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Low frequency noise of high-Tc radio-frequency SQUIDs based on grain boundary Josephson junctions
Physica C 377 (2002) 516–520 www.elsevier.com/locate/physc
Low frequency noise of high-Tc radio-frequency SQUIDs based on grain boundary Josephson junctions E. Il’ichev a
a,*
, G.S. Krivoy b, R.P.J. IJsselsteijn
a
Department of Cryoelectronics, Institute for Physical High Technology, P.O. Box 100239, D-07702 Jena, Germany b FINO AG, Am Flugplatz 13, D-31137 Hildesheim, Germany Received 18 September 2001; received in revised form 6 December 2001; accepted 7 December 2001
Abstract Noise properties of single-layer washer-type high-Tc YBa2 Cu3 O7x rf SQUIDs with 30° grain boundary Josephson junctions have been investigated. We show experimentally that the additional low-frequency noise is produced by the magnetic flux dynamics in the ‘‘unwanted’’ junction in high-Tc rf SQUIDs which is formed by the grain boundary running through the washer of the SQUIDs on bicrystal substrates. In order to decrease the low-frequency noise we have designed rf SQUIDs with two strongly asymmetrical Josephson junctions. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 74.50:þr; 85.25.Cp Keywords: SQUID; Josephson junction
A small value of the low-frequency noise, usually of the 1=f -type, is one of the crucial requirements for real applications of SQUID-based instruments. The 1=f noise can arise either from critical current fluctuations or is due to thermally activated hopping of flux vortices between pinning centers in the superconductor. In the simplest case single-layer SQUID sensors are designed as socalled washer type SQUIDs in order to use the magnetic field focusing effects to increase their pick-up area. Due to the large demagnetization factor of a washer even small external magnetic
*
Corresponding author. Tel.: +49-3641-206121; fax: +493641-206199. E-mail address: [email protected] (E. Il’ichev).
fields can promote the nucleation and subsequent displacement of vortices in such washers [1]. Using bicrystals still is the easiest and most reproducable way to produce high-Tc Josephson junctions. However, because the grain boundary is crossing the complete substrate, an additional junction (‘‘unwanted’’ junction) crosses the washer (see Fig. 1a). This place with a smaller critical current density a priori is a potential source of additional 1=f noise due to thermally activated flux creep in the grain boundary. Such a flux creep has been recently observed directly by making use of a superconducting thin-film coil and Nb-based SQUID [2]. Moreover, as was shown before [3], the drop of the SQUID signal at a finite magnetic field is originated by the penetration of the magnetic field into the unwanted junction.
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 1 ) 0 1 3 1 4 - 4
E. Il’ichev et al. / Physica C 377 (2002) 516–520
517
Fig. 1. (a) Schematic representation of a high-Tc rf SQUID on a bicrystal. (b) SEM picture of the central part of a rf SQUID on a bicrystal with additional second slit (right).
Below we will show that a considerable proportion of the 1=f noise is originated by the unwanted junction. In order to decrease the low-frequency noise we have designed rf SQUIDs with two strongly asymmetrical Josephson junctions. All high-Tc rf SQUIDs were prepared on symmetric 30° SrTiO3 bicrystals. A 100 nm thick YBa2 Cu3 O7x (YBCO) layer, deposited by pulsed laser deposition, was structured using electronbeam lithography in combination with a special C–Ti mask-technology and ion-beam etch processes. This structuring technology results in steep structure edges, reducing the flux penetration into the YBCO layer. The SQUIDs have a geometric inductance LSQ of about 300 pH. For the desired SQUID parameter ßL ¼ 2pLSQ Ic =U0 (U0 is the flux quanta) to be about one, an effective critical current Ic of about 1 lA is required. At a temperature of 77 K, this value was obtained for a 100 nm thick, 1 lm wide Josephson junction on a symmetric 30° bicrystal. Smaller grain boundary angles, like e.g. 24°, require much smaller Josephson junction widths or a smaller YBCO layer thickness, larger grain boundary angles cause increased noise levels of the junctions. For the experiments, we prepared and characterized two pairs of rf SQUIDs. One of the pairs has a 3.5 mm washer side, and the other one 8 mm. The YBCO layer was deposited using standard onaxis pulsed laser deposition. The critical temperature Tc and critical current density jc of the layers are typically 89 K and 2 106 A/cm2 at 77 K, respectively. As a next step, Au alignment markers
