- Email: [email protected]
Phase transition study of superheated planar arrays of tin cylinders
Nuclear Instruments and Methods in Physics Research A 459 (2001) 469}474
Phase transition study of superheated planar arrays of tin cylinders S. Casalbuoni , G. Czapek , F. Hasenbalg , M. Hauser , S. Janos , K. Pretzl *, S. Calatroni, S. Sgobba, W. Vollenberg Laboratory for High Energy Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland CERN, CH-1211 Geneva 23, Switzerland Received 30 June 2000; accepted 5 August 2000
Abstract We have investigated the superheating and the supercooling "elds of a planar array of tin cylinders with diameters ranging from 40 to 80 m and thickness 8.3 m evaporated onto a glass substrate and onto a kapton foil. Experimental values of the Ginzburg}Landau parameter have been obtained and compared with results from tin spheres. The spread of the superheating curves is below 5%. 2001 Elsevier Science B.V. All rights reserved. PACS: 74.80.Dm; 95.55.Vj; 95.35. td Keywords: Superconducting arrays; Tin metastability; Dark Matter
1. Introduction Metastable superconducting detectors made of a suspension of superheated superconducting granules (SSG) embedded in dielectric "lling material or consisting of planar arrays of regularly spaced superheated superconducting microstructures (PASS), are under investigation for di!erent applications like for example dark matter detection [1,2]. Thin-"lm photolithographic technique for a microstructure detector combined with melting of indium dots in the presence of a wetting agent has been used "rst by Le Gros et al. [3], who fabricated * Corresponding author. Tel.: #41-31-631-8566; fax: #4131-631-4487. E-mail address: [email protected] (K. Pretzl).
a planar array of indium spheres on a mylar substrate. The spread in transition temperature for such an array was reported to be an order of magnitude smaller than that for a suspension of granules [3]. Subsequent experimental investigations [4}7] of indium cylinders produced by photolithography and lift-o! technique have shown that the spread in both superheating and supercooling "eld distributions was below 2%, which is much better than the typical values of 10}30% observed in suspensions of granules [8,9]. In our previous papers [5,6], we have studied planar indium arrays of cylinders. However, indium has a relatively high content of radioactive isotopes and also the gradient of the superheating to normal phase lines B vs. ¹ is relatively small. Previous experiments [10] with a planar array of tin spheres show a
0168-9002/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 0 ) 0 1 0 5 0 - 0
470
S. Casalbuoni et al. / Nuclear Instruments and Methods in Physics Research A 459 (2001) 469}474
considerable reduction in the spread of the transition temperature. Thus, we decided to investigate a planar array of tin cylinders. In view of a potential application for dark matter search, where a large detector mass is needed, we have developed a new method of fabrication of a planar array of tin cylinders, which, in principle, allows mass production.
2. Preparation of the cylinders Cylindrical tin structures were produced at CERN with diameters of 40, 60 and 80 m ordered in regular arrays. The distance between the cylinders from centre to centre is &3}5 times the diameter of the cylinders. Two di!erent procedures have been used: (a) Sn evaporation onto a kapton foil as well as onto a glass substrate, followed by acid lithography of the cylinders. Coating is carried out with an electron beam evaporator in a residual vacuum of about 5;10\ mbar and a coating rate of 1 nm/s, in four steps to avoid overheating of the substrate. The surface of the kapton foil has been depolished by sand-blasting and cleaned with ethanol. The glass substrate has been cleaned with a tensioactive detergent, rinsed and dried with ethanol. The total thickness of the Sn coating is 8.3 m. The cylinders are prepared by standard photolithographic methods using FeCl as etching agent. (b) Sn evaporation onto a kapton foil and onto a glass substrate through a mask. Coating is done as above, but the substrate is now covered by a Ni-plated 50 m thick CuBe mask where holes have been etched. The mask is clamped to the substrate and kept adherent to the surface at every point by magnets placed behind the substrate. The total thickness of the coating is again 8.3 m.
