- Email: [email protected]
Resistive transitions of superconducting thin films in strong electric fields
Volume 47A, number 3
PHYSICS LETTERS
25 March 1974
RESISTIVE TRANSITIONS OF SUPERCONDUCTING THIN FILMS IN S T R O N G E L E C T R I C F I E L D S * P. MONCEAU University o f Southern Califorma, Los Angeles, California 90007, USA and Centre de Recherches sur les Tres Basses Temperatures (C.N.R S.), Cedex 166, 38042 - Grenoble, France
Received 11 Feburary 1974 We report dtscontinuous current-induced transitions to the normal state of superconducting thin films in the mixed state. The results obtained are in qualitative agreement with the recent theory of Thompson and Hu of dynamic instabilities of vortices. It is well known that when a current higher than a critical current is applied, the vortex pattern of a thin superconducting f'dm in the mixed state is moved by the Lorentz force and that a voltage g = - o X B is generated. Very recently Thompson and Hu [ 1] showed that except in the vicinity of He2 there is a maximum velocity for the vortex structure above which the vortices becomes unstables and above which a negative differential conductivity region may be established. This instability can be observed by a sharp transition to the normal state in the voltage-current characteristics of the film. However this transition has to be distinguish from the thermally imtiated instabilities which are usually encountered in critical current measurements. The calculations of Thompson and Hu were made for superconductors with magnetic impurities such that their critical temperature T c was much smaller than the To0 of the matrix. However their theory must be qualitatively correct in more general cases. There we present measurements of resistive transitions on aluminium and erbium-dopes aluminium films, thin enough to be type II superconductors [2]. The films were evaporated on nitrogen-cooled substrates from a stranded tungsten wire in a vacuum better then 10 -6 torr. A SiO layer was deposited just after the evaporation to avoid oxydation. The films were warmed up to room temperature before measurements. The aluminium and 0.3 at. % erbium thin film was made as described by Craven et al. [3]. For this film we estimate that the critical temperature * Supported by the National Science Foundation.
Table 1 Pn(Un cm)
R o(lZ)
d(A)
Tc(K)
AI
25
9.6
260
1.705
A1with 0.3% at. Er
15.5
6
260
1.658
was 0.15 K below that for a pure aluminium film having the same resistivity ratio. This depression is of the same order as that found in [3]. The dimensions of the films are typically 6 mm X, 0.6 mm and 250 A thick and the edges were cut with a sharp razor blade. The characteristics of the film are shown in table 1. We have measured the transition curve in zero magnetic field as a function of temperature. The difference in temperature between R [ R n = 0.90 and R [ R n = 0.10 is 0.014 K for the aluminium ftlm and 0.044 K for the erbium-doped aluminium film. After a slight decrease in resistance when the temperature was reduced from well above Tc these films showed a sharp peak in resistance just before the transition to the the superconducting state. The amplitude of this peak for the aluminium film was 1.4 R n (R n the normal resistance of the film for T >> To). Such peaks have been reported before [ 4 - 6 ] but never with such a large amphtude. It has been suggested that this increase in resistance can be related to the surface grain structure of the film [4]. Typical 1I(/) characteristics for the erbinm-doped aluminium film are shown in fig. 1. The current was delivered by a constant-current source and swept slowly. Discontinuities similar to those observed in 193
Volume 4lA, number 3 Al . a3 v.
PHYSICS LETTERS
01
Er t =0755
Fig. 1 Voltage-current characteristics of the erbmm-doped alummmm thm film for dtfferent values of B/H,* Power dissipated in A 105 pW, m B 78 PW
low magnetic fields have been reported [7-9] but for much higher current densities. We think that the transition curves are isothermal because we used (a) quartz whose thermal conductivity at low temperatures is much better than of glass as substrate, (b) thin films thus reducing current necessary for the measurements, (c) a superconductor with re below the superfluid temperature of helium and (d) because the power dissipated in the film at the beginning of the discontinuity decreases when H is reduced (for instance m fig. 1 the power dissipated in A is 105 /JW and 78 nW in B). We can summarize the results obtamed as follows: 1) in the flux flow regime we observe that the V(1) curves have no linear region. Horn and Parks [lo] showed that thus non-linearity for low currentdensities could not be explained by pinning, the selffield arising from the transport current or the heating of the sample. This effect seems to be intrinsic to thm films. 2) at low reduced temperatures, the flux flow reststivity pf = dV/dl does not follow the empirical Kim’rule. pr/p,, = B/H,2 [ 111. We find pr/pn @ B/H,, m agreement with refs. [4] and [lo] _These results require a careful reexaminatron of the flux-flow concept m this films. 3) Fig. 1 shows a qualitative agreement with the Thompson and Hu theory. At high B/Hc2 the transition curves are smooth as for a second order transition. At low B/H,_, the transitions, which are much steeper for the erbium-doped aluminium film than for the 194
25 March 1974
pure aluminium film, have a step structure. The transition (CD) occurs after a small current variation (AC) beyond the flux-flow state that we cannot explain. It can be seen too that hysteresis is only observed when a discontinuity appears in the V(1) characteristics indicatmg a change m the order of the transition. The calculations of Thompson and Hu are based on the Ginsburg-Landau theory and are only valid near T,. In particular they found for a fixed value of B/H,_2 a (1 - f)3’2 temperature dependence of the instability current. This is the same as that calculated by Bardeen [12] for the critical current in zero magnetic field and which has been observed near T, [ 131. Clearly more measurements m this temperature range should be made. To reveal more fully the V(Z) characteristics voltage-biased measurements are more suitable. The first measurements we have made using this method showed a small negative conductivrty region for low B/Hc2 as predicted by Thompson and Hu but other measurements are needed to clarify this point. This work was carried out during a stay at USC. and it is a pleasure for me to thank the staff of the Physics Department for their kind hospitality. I am particulary grateful to M. Daybell, C.R. Hu, Y.B. Kim, R.S. Thompson and T.I. Smith for fruitful discussions.