for the electron beam lithography process are deposited using a lift-off process. These markers allow a positioning accuracy of 0.5 lm of the rf SQUID layout with respect to the grain boundary. After deposition of a 80 nm thick C layer and a 20 nm thick Ti layer by secondary ion deposition, a 300 nm thick PMMA electron beam resist layer is spun onto the substrate. Rf SQUIDs with 8 mm 8 mm or 3:5 mm 3:5 mm washers, with the SQUID hole in the center of the washer, and a 1 lm wide Josephson junction are now exposed by the electron beam exposure system ZBA 23H. After etching the Ti layer with Ar ion-beam etching and the C layer with oxygen ion etching, the YBCO layer is etched with Ar ion-beam etching using the C layer as a mask. Because the etch rate of carbon is a factor of five lower as that of YBCO, steep YBCO structure edges are obtained. In a typical washer design (see Fig. 1a) realized on a bicrystal substrate a long unwanted grain boundary lies across the washer. This grain boundary can be considered as an unwanted junction. If the flux creep in the unwanted junction originates additional low-frequency noise, there are two ways to suppress the flux motion. First is to create artificial pinning sites by the preparation of a network of submicrometer holes [4]. The lowfrequency noise reduction of high-Tc SQUIDs, by introducing artificial defects in a superconducting thin film device, was demonstrated in [5,6]. The second way is to decrease the probability for vortices to be trapped. Actually, if the width of the unwanted junction is of the order of the Josephson penetration depth kj , the probability that vortices
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are in this junction is decreased strongly; hence the flux creep effect should also be decreased [7]. More precisely, a crossover from a wide to a narrow junction is observed at w=kj 4, where w is the junction width [8]. As far as for our grain boundaries kj 5 lm, the critical width is of the order of 20 lm. Following these ideas we etched a 10 lm wide additional slit in two rf SQUIDs, in one piece of every couple, (see Fig. 1b) using standard photolithography and Ar ion-beam etching. In this way, the width of the remaining unwanted junction was reduced to 50 lm, both for the small and the large washer. Below we show that this width suffices to reduce the 1=f noise drastically. For measurements we used a standard rf SQUID electronics operating with a pump frequency of about 180 MHz [9]. The rf SQUID is coupled inductively to a tank circuit consisting of a coil Lt and a capacitor Ct . For the rf pumping, SQUID response transmission, and feedback a half-wavelength coaxial cable is used. Such a cable has a relatively high impedance, and thus it can be used for a good matching of the high impedance of a parallel tank circuit driven close to the resonance frequency and a low-noise rf amplifier with a high input impedance. In this way the rf voltage V across the tank circuit is directly led to the amplifier. The amplifier is working at room temperature and has an input stage based on a GaAsFET. The intrinsic noise of the whole amplifier related to its input is about 1 nV/Hz1=2 for the case of shorted input nodes. The current component of the amplifier noise is about 0.7 pA/Hz1=2 resulting in a contribution to the common amplifier noise of 1.3 nV/Hz1=2 , taking into account that in our case the effective impedance of the tank circuit near to the resonance frequency is about 1.8 kX on the first plateau of its current–voltage characteristics if coupled to a SQUID. The modulation voltage swing across the tank circuit coupled to a SQUID could be measured directly after the first stage of the rf amplifier and was typically 12 lV, i.e., the conversion factor from the SQUID to the tank circuit is 24 lV=U0 . Thus the noise contribution of the amplifier is about 5:3 105 U0 =Hz1=2 . Usual techniques for the modulation and synchronous detection at 50 kHz are used to reduce