3. Results and discussion The #ip (#op) "eld distribution is called superheating (supercooling) curve. These curves were
measured in a standard way, as described in Ref. [9]. The investigated probes have about 100 cylinders each. The probes have been mounted in the centre of a pickup coil with the cylinder axis perpendicular to the pickup coil axis and immersed directly into a pumped He bath at ¹"1.4 K. Phase transition of the granules from the superconducting to the normal state is induced by sweeping an external magnetic "eld. The "eld was produced by a pair of Helmholtz coils, and was swept from 0 to 45 mT. The size of the signal, which is a damped oscillation, is very sensitive to the orientation of the magnetic "eld with respect to the axis of the cylinders. The maximum signal is expected when the magnetic "eld is perpendicular to the axis of the cylinders, thus parallel to the pickup coil axis. In practice, however, the probe is tilted with respect to the pickup coil axis and the maximum signal is observed at an angle between the applied "eld and the pickup coil axis. With our experimental apparatus it is not possible to establish the angle between the magnetic "eld and the axis of the cylinders with an accuracy higher than one degree. Thus, it is quite di$cult to "nd the right position to reach the maximum e$ciency E, i.e. the number of #ips observed divided by the total number of cylinders of a probe. The superconducting behaviour of the cylinders does not depend on the substrate used. The cylinders produced with the "rst procedure neither #ip nor #op. Measurements performed by Pozzi [11] in Bern show that metastability is strongly reduced and sometimes completely suppressed by the corrosion of acids on the Sn granules. Only in the case of weak acids, such as formic acid, metastability is still observed. Acid corrosion acts with di!erent velocities on the di!erent crystallographic planes [12]. A modi"cation of the crystalline structure may be responsible for the loss of metastability. The cylinders produced with the second procedure are metastable. Fig. 1 shows the superheating and the supercooling curves of a probe made by about 200 cylinders with 80 m diameter on a glass substrate which have been measured at +103 (a, b) and at +93 (c, d). There is evidence of the intermediate state occurring at +93 because
S. Casalbuoni et al. / Nuclear Instruments and Methods in Physics Research A 459 (2001) 469}474
471
Fig. 1. Plots of the superheating and the supercooling "elds of the same probe (about 200 cylinders with 80 m diameter on a glass substrate) measured at +103 (a, b) and at +93 (c, d).
(a) The superheating "elds at +9 are lower. A shift is observed from B "29.88 mT at +103 to B "28.34 mT at +93. (b) The e$ciency (e!) at +93 (70%) is lower than the one at +103 (86%). (c) The #ipping time at +93 (1.5 s) is longer than the one at +103 (1.0 s).
Fig. 2 reports the phase diagram for a sample of about 200 cylinders with diameter of the order of 80 m, evaporated onto a glass substrate through a mask. The dashed line is the thermodynamical critical "eld for a sample of bulk Sn. The two continuous lines are the best "ts obtained for superheating and supercooling. The function used to "t the data is
Despite the di$culty in realizing a precise orientation (within at least 13) of the cylinders, encouraging results are obtained. Even with our rough system to orient the cylinders the e$ciency for superheating is '75%. The most important results are shown in Table 1: the probes are characterised by a sharp superheating curve with B/B(5%.
¹ ¹ where, for superheating, the parameters are B(0) and ¹ . The "t of the supercooling data is made by changing only B(0) and using the value of ¹ ob tained for superheating. ¹ is about 0.2 K lower than the critical temperature of bulk tin (3.72 K).
B(¹)"B(0) 1!
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S. Casalbuoni et al. / Nuclear Instruments and Methods in Physics Research A 459 (2001) 469}474
Table 1 Mean "eld values B, spread of the critical "elds B/B, and e$ciency E for each of the probes measured. The angle between the applied "eld and the axis of the pickup coil, , is also quoted Probes on glass 80 m superheating 80 m superheating 80 m supercooling 80 m supercooling 60 m superheating 60 m supercooling 40 m superheating Probes on kapton 80 m superheating 80 m supercooling 60 m superheating 40 m superheating
B (mT)
B/B
E
103
29.88
5%
86%
93
28.34
4%
70%
103
24.72
3%
16%
93
25.13
3%
18%
1953
29.92
5%
84%
1953
25.41
4%
13%
1953
30.43
4%
86%
2003
29.33
4%
88%
2003
22.03
4%
34%
2003
29.27
6%
77%
1703
29.92
4%
76%
By cooling to liquid-helium temperature Sn cylinders do not follow the thermal contraction of the substrate and are under stress conditions. The stress e!ect may be tensile or compressive, depending on the relative thermal contraction of Sn and the substrate. A compressive stress generally decreases ¹ , while a tensile stress increases ¹ . Lock [13] observed for evaporated Sn "lms on a mica glass substrate an increase in ¹ of up to 3.87 K. However, using a distrene foil, which has a much higher expansion coe$cient than Sn, he observed ¹ "3.53 K. Blumberg et al. [14] studied the e!ect of tensile stress on ¹ of evaporated Sn "lms on glass substrates and observed that ¹ increases by 0.23 K. Muench [15], Jennings and Swenson [16], and Wittig [17] studied the e!ect of a compressive stress on bulk Sn samples and observed a decrease of ¹ . Since our Sn cylinders were evaporated on a glass substrate, which has a lower expansion
Fig. 2. Phase diagram of the cylinders sample.
