one. The SQUID with a moat had an average noise 36 lU0 =Hz1=2 (at 0.2 Hz) smaller than the bold SQUID, but the spread was comparable. The ‘‘zipper-slit’’ SQUID showed a smaller average noise (37 lU0 =Hz1=2 at 0.2 Hz)
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E. Bartolome et al. / Physica C 372–376 (2002) 233–236
and spread than the bold one, probably thanks to the combined effect of having a smaller trapping area and the pinning of vortices at the slit. However the method is less effective than the slots in reducing the average flicker noise.
Acknowledgements
4. Conclusions
References
We have shown that slotted and holed washers can be used to reduce the 1=f noise due to flux hopping in LTS SQUIDs. Noise measurements at different constant fields should be done in the future to determine the threshold field for expulsion of vortices. The average reduction of noise attained using slots was larger than the one reached using alternative moat and zipper-slit structures.
[1] K. Harvey, Rev. Sci. Instrum. 43 (1972) 1626. [2] J. Gail et al., Appl. Phys. Lett. 73 (1998) 2663. [3] M. Huber et al., IEEE Trans. Appl. Supercond. 7 (1997) 2882. [4] E. Dantsker et al., Appl. Phys. Lett. 70 (1997) 2037. [5] M. Jeffery et al., Appl. Phys. Lett. 67 (1995) 1769. [6] K. Suzuki et al., IEEE Trans. Appl. Supercond. 11 (2001) 238. [7] A. Jansman et al., IEEE Trans. Appl. Supercond. 9 (1999) 3290. [8] J.R. Clem, Phys. Rev. Lett. B. 43 (1991) 7837, and personal communication.
The authors would like to thank J.R. Clem for discussions. This work was funded by the STW organization, The Netherlands.