the 1=f noise. A SQUID-based flux locked loop is build by means of an integrator connected to the output of the synchronous detector and a feedback circuit. The feedback signal is fed directly to the coaxial cable through a resistor placed close to the input of the rf preamplifier. For both SQUID sizes (large with 8 mm washer and small with 3.5 mm washer) the same tank circuit, cable and electronics were used. This allowed us a direct comparison of the sensitivities and noise levels of both SQUID sizes. Noise spectra were measured on the output of the integrator using a spectrum analyzer with an intrinsic noise level of about 2 nV/Hz1=2 . Measured output white noise levels of the flux locked loop were above 130 lV=Hz1=2 . The lower 3 dB cut-off frequency of the spectrum analyzer was 16 mHz. The SQUIDs with the tank circuit were placed inside a three-layer l-metal magnetic shielding in a liquid nitrogen dewar at T ¼ 77 K. Due to the second slit such SQUIDs must have a little bit lower transfer factor W ¼ @u=@B from the field B to the magnetic flux u, compared to the case of a SQUID with the same washer dimensions but without the second slit. To estimate the influence of the second slit the transfer factor W was measured by means of a Helmholtz coil positioned centrally around the SQUID outside the dewar. The second slit does influence not only the transfer factor W but also the coupling factor k between the SQUID and the tank circuit coil Lt . The coupling factor k together with other tank circuit parameters [10] defines the SQUID output voltage and can be estimated from the measured value of the mutual inductance M between the tank circuit coil and the SQUID. If the inductances of both the tank circuit coil and the SQUID loop are known, the coupling factor can be found as k ¼ M= 1=2 ðLt LSQ Þ . This approach gives more adequate results than the other known method for the calculation of k from the resonance frequency change for the cases when the SQUID is in (i) the nonsuperconducting state and in (ii) the superconducting state. The resonance frequency of the tank circuit does change not only due to the coupling to the SQUID loop but also due to the screening effect of the washer. As a result, the k values calculated by this way are always larger than the real ones. Thus we use the estimation of the coupling
E. Il’ichev et al. / Physica C 377 (2002) 516–520
519
Table 1 Comparison of the SQUID parameters with and without second slit SQUID number and design
Washer dimensions, mm
Hole dimensions, mm
Coupling factor k
Transfer factor W, U0 =nT
#1, #2, #3, #4,
3:5 3:5 3:5 3:5 88 88
0:2 0:2 0:2 0:2 0:2 0:2 0:2 0:2
0.37 0.33 0.36 0.33
0.273 0.213 0.546 0.431
no second slit with second slit no second slit with second slit
factor from the measured values of M and Lt and from the well calculated value of LSQ . The coupling factor also depends on the mutual position of the SQUID and the coil Lt . To ensure that the position is always the same for different SQUIDs the coil holder was marked with a cross, and positioning of the SQUIDs was done under a microscope. The results are given in Table 1. Fig. 2 shows typical noise spectra of the output SQUID signal for two different SQUIDs (#1 and #2 in Table 1) with the same basic design from which one of them is made with an additional (second) slit with a width of 10 lm. We have performed a number of noise measurements with all the SQUIDs to be investigated. Each SQUID was cooled down, measured and then warmed up at least five times. Only a non-significant difference in noise spectra obtained at different cooling sessions was observed, namely only in the lowest frequency range but never in the white noise range, which was above 30 Hz for all the SQUIDs. Each spectrum was averaged seven times during mea-
Fig. 2. Noise spectra of two SQUIDs with washer dimensions of 3:5 mm 3:5 mm and hole dimensions of 0:2 mm 0:2 mm.