Table 2 Fitted values of B(0) calculated from the superheating and from the supercooling data and of ¹ calculated only from the super heating data
Superheating Supercooling
B(0) (mT)
¹ (K)
35.00$0.33 29.32$0.09
3.54$0.03 3.54
1.2 9.8
coe$cient than Sn, we cannot explain the observed large decrease in ¹ as being due to stress e!ects. In Table 2 the values of the parameters, the errors and the of the "ts are shown. From the measurements of superheating and supercooling the experimental parameter (¹) [23,24] can be deduced
B "0.498 . B No temperature dependence (within the errors) of (¹) is observed. Fig. 3 shows the comparison of (¹) for the cylinders with the values obtained by Feder and MacLachlan [23] on a single Sn sphere of 48 m and with the value obtained by us [25] from the best "ts of the measured B and B of a sample made by about 300 Sn spheres with diameter ranging from 30 to 35 m.
S. Casalbuoni et al. / Nuclear Instruments and Methods in Physics Research A 459 (2001) 469}474
Fig. 3. Obtained values of (¹) for tin cylinders.
Table 3 Values of , the corresponding electrical resistivity , and mean free path l
Cylinders
$
$ ( cm) l $l (m)
0.444$0.003
1.44$0.02
0.06$0.01
Table 3 lists the electrical resistivity calculated from the GorkE ov}Goodman relation [26] together with the best "ts of (¹) ("0.8), " #7.5;10 (1) where "0.087$0.002 [24] is the value of at ¹"¹ for pure Sn, "1092 erg/cm K [27] is the Sommerfeld constant of Sn and is given in cm. Also shown in Table 3 is the mean free path l , which using the free electron model for Sn is given by 1 l " cm. 1.21;10( cm)
(2)
Usually, the residual resistivity of pure polycrystalline tin "lms is &0.1 cm [18]. The high value of "1.44 cm shown by our sample at liquid-
473
helium temperature corresponds to an impurity content in Sn of about a few at% [19]. The e!ect of Sb, In and Zn impurities up to 2 at% on the superconducting transition temperature of Sn crystals has been studied by Burckbuchler et al. [20]. A decrease up to 140 mK for a Zn-doped sample with residual impurity resistivity "1 cm was observed. Smith et al. [24] obtained for a thick Sn foil (&80 m thickness) with an In impurity content of 2.75 at% "0.46, a decrease in ¹ of 100 mK and an electron mean free path l "0.058 m, which is very near to the value com puted for our sample. The observed decrease in ¹ in our Sn "lm cylinders can be due to the 1}2 at% impurity content. Another possibility is that the cylinders contain a few hundred ppm of magnetic impurities, as Mn [21], Cr, Fe or Co [22], which are very e!ective in decreasing ¹ . However, such a low magnetic impurity content does not correspond to the high value of obtained for our sample. It is well known that superconducting properties of Sn "lms depend very critically on the content of residual gases (e.g. N S, O ) when evap orating in vacuum. However, Caswell [18] observed in tin "lms with residual gas content no decrease in ¹ . Some of the samples showed almost no change, others even an increase of ¹ up to 3.89 K. Thus, we believe that the observed decrease in ¹ of the cylinders, is due to nonmagnetic impu rities. The origin of such impurities in our samples is, however, not clear.