References [l] R.S. Thompson and C.R. Hu, Phys. Rev. Lett. 31 (1973) 883 [2] M. Tinkjsam, Phys. Rev. 129 (1963) 2413. (31 R A. Craven, GA. Thomas and R.D. Parks, Phys Rev. B4 (1971) 2185. [4] T. Ogushi, Y. Onodera and Y. Shibuya, Phys. Lett 30A (1969) 406. [S] A D.C. Grassie and D.B. Green, Phys. Lett. 31A (1970) 135. (61 J S. Escher and D.M. Gmsberg, Phys. Rev. B3 (1971) 735 [7] P. Tholfsen and H. Meissner, Phys. Rev. 185 (1969) 653 [8] T Ogushi and Y. Shibuya, J. of Phys. Sot. (Japan) 32 (1972) 400. 191 T.I. Smith, unpubhshed. [ 101 P.M. Horn and R.D. Parks, Phys. Rev. B4 (1971) 2178 [ 1 l] Y.B. Kim, C.F. Hempstead and A.R. Strnad, Phys Rev. 139 (1965) 1163. [ 12) J. Bardeen, Rev of Mod. Phys 34 (1962) 667. [ 131 J F Mercereau and L.T. Crane, Phys Rev. Lett 9 (1962) 381.
PHYSICS LETTERS
25 March 1974
RESISTIVE TRANSITIONS OF SUPERCONDUCTING THIN FILMS IN S T R O N G E L E C T R I C F I E L D S * P. MONCEAU University o f Southern Califorma, Los Angeles, California 90007, USA and Centre de Recherches sur les Tres Basses Temperatures (C.N.R S.), Cedex 166, 38042 - Grenoble, France
Received 11 Feburary 1974 We report dtscontinuous current-induced transitions to the normal state of superconducting thin films in the mixed state. The results obtained are in qualitative agreement with the recent theory of Thompson and Hu of dynamic instabilities of vortices. It is well known that when a current higher than a critical current is applied, the vortex pattern of a thin superconducting f'dm in the mixed state is moved by the Lorentz force and that a voltage g = - o X B is generated. Very recently Thompson and Hu [ 1] showed that except in the vicinity of He2 there is a maximum velocity for the vortex structure above which the vortices becomes unstables and above which a negative differential conductivity region may be established. This instability can be observed by a sharp transition to the normal state in the voltage-current characteristics of the film. However this transition has to be distinguish from the thermally imtiated instabilities which are usually encountered in critical current measurements. The calculations of Thompson and Hu were made for superconductors with magnetic impurities such that their critical temperature T c was much smaller than the To0 of the matrix. However their theory must be qualitatively correct in more general cases. There we present measurements of resistive transitions on aluminium and erbium-dopes aluminium films, thin enough to be type II superconductors [2]. The films were evaporated on nitrogen-cooled substrates from a stranded tungsten wire in a vacuum better then 10 -6 torr. A SiO layer was deposited just after the evaporation to avoid oxydation. The films were warmed up to room temperature before measurements. The aluminium and 0.3 at. % erbium thin film was made as described by Craven et al. [3]. For this film we estimate that the critical temperature * Supported by the National Science Foundation.