surements. The SQUIDs without additional slit always had flux jumps which were clearly seen on the flux–voltage characteristics. Obviously these jumps are like telegraph noise and produce a high low-frequency noise contribution as described below. The SQUIDs with the second slit never had such jumps and thus had lower 1=f noise. This is a qualitative and not only a quantitative difference in noise behavior of these two kinds of SQUIDs which is resulting in a better noise performance of the SQUIDs with additional slit. Thus the effect of the second slit is (i) the reduction of the 1=f noise, as seen from Fig. 2, and (ii) a slight decrease of both the coupling factor and the transfer factor, as seen from Table 1, comparing the rows 1 and 2 or 3 and 4. The decrease of the coupling factor k is about 10%, and that of the transfer factor W is about 20% for both washer dimensions. We think, this can be explained by taking into account different areas of the washers, acting, from one side, in the coupling with the tank circuit coil and, from the other side, in the coupling with the external field. The lost 20% of the transfer factor is an appropriate price paid for the essential reduction of the 1=f noise. The other but unexpected effect of the second slit in SQUID #2 was the simultaneous reduction of noise in the frequency range above 30 Hz. This noise is usually considered as white noise because its spectral density is practically independent on the frequency. With the second slit we obtained also a reduced white noise when measured in flux quanta. This results in practically the same white noise level if recalculated in tesla using the transfer factor W (see Table 1). We cannot explain this effect from the physical basics. A possible reason could be, for instance, a different quality of the SQUIDs #1 and #2 themselves. SQUID #4 (8 mm
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washer with the second slit) does not demonstrate a reduction of white noise compared to SQUID #3 (8 mm washer without the additional slit) if measured in flux quanta. Thus we assume that the obtained white noise reduction in SQUID #2 is not caused by the second slit. To conclude, we have shown experimentally, that the low-frequency noise of grain boundary rf SQUIDs is mostly originated by the flux creep in the ‘‘unwanted’’ junction. In order to decrease this noise we propose and implement the rf SQUID design as a strongly asymmetrical dc SQUID. The reduction of the low-frequency noise was experimentally demonstrated. Up to now we have produced many SQUIDs with a second slit and no one of them has shown flux jumps and a corresponding high 1=f noise level. Acknowledgement The authors would like to thank V. Zakosarenko for fruitful discussions.
References [1] R.H. Koch, J. Clarke, W.M. Goubau, J.M. Martins, C.M. Pegrum, D.J. van Harlingen, J. Low Temp. Phys. 51 (1983) 207. [2] S. Hirano, H. Oyama, M. Matsuda, T. Morooka, S. Nakayama, S. Kuriki, IEEE Trans. Appl. Supercond. 11 (2001) 924. [3] E. Il’ichev, V. Schultze, R.P.J. IJsselsteijn, R. Stolz, V. Zakosarenko, H.E. Hoenig, H.-G. Meyer, M. Siegel, Physica C 330 (2000) 155. [4] A. Lykov, Solid State Commun. 86 (1993) 531. [5] P. Selders, A.M. Castellanos, M. Vaupel, R. W€ ordenweber, IEEE Trans. Appl. Supercond. 9 (1999) 2967. [6] P. Selders, R. W€ ordenweber, IEEE Trans. Appl. Supercond. 11 (2001) 928. [7] Recently the similar aproach was used by the Juelich group: M. Fardmanesh, J. Schubert, R. Akram, M. Banzet, W. Zander, H.-J. Krause, 5th European Conference on Applied Superconductivity 2001 (EUCAS 2001), Abstract book, 115, D1.2–12. [8] B. Mayer, S. Schuster, A. Beck, L. Alf, R. Gross, Appl. Phys. Lett. 62 (1993) 783. [9] FINO AG, Am Flugplatz 13, D-31137 Hildesheim, Germany. [10] K.K. Likharev, Dynamics of Josephson Junctions and Circuits, Gordon and Breach, Philadelphia, 1986.
Low frequency noise of high-Tc radio-frequency SQUIDs based on grain boundary Josephson junctions E. Il’ichev a
a,*
, G.S. Krivoy b, R.P.J. IJsselsteijn
a
Department of Cryoelectronics, Institute for Physical High Technology, P.O. Box 100239, D-07702 Jena, Germany b FINO AG, Am Flugplatz 13, D-31137 Hildesheim, Germany Received 18 September 2001; received in revised form 6 December 2001; accepted 7 December 2001
Abstract Noise properties of single-layer washer-type high-Tc YBa2 Cu3 O7x rf SQUIDs with 30° grain boundary Josephson junctions have been investigated. We show experimentally that the additional low-frequency noise is produced by the magnetic flux dynamics in the ‘‘unwanted’’ junction in high-Tc rf SQUIDs which is formed by the grain boundary running through the washer of the SQUIDs on bicrystal substrates. In order to decrease the low-frequency noise we have designed rf SQUIDs with two strongly asymmetrical Josephson junctions. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 74.50:þr; 85.25.Cp Keywords: SQUID; Josephson junction
A small value of the low-frequency noise, usually of the 1=f -type, is one of the crucial requirements for real applications of SQUID-based instruments. The 1=f noise can arise either from critical current fluctuations or is due to thermally activated hopping of flux vortices between pinning centers in the superconductor. In the simplest case single-layer SQUID sensors are designed as socalled washer type SQUIDs in order to use the magnetic field focusing effects to increase their pick-up area. Due to the large demagnetization factor of a washer even small external magnetic
*
Corresponding author. Tel.: +49-3641-206121; fax: +493641-206199. E-mail address: [email protected] (E. Il’ichev).