4. Conclusions The main result coming from the study of the tin cylinders produced through a mask and arranged in a planar array con"guration is the sharp distribution of their superheating curves B/B(5%. Mass production is in principle possible. Applications to SSG detectors are possible, if a precise orientation ((13) of a large amount of cylinders can be reached. A test experiment of an SSG detector in a 70 MeV neutron beam at Paul Scherrer Institute has shown that energy thresholds down to &1 keV were reached in SSG detectors made of
474
S. Casalbuoni et al. / Nuclear Instruments and Methods in Physics Research A 459 (2001) 469}474
Sn spheres with diameters of 15}20 m [28]. The Sn cylinders of 40 m diameter and 8 m height should then be able, assuming a linear dependence between the volume of a single granule and the energy threshold, to reach energy thresholds of about 0.1 keV.
Acknowledgements This work was supported by the Schweizerischer Nationalfonds zur FoK rderung der wissenschaftlichen Forschung and by the Bernische Stiftung zur FoK rderung der wissenschaftlichen Forschung an der UniversitaK t Bern.
References [1] B. van den Brandt et al., Nucl. Phys. B (Proc. Suppl.) 70 (1999) 101. [2] M. Aplanalp et al., Nucl. Instr. and Meth. A 370 (1996) 227. [3] M. Le Gros et al., Appl. Phys. Lett. 56 (22) (1990) 2234. [4] G. Meagher et al., Proceedings of the International Workshop on Superconductivity and Particle Detection, Toledo, Spain, World Scienti"c, Singapore, 20}24 April 1994. [5] R. Leoni et al., J. Low Temp. Phys. 93 (1993) 503. [6] Ch. Berger et al., J. Low Temp. Phys. 93 (1993) 509.
[7] R. Leoni et al., Proceedings of the International Workshop on Superconductivity and Particle Detection, Toledo, Spain, World Scienti"c, Singapore, 20}24 April 1994. [8] K. Pretzl, J. Low Temp. Phys. 93 (1993) 439. [9] M. Frank et al., Nucl. Instr. and Meth. A 287 (1990) 583. [10] G. Meagher et al., J. Low Temp. Phys. 93 (1993) 461. [11] R. Pozzi, Magnetische Wechselwirkung Zwischen Supraleitenden ZinnkuK gelchen, Diplomarbeit, UniversitaK t Bern, 1995. [12] M.J. Pryor, R.V. Staehle, Treatise on solid state chemistry, in: N.B. Hannay (Ed.), Reactivity of Solids, Vol. 4, Plenum Press, New York, 1976, p. 510. [13] J.M. Lock, Proc. Roy. Soc. A 208 (1951) 391. [14] R.H. Blumberg, D.P. Seraphin, J. Appl. Phys. 33 (1962) 163. [15] N.L. Muench, Phys. Rev. 99 (1955) 1814. [16] L.D. Jennings, C.A. Swenson, Phys. Rev. 112 (1958) 31. [17] J. Wittig, Z. Phys. 195 (1966) 228. [18] H.L. Caswell, J. Appl. Phys. 32 (1961) 105. [19] F.V. Burckbuchler, C.A. Reynolds, Phys. Rev. 175 (1968) 550. [20] F.V. Burckbuchler et al., Phys. Rev. 175 (1968) 543. [21] W. Buckel et al., Z. Phys. 245 (1971) 283. [22] A. Schertel, Phys. Verh. 2 (1951) 102. [23] J. Feder, D.S. McLachlan, Phys. Rev. 177 (1969) 763. [24] F.W. Smith, A. Barto!, M. Cardona, Phys. Kondens. Mater. 12 (1970) 145. [25] S. Calatroni et al., Nucl. Instr. and Meth. A 444 (2000) 285. [26] B.B. Goodman, IBM J. Res. Dev. 6 (1962) 63. [27] D.K. Finnemore, D.E. Mapother, Phys. Rev. 140 (1965) A507. [28] M. Abplanalp et al., Nucl. Instr. and Meth. A 360 (1995) 616.