Table 1 Pn(Un cm)
R o(lZ)
d(A)
Tc(K)
AI
25
9.6
260
1.705
A1with 0.3% at. Er
15.5
6
260
1.658
was 0.15 K below that for a pure aluminium film having the same resistivity ratio. This depression is of the same order as that found in [3]. The dimensions of the films are typically 6 mm X, 0.6 mm and 250 A thick and the edges were cut with a sharp razor blade. The characteristics of the film are shown in table 1. We have measured the transition curve in zero magnetic field as a function of temperature. The difference in temperature between R [ R n = 0.90 and R [ R n = 0.10 is 0.014 K for the aluminium ftlm and 0.044 K for the erbium-doped aluminium film. After a slight decrease in resistance when the temperature was reduced from well above Tc these films showed a sharp peak in resistance just before the transition to the the superconducting state. The amplitude of this peak for the aluminium film was 1.4 R n (R n the normal resistance of the film for T >> To). Such peaks have been reported before [ 4 - 6 ] but never with such a large amphtude. It has been suggested that this increase in resistance can be related to the surface grain structure of the film [4]. Typical 1I(/) characteristics for the erbinm-doped aluminium film are shown in fig. 1. The current was delivered by a constant-current source and swept slowly. Discontinuities similar to those observed in 193
Volume 4lA, number 3 Al . a3 v.
PHYSICS LETTERS
01
Er t =0755
Fig. 1 Voltage-current characteristics of the erbmm-doped alummmm thm film for dtfferent values of B/H,* Power dissipated in A 105 pW, m B 78 PW
low magnetic fields have been reported [7-9] but for much higher current densities. We think that the transition curves are isothermal because we used (a) quartz whose thermal conductivity at low temperatures is much better than of glass as substrate, (b) thin films thus reducing current necessary for the measurements, (c) a superconductor with re below the superfluid temperature of helium and (d) because the power dissipated in the film at the beginning of the discontinuity decreases when H is reduced (for instance m fig. 1 the power dissipated in A is 105 /JW and 78 nW in B). We can summarize the results obtamed as follows: 1) in the flux flow regime we observe that the V(1) curves have no linear region. Horn and Parks [lo] showed that thus non-linearity for low currentdensities could not be explained by pinning, the selffield arising from the transport current or the heating of the sample. This effect seems to be intrinsic to thm films. 2) at low reduced temperatures, the flux flow reststivity pf = dV/dl does not follow the empirical Kim’rule. pr/p,, = B/H,2 [ 111. We find pr/pn @ B/H,, m agreement with refs. [4] and [lo] _These results require a careful reexaminatron of the flux-flow concept m this films. 3) Fig. 1 shows a qualitative agreement with the Thompson and Hu theory. At high B/Hc2 the transition curves are smooth as for a second order transition. At low B/H,_, the transitions, which are much steeper for the erbium-doped aluminium film than for the 194
25 March 1974
pure aluminium film, have a step structure. The transition (CD) occurs after a small current variation (AC) beyond the flux-flow state that we cannot explain. It can be seen too that hysteresis is only observed when a discontinuity appears in the V(1) characteristics indicatmg a change m the order of the transition. The calculations of Thompson and Hu are based on the Ginsburg-Landau theory and are only valid near T,. In particular they found for a fixed value of B/H,_2 a (1 - f)3’2 temperature dependence of the instability current. This is the same as that calculated by Bardeen [12] for the critical current in zero magnetic field and which has been observed near T, [ 131. Clearly more measurements m this temperature range should be made. To reveal more fully the V(Z) characteristics voltage-biased measurements are more suitable. The first measurements we have made using this method showed a small negative conductivrty region for low B/Hc2 as predicted by Thompson and Hu but other measurements are needed to clarify this point. This work was carried out during a stay at USC. and it is a pleasure for me to thank the staff of the Physics Department for their kind hospitality. I am particulary grateful to M. Daybell, C.R. Hu, Y.B. Kim, R.S. Thompson and T.I. Smith for fruitful discussions.
References [l] R.S. Thompson and C.R. Hu, Phys. Rev. Lett. 31 (1973) 883 [2] M. Tinkjsam, Phys. Rev. 129 (1963) 2413. (31 R A. Craven, GA. Thomas and R.D. Parks, Phys Rev. B4 (1971) 2185. [4] T. Ogushi, Y. Onodera and Y. Shibuya, Phys. Lett 30A (1969) 406. [S] A D.C. Grassie and D.B. Green, Phys. Lett. 31A (1970) 135. (61 J S. Escher and D.M. Gmsberg, Phys. Rev. B3 (1971) 735 [7] P. Tholfsen and H. Meissner, Phys. Rev. 185 (1969) 653 [8] T Ogushi and Y. Shibuya, J. of Phys. Sot. (Japan) 32 (1972) 400. 191 T.I. Smith, unpubhshed. [ 101 P.M. Horn and R.D. Parks, Phys. Rev. B4 (1971) 2178 [ 1 l] Y.B. Kim, C.F. Hempstead and A.R. Strnad, Phys Rev. 139 (1965) 1163. [ 12) J. Bardeen, Rev of Mod. Phys 34 (1962) 667. [ 131 J F Mercereau and L.T. Crane, Phys Rev. Lett 9 (1962) 381.