fields can promote the nucleation and subsequent displacement of vortices in such washers [1]. Using bicrystals still is the easiest and most reproducable way to produce high-Tc Josephson junctions. However, because the grain boundary is crossing the complete substrate, an additional junction (‘‘unwanted’’ junction) crosses the washer (see Fig. 1a). This place with a smaller critical current density a priori is a potential source of additional 1=f noise due to thermally activated flux creep in the grain boundary. Such a flux creep has been recently observed directly by making use of a superconducting thin-film coil and Nb-based SQUID [2]. Moreover, as was shown before [3], the drop of the SQUID signal at a finite magnetic field is originated by the penetration of the magnetic field into the unwanted junction.
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 1 ) 0 1 3 1 4 - 4
E. Il’ichev et al. / Physica C 377 (2002) 516–520
517
Fig. 1. (a) Schematic representation of a high-Tc rf SQUID on a bicrystal. (b) SEM picture of the central part of a rf SQUID on a bicrystal with additional second slit (right).
Below we will show that a considerable proportion of the 1=f noise is originated by the unwanted junction. In order to decrease the low-frequency noise we have designed rf SQUIDs with two strongly asymmetrical Josephson junctions. All high-Tc rf SQUIDs were prepared on symmetric 30° SrTiO3 bicrystals. A 100 nm thick YBa2 Cu3 O7x (YBCO) layer, deposited by pulsed laser deposition, was structured using electronbeam lithography in combination with a special C–Ti mask-technology and ion-beam etch processes. This structuring technology results in steep structure edges, reducing the flux penetration into the YBCO layer. The SQUIDs have a geometric inductance LSQ of about 300 pH. For the desired SQUID parameter ßL ¼ 2pLSQ Ic =U0 (U0 is the flux quanta) to be about one, an effective critical current Ic of about 1 lA is required. At a temperature of 77 K, this value was obtained for a 100 nm thick, 1 lm wide Josephson junction on a symmetric 30° bicrystal. Smaller grain boundary angles, like e.g. 24°, require much smaller Josephson junction widths or a smaller YBCO layer thickness, larger grain boundary angles cause increased noise levels of the junctions. For the experiments, we prepared and characterized two pairs of rf SQUIDs. One of the pairs has a 3.5 mm washer side, and the other one 8 mm. The YBCO layer was deposited using standard onaxis pulsed laser deposition. The critical temperature Tc and critical current density jc of the layers are typically 89 K and 2 106 A/cm2 at 77 K, respectively. As a next step, Au alignment markers
for the electron beam lithography process are deposited using a lift-off process. These markers allow a positioning accuracy of 0.5 lm of the rf SQUID layout with respect to the grain boundary. After deposition of a 80 nm thick C layer and a 20 nm thick Ti layer by secondary ion deposition, a 300 nm thick PMMA electron beam resist layer is spun onto the substrate. Rf SQUIDs with 8 mm 8 mm or 3:5 mm 3:5 mm washers, with the SQUID hole in the center of the washer, and a 1 lm wide Josephson junction are now exposed by the electron beam exposure system ZBA 23H. After etching the Ti layer with Ar ion-beam etching and the C layer with oxygen ion etching, the YBCO layer is etched with Ar ion-beam etching using the C layer as a mask. Because the etch rate of carbon is a factor of five lower as that of YBCO, steep YBCO structure edges are obtained. In a typical washer design (see Fig. 1a) realized on a bicrystal substrate a long unwanted grain boundary lies across the washer. This grain boundary can be considered as an unwanted junction. If the flux creep in the unwanted junction originates additional low-frequency noise, there are two ways to suppress the flux motion. First is to create artificial pinning sites by the preparation of a network of submicrometer holes [4]. The lowfrequency noise reduction of high-Tc SQUIDs, by introducing artificial defects in a superconducting thin film device, was demonstrated in [5,6]. The second way is to decrease the probability for vortices to be trapped. Actually, if the width of the unwanted junction is of the order of the Josephson penetration depth kj , the probability that vortices
518
E. Il’ichev et al. / Physica C 377 (2002) 516–520