Phase transition study of superheated planar arrays of tin cylinders S. Casalbuoni , G. Czapek , F. Hasenbalg , M. Hauser , S. Janos , K. Pretzl *, S. Calatroni, S. Sgobba, W. Vollenberg Laboratory for High Energy Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland CERN, CH-1211 Geneva 23, Switzerland Received 30 June 2000; accepted 5 August 2000
Abstract We have investigated the superheating and the supercooling "elds of a planar array of tin cylinders with diameters ranging from 40 to 80 m and thickness 8.3 m evaporated onto a glass substrate and onto a kapton foil. Experimental values of the Ginzburg}Landau parameter have been obtained and compared with results from tin spheres. The spread of the superheating curves is below 5%. 2001 Elsevier Science B.V. All rights reserved. PACS: 74.80.Dm; 95.55.Vj; 95.35. td Keywords: Superconducting arrays; Tin metastability; Dark Matter
1. Introduction Metastable superconducting detectors made of a suspension of superheated superconducting granules (SSG) embedded in dielectric "lling material or consisting of planar arrays of regularly spaced superheated superconducting microstructures (PASS), are under investigation for di!erent applications like for example dark matter detection [1,2]. Thin-"lm photolithographic technique for a microstructure detector combined with melting of indium dots in the presence of a wetting agent has been used "rst by Le Gros et al. [3], who fabricated * Corresponding author. Tel.: #41-31-631-8566; fax: #4131-631-4487. E-mail address: [email protected] (K. Pretzl).
a planar array of indium spheres on a mylar substrate. The spread in transition temperature for such an array was reported to be an order of magnitude smaller than that for a suspension of granules [3]. Subsequent experimental investigations [4}7] of indium cylinders produced by photolithography and lift-o! technique have shown that the spread in both superheating and supercooling "eld distributions was below 2%, which is much better than the typical values of 10}30% observed in suspensions of granules [8,9]. In our previous papers [5,6], we have studied planar indium arrays of cylinders. However, indium has a relatively high content of radioactive isotopes and also the gradient of the superheating to normal phase lines B vs. ¹ is relatively small. Previous experiments [10] with a planar array of tin spheres show a
0168-9002/01/$ - see front matter 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 0 0 ) 0 1 0 5 0 - 0
470
S. Casalbuoni et al. / Nuclear Instruments and Methods in Physics Research A 459 (2001) 469}474
considerable reduction in the spread of the transition temperature. Thus, we decided to investigate a planar array of tin cylinders. In view of a potential application for dark matter search, where a large detector mass is needed, we have developed a new method of fabrication of a planar array of tin cylinders, which, in principle, allows mass production.
2. Preparation of the cylinders Cylindrical tin structures were produced at CERN with diameters of 40, 60 and 80 m ordered in regular arrays. The distance between the cylinders from centre to centre is &3}5 times the diameter of the cylinders. Two di!erent procedures have been used: (a) Sn evaporation onto a kapton foil as well as onto a glass substrate, followed by acid lithography of the cylinders. Coating is carried out with an electron beam evaporator in a residual vacuum of about 5;10\ mbar and a coating rate of 1 nm/s, in four steps to avoid overheating of the substrate. The surface of the kapton foil has been depolished by sand-blasting and cleaned with ethanol. The glass substrate has been cleaned with a tensioactive detergent, rinsed and dried with ethanol. The total thickness of the Sn coating is 8.3 m. The cylinders are prepared by standard photolithographic methods using FeCl as etching agent. (b) Sn evaporation onto a kapton foil and onto a glass substrate through a mask. Coating is done as above, but the substrate is now covered by a Ni-plated 50 m thick CuBe mask where holes have been etched. The mask is clamped to the substrate and kept adherent to the surface at every point by magnets placed behind the substrate. The total thickness of the coating is again 8.3 m.
3. Results and discussion The #ip (#op) "eld distribution is called superheating (supercooling) curve. These curves were
measured in a standard way, as described in Ref. [9]. The investigated probes have about 100 cylinders each. The probes have been mounted in the centre of a pickup coil with the cylinder axis perpendicular to the pickup coil axis and immersed directly into a pumped He bath at ¹"1.4 K. Phase transition of the granules from the superconducting to the normal state is induced by sweeping an external magnetic "eld. The "eld was produced by a pair of Helmholtz coils, and was swept from 0 to 45 mT. The size of the signal, which is a damped oscillation, is very sensitive to the orientation of the magnetic "eld with respect to the axis of the cylinders. The maximum signal is expected when the magnetic "eld is perpendicular to the axis of the cylinders, thus parallel to the pickup coil axis. In practice, however, the probe is tilted with respect to the pickup coil axis and the maximum signal is observed at an angle between the applied "eld and the pickup coil axis. With our experimental apparatus it is not possible to establish the angle between the magnetic "eld and the axis of the cylinders with an accuracy higher than one degree. Thus, it is quite di$cult to "nd the right position to reach the maximum e$ciency E, i.e. the number of #ips observed divided by the total number of cylinders of a probe. The superconducting behaviour of the cylinders does not depend on the substrate used. The cylinders produced with the "rst procedure neither #ip nor #op. Measurements performed by Pozzi [11] in Bern show that metastability is strongly reduced and sometimes completely suppressed by the corrosion of acids on the Sn granules. Only in the case of weak acids, such as formic acid, metastability is still observed. Acid corrosion acts with di!erent velocities on the di!erent crystallographic planes [12]. A modi"cation of the crystalline structure may be responsible for the loss of metastability. The cylinders produced with the second procedure are metastable. Fig. 1 shows the superheating and the supercooling curves of a probe made by about 200 cylinders with 80 m diameter on a glass substrate which have been measured at +103 (a, b) and at +93 (c, d). There is evidence of the intermediate state occurring at +93 because
S. Casalbuoni et al. / Nuclear Instruments and Methods in Physics Research A 459 (2001) 469}474
471
Fig. 1. Plots of the superheating and the supercooling "elds of the same probe (about 200 cylinders with 80 m diameter on a glass substrate) measured at +103 (a, b) and at +93 (c, d).
(a) The superheating "elds at +9 are lower. A shift is observed from B "29.88 mT at +103 to B "28.34 mT at +93. (b) The e$ciency (e!) at +93 (70%) is lower than the one at +103 (86%). (c) The #ipping time at +93 (1.5 s) is longer than the one at +103 (1.0 s).
Fig. 2 reports the phase diagram for a sample of about 200 cylinders with diameter of the order of 80 m, evaporated onto a glass substrate through a mask. The dashed line is the thermodynamical critical "eld for a sample of bulk Sn. The two continuous lines are the best "ts obtained for superheating and supercooling. The function used to "t the data is
Despite the di$culty in realizing a precise orientation (within at least 13) of the cylinders, encouraging results are obtained. Even with our rough system to orient the cylinders the e$ciency for superheating is '75%. The most important results are shown in Table 1: the probes are characterised by a sharp superheating curve with B/B(5%.
¹ ¹ where, for superheating, the parameters are B(0) and ¹ . The "t of the supercooling data is made by changing only B(0) and using the value of ¹ ob tained for superheating. ¹ is about 0.2 K lower than the critical temperature of bulk tin (3.72 K).
B(¹)"B(0) 1!
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S. Casalbuoni et al. / Nuclear Instruments and Methods in Physics Research A 459 (2001) 469}474
Table 1 Mean "eld values B, spread of the critical "elds B/B, and e$ciency E for each of the probes measured. The angle between the applied "eld and the axis of the pickup coil, , is also quoted Probes on glass 80 m superheating 80 m superheating 80 m supercooling 80 m supercooling 60 m superheating 60 m supercooling 40 m superheating Probes on kapton 80 m superheating 80 m supercooling 60 m superheating 40 m superheating
B (mT)
B/B
E
103
29.88
5%
86%
93
28.34
4%
70%
103
24.72
3%
16%
93
25.13
3%
18%
1953
29.92
5%
84%
1953
25.41
4%
13%
1953
30.43
4%
86%
2003
29.33
4%
88%
2003
22.03
4%
34%
2003
29.27
6%
77%
1703
29.92
4%
76%
By cooling to liquid-helium temperature Sn cylinders do not follow the thermal contraction of the substrate and are under stress conditions. The stress e!ect may be tensile or compressive, depending on the relative thermal contraction of Sn and the substrate. A compressive stress generally decreases ¹ , while a tensile stress increases ¹ . Lock [13] observed for evaporated Sn "lms on a mica glass substrate an increase in ¹ of up to 3.87 K. However, using a distrene foil, which has a much higher expansion coe$cient than Sn, he observed ¹ "3.53 K. Blumberg et al. [14] studied the e!ect of tensile stress on ¹ of evaporated Sn "lms on glass substrates and observed that ¹ increases by 0.23 K. Muench [15], Jennings and Swenson [16], and Wittig [17] studied the e!ect of a compressive stress on bulk Sn samples and observed a decrease of ¹ . Since our Sn cylinders were evaporated on a glass substrate, which has a lower expansion
Fig. 2. Phase diagram of the cylinders sample.