are in this junction is decreased strongly; hence the flux creep effect should also be decreased [7]. More precisely, a crossover from a wide to a narrow junction is observed at w=kj 4, where w is the junction width [8]. As far as for our grain boundaries kj 5 lm, the critical width is of the order of 20 lm. Following these ideas we etched a 10 lm wide additional slit in two rf SQUIDs, in one piece of every couple, (see Fig. 1b) using standard photolithography and Ar ion-beam etching. In this way, the width of the remaining unwanted junction was reduced to 50 lm, both for the small and the large washer. Below we show that this width suffices to reduce the 1=f noise drastically. For measurements we used a standard rf SQUID electronics operating with a pump frequency of about 180 MHz [9]. The rf SQUID is coupled inductively to a tank circuit consisting of a coil Lt and a capacitor Ct . For the rf pumping, SQUID response transmission, and feedback a half-wavelength coaxial cable is used. Such a cable has a relatively high impedance, and thus it can be used for a good matching of the high impedance of a parallel tank circuit driven close to the resonance frequency and a low-noise rf amplifier with a high input impedance. In this way the rf voltage V across the tank circuit is directly led to the amplifier. The amplifier is working at room temperature and has an input stage based on a GaAsFET. The intrinsic noise of the whole amplifier related to its input is about 1 nV/Hz1=2 for the case of shorted input nodes. The current component of the amplifier noise is about 0.7 pA/Hz1=2 resulting in a contribution to the common amplifier noise of 1.3 nV/Hz1=2 , taking into account that in our case the effective impedance of the tank circuit near to the resonance frequency is about 1.8 kX on the first plateau of its current–voltage characteristics if coupled to a SQUID. The modulation voltage swing across the tank circuit coupled to a SQUID could be measured directly after the first stage of the rf amplifier and was typically 12 lV, i.e., the conversion factor from the SQUID to the tank circuit is 24 lV=U0 . Thus the noise contribution of the amplifier is about 5:3 105 U0 =Hz1=2 . Usual techniques for the modulation and synchronous detection at 50 kHz are used to reduce
the 1=f noise. A SQUID-based flux locked loop is build by means of an integrator connected to the output of the synchronous detector and a feedback circuit. The feedback signal is fed directly to the coaxial cable through a resistor placed close to the input of the rf preamplifier. For both SQUID sizes (large with 8 mm washer and small with 3.5 mm washer) the same tank circuit, cable and electronics were used. This allowed us a direct comparison of the sensitivities and noise levels of both SQUID sizes. Noise spectra were measured on the output of the integrator using a spectrum analyzer with an intrinsic noise level of about 2 nV/Hz1=2 . Measured output white noise levels of the flux locked loop were above 130 lV=Hz1=2 . The lower 3 dB cut-off frequency of the spectrum analyzer was 16 mHz. The SQUIDs with the tank circuit were placed inside a three-layer l-metal magnetic shielding in a liquid nitrogen dewar at T ¼ 77 K. Due to the second slit such SQUIDs must have a little bit lower transfer factor W ¼ @u=@B from the field B to the magnetic flux u, compared to the case of a SQUID with the same washer dimensions but without the second slit. To estimate the influence of the second slit the transfer factor W was measured by means of a Helmholtz coil positioned centrally around the SQUID outside the dewar. The second slit does influence not only the transfer factor W but also the coupling factor k between the SQUID and the tank circuit coil Lt . The coupling factor k together with other tank circuit parameters [10] defines the SQUID output voltage and can be estimated from the measured value of the mutual inductance M between the tank circuit coil and the SQUID. If the inductances of both the tank circuit coil and the SQUID loop are known, the coupling factor can be found as k ¼ M= 1=2 ðLt LSQ Þ . This approach gives more adequate results than the other known method for the calculation of k from the resonance frequency change for the cases when the SQUID is in (i) the nonsuperconducting state and in (ii) the superconducting state. The resonance frequency of the tank circuit does change not only due to the coupling to the SQUID loop but also due to the screening effect of the washer. As a result, the k values calculated by this way are always larger than the real ones. Thus we use the estimation of the coupling