Table 2 Fitted values of B(0) calculated from the superheating and from the supercooling data and of ¹ calculated only from the super heating data
Superheating Supercooling
B(0) (mT)
¹ (K)
35.00$0.33 29.32$0.09
3.54$0.03 3.54
1.2 9.8
coe$cient than Sn, we cannot explain the observed large decrease in ¹ as being due to stress e!ects. In Table 2 the values of the parameters, the errors and the of the "ts are shown. From the measurements of superheating and supercooling the experimental parameter (¹) [23,24] can be deduced
B "0.498 . B No temperature dependence (within the errors) of (¹) is observed. Fig. 3 shows the comparison of (¹) for the cylinders with the values obtained by Feder and MacLachlan [23] on a single Sn sphere of 48 m and with the value obtained by us [25] from the best "ts of the measured B and B of a sample made by about 300 Sn spheres with diameter ranging from 30 to 35 m.
S. Casalbuoni et al. / Nuclear Instruments and Methods in Physics Research A 459 (2001) 469}474
Fig. 3. Obtained values of (¹) for tin cylinders.
Table 3 Values of , the corresponding electrical resistivity , and mean free path l
Cylinders
$
$ ( cm) l $l (m)
0.444$0.003
1.44$0.02
0.06$0.01
Table 3 lists the electrical resistivity calculated from the GorkE ov}Goodman relation [26] together with the best "ts of (¹) ("0.8), " #7.5;10 (1) where "0.087$0.002 [24] is the value of at ¹"¹ for pure Sn, "1092 erg/cm K [27] is the Sommerfeld constant of Sn and is given in cm. Also shown in Table 3 is the mean free path l , which using the free electron model for Sn is given by 1 l " cm. 1.21;10( cm)
(2)
Usually, the residual resistivity of pure polycrystalline tin "lms is &0.1 cm [18]. The high value of "1.44 cm shown by our sample at liquid-
473
helium temperature corresponds to an impurity content in Sn of about a few at% [19]. The e!ect of Sb, In and Zn impurities up to 2 at% on the superconducting transition temperature of Sn crystals has been studied by Burckbuchler et al. [20]. A decrease up to 140 mK for a Zn-doped sample with residual impurity resistivity "1 cm was observed. Smith et al. [24] obtained for a thick Sn foil (&80 m thickness) with an In impurity content of 2.75 at% "0.46, a decrease in ¹ of 100 mK and an electron mean free path l "0.058 m, which is very near to the value com puted for our sample. The observed decrease in ¹ in our Sn "lm cylinders can be due to the 1}2 at% impurity content. Another possibility is that the cylinders contain a few hundred ppm of magnetic impurities, as Mn [21], Cr, Fe or Co [22], which are very e!ective in decreasing ¹ . However, such a low magnetic impurity content does not correspond to the high value of obtained for our sample. It is well known that superconducting properties of Sn "lms depend very critically on the content of residual gases (e.g. N S, O ) when evap orating in vacuum. However, Caswell [18] observed in tin "lms with residual gas content no decrease in ¹ . Some of the samples showed almost no change, others even an increase of ¹ up to 3.89 K. Thus, we believe that the observed decrease in ¹ of the cylinders, is due to nonmagnetic impu rities. The origin of such impurities in our samples is, however, not clear.
4. Conclusions The main result coming from the study of the tin cylinders produced through a mask and arranged in a planar array con"guration is the sharp distribution of their superheating curves B/B(5%. Mass production is in principle possible. Applications to SSG detectors are possible, if a precise orientation ((13) of a large amount of cylinders can be reached. A test experiment of an SSG detector in a 70 MeV neutron beam at Paul Scherrer Institute has shown that energy thresholds down to &1 keV were reached in SSG detectors made of
474
S. Casalbuoni et al. / Nuclear Instruments and Methods in Physics Research A 459 (2001) 469}474
Sn spheres with diameters of 15}20 m [28]. The Sn cylinders of 40 m diameter and 8 m height should then be able, assuming a linear dependence between the volume of a single granule and the energy threshold, to reach energy thresholds of about 0.1 keV.
Acknowledgements This work was supported by the Schweizerischer Nationalfonds zur FoK rderung der wissenschaftlichen Forschung and by the Bernische Stiftung zur FoK rderung der wissenschaftlichen Forschung an der UniversitaK t Bern.
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