E. Il’ichev et al. / Physica C 377 (2002) 516–520
519
Table 1 Comparison of the SQUID parameters with and without second slit SQUID number and design
Washer dimensions, mm
Hole dimensions, mm
Coupling factor k
Transfer factor W, U0 =nT
#1, #2, #3, #4,
3:5 3:5 3:5 3:5 88 88
0:2 0:2 0:2 0:2 0:2 0:2 0:2 0:2
0.37 0.33 0.36 0.33
0.273 0.213 0.546 0.431
no second slit with second slit no second slit with second slit
factor from the measured values of M and Lt and from the well calculated value of LSQ . The coupling factor also depends on the mutual position of the SQUID and the coil Lt . To ensure that the position is always the same for different SQUIDs the coil holder was marked with a cross, and positioning of the SQUIDs was done under a microscope. The results are given in Table 1. Fig. 2 shows typical noise spectra of the output SQUID signal for two different SQUIDs (#1 and #2 in Table 1) with the same basic design from which one of them is made with an additional (second) slit with a width of 10 lm. We have performed a number of noise measurements with all the SQUIDs to be investigated. Each SQUID was cooled down, measured and then warmed up at least five times. Only a non-significant difference in noise spectra obtained at different cooling sessions was observed, namely only in the lowest frequency range but never in the white noise range, which was above 30 Hz for all the SQUIDs. Each spectrum was averaged seven times during mea-
Fig. 2. Noise spectra of two SQUIDs with washer dimensions of 3:5 mm 3:5 mm and hole dimensions of 0:2 mm 0:2 mm.
surements. The SQUIDs without additional slit always had flux jumps which were clearly seen on the flux–voltage characteristics. Obviously these jumps are like telegraph noise and produce a high low-frequency noise contribution as described below. The SQUIDs with the second slit never had such jumps and thus had lower 1=f noise. This is a qualitative and not only a quantitative difference in noise behavior of these two kinds of SQUIDs which is resulting in a better noise performance of the SQUIDs with additional slit. Thus the effect of the second slit is (i) the reduction of the 1=f noise, as seen from Fig. 2, and (ii) a slight decrease of both the coupling factor and the transfer factor, as seen from Table 1, comparing the rows 1 and 2 or 3 and 4. The decrease of the coupling factor k is about 10%, and that of the transfer factor W is about 20% for both washer dimensions. We think, this can be explained by taking into account different areas of the washers, acting, from one side, in the coupling with the tank circuit coil and, from the other side, in the coupling with the external field. The lost 20% of the transfer factor is an appropriate price paid for the essential reduction of the 1=f noise. The other but unexpected effect of the second slit in SQUID #2 was the simultaneous reduction of noise in the frequency range above 30 Hz. This noise is usually considered as white noise because its spectral density is practically independent on the frequency. With the second slit we obtained also a reduced white noise when measured in flux quanta. This results in practically the same white noise level if recalculated in tesla using the transfer factor W (see Table 1). We cannot explain this effect from the physical basics. A possible reason could be, for instance, a different quality of the SQUIDs #1 and #2 themselves. SQUID #4 (8 mm
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E. Il’ichev et al. / Physica C 377 (2002) 516–520
washer with the second slit) does not demonstrate a reduction of white noise compared to SQUID #3 (8 mm washer without the additional slit) if measured in flux quanta. Thus we assume that the obtained white noise reduction in SQUID #2 is not caused by the second slit. To conclude, we have shown experimentally, that the low-frequency noise of grain boundary rf SQUIDs is mostly originated by the flux creep in the ‘‘unwanted’’ junction. In order to decrease this noise we propose and implement the rf SQUID design as a strongly asymmetrical dc SQUID. The reduction of the low-frequency noise was experimentally demonstrated. Up to now we have produced many SQUIDs with a second slit and no one of them has shown flux jumps and a corresponding high 1=f noise level. Acknowledgement The authors would like to thank V. Zakosarenko for fruitful discussions.
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