X. D. A. Baumans,1 A. Fern´andez-Rodr´ıguez,2N. Mestres,2S. Collienne,1 J. Van de Vondel,3 A. Palau,2 and A. V. Silhanek1
1Experimental Physics of Nanostructured Materials, Q-MAT,
CESAM, Universit´e de Li`ege, B-4000 Sart Tilman, Belgium.
2
Insititut de Ci`encia de Materials de Barcelona, ICMAB-CSIC, Campus UAB, 08193 Bellaterra, Spain
3Laboratory of Solid-State Physics and Magnetism,
KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium (Dated: December 8, 2018)
The current stimulated atomic diffusion in YBa2Cu3O7−δsuperconducting bridges is investigated.
A superconductor to insulator transition can be induced by current controlled electromigration process whereas partial recovery of the superconducting state can be achieved by inverting the polarity of the bias. Interestingly, the temperature dependence of the current density JEM(T ),
above which atomic migration takes place intersects the critical current density Jc(T ) at certain
temperature T∗. Therefore, for T < T∗the superconducting dissipative state cannot be accessed without leading to irreversible modifications of the material properties. This phenomenon could also lead to the local deterioration of high critical temperature superconducting films abruptly penetrated by thermomagnetic instabilities.
Atomic migration is a thermally activated process that can be stimulated by the directional momentum transfer of charge carriers [1]. Typically, this effect is only visible in rather small devices able to sustain sufficiently large current densities without triggering a thermal runaway ending in melting. Electromigration (EM) has been and continues to be a real problem in metallic interconnects in integrated circuits and may also play a role in the premature wearing out of plasmonic metamaterials [2, 3] and spintronic devices requiring high current densitites such as in domain-wall memories [4, 5].
In principle, superconducting nanocircuits are not con-cerned by atomic migration problems chiefly because within the non-dissipative superconducting state there is no net momentum transfer between the carriers (Cooper pairs) and the atomic lattice. Furthermore, in low critical temperature superconductors, the critical current density Jclies well below the current density JEM needed to start
displacing atoms [6].
Interestingly, this scenario may no longer hold for cuprate superconductors. The reason is twofold, on the one hand, the atomic diffusion barrier can be relatively weak for certain atoms like oxygen in YBa2Cu3O7−δ
(YBCO) [7–10], consequently reducing JEM. On the
other hand, these compounds exhibit high superconduct-ing critical current densities. Under these circumstances, when the dissipative state is accessed by applying a cur-rent density J > Jc, the component of the current
car-ried by the quasiparticles can surpass JEM and produce
irreversible damages to the material even at local tem-peratures substantially smaller than the melting point of the compound. This phenomenon seems to have been largely oversighted so far.
Motivated by these thoughts, we explored the temper-ature dependence of the electromigration current density in cuprate superconductors and compare it with their corresponding superconducting critical current density. We observe that for YBCO there is a temperature range
where the critical current density can exceed the current needed to trigger electromigration. As a consequence, within this region, surpassing the critical current density and reaching the dissipative state might lead to severe detrimental consequences on the circuits, such as local change of doping [11], sample deformation [12], or gener-ation of nanogaps [13]. This phenomenon could become visible in the abrupt penetration of flux due to thermo-magnetic instabilities as recently reported in Ref. [14] and limits the lifetime of devices based on the supercon-ducting dissipative state such as single photon detectors [15].
The investigated superconducting samples are thin films patterned in a narrow constriction shape. A rep-resentative image of a YBCO constriction is shown in Fig.1(a). The YBCO films have a thickness of 100 nm and were grown by chemical solution deposition[16] on LaAlO3 single crystal substrate. Square 300 µm × 300
µm Ag electrodes with 200 nm of thickness were sput-tered and annealed by heating in an oxygen environ-ment in order to reduce the contact resistance. Trans-port bridges of 1-2 µm width and 2-3 µm length were patterned with a 4-point geometry by photolithography followed by ion-beam etching. More than 10 samples with sharp superconducting transitions at Tc = 90 K,
were analyzed in this work.
In order to induce the electromigration process, we ramp up the voltage while simultaneously monitoring the change in conductance dG/dt. A home-made soft-ware controls the bias voltage to keep dG/dt in a pre-set range. Details of the controlled feedback loop have been presented in Ref.[17]. A typical resistance-current curve, R(I), obtained at T = 110 K > Tc is shown in
Fig.1(b). At low drives, R(I) exhibits a nearly parabolic increase mainly due to heating effects[18]. At about 12 mA, corresponding to a current density J ≈ 7.8 MA/cm2,
a change of sign in the slope indicates that electromigra-tion has been launched, as suggested by the fact that
YBCO LaAlO3 V + V -I -I + 2 μm R ( Ω ) 10−1 100 101 102 103 T (K) 0 20 40 60 80 100 (a) Virgin EM1 EM2 EM3 EM4 EM5 (c) (b) 5 10 0 150 100 R ( Ω ) I (mA) 50
FIG. 1. (a) Scanning electron microscopy image of a YBCO constriction. Electromigration takes place in between volt-age constants where the current density reaches its maximum value. (b) Evolution of the constriction resistance as a func-tion of the feedback controlled current through the device during the electromigration run at 110 K. (c) Sample resis-tance versus temperature obtained at low drives (1 µA) after a series of electromigration (EM) processes. Numbers refer to the chronological order and the arrows indicate the current direction during electromigration.
less and less current is needed to increase the resistance. In order to investigate the effect of electromigration on the electrical properties of the YBCO, we performed sev-eral electromigration runs in the very same sample and measure the R(T ) characteristics in between consecutive runs. The results presented in Fig.1(c) show a systematic decrease of Tc and an increase of the normal state
resis-tance after electromigration. The fact that the critical temperature Tc of YBCO is related to the oxygen
dop-ing level[19, 20] suggests that the observed modification after electromigration can be associated to a selective electromigration process mainly leading to the displace-ment of oxygen atoms and hence to a local change of doping[10, 11, 21]. Note that the EM takes place only at the isthmus of the structure where current crowding is maximum. In other words, part of the structure in between the voltage contacts remains unchanged. This naturally explains the two steps observed in EM2. Even-tually, for high enough normal state resistance, a R(T ) response characteristic of an insulating-like state is ob-served (curve EM3). By reversing the polarity of the bias current it is possible to partially heal the constric-tion as evidenced by a reducconstric-tion of the normal state resis-tance and the reappearance of a superconducting tran-sition (curve EM4). This initial healing is followed by a deterioration of the superconducting properties and a lowering of the normal state resistance, as shown by the curve EM5. Further electromigration leads to simultane-ous degradation of both the superconducting and normal state properties of the bridges. Note that at intermedi-ate electromigration stages the sample resistance remains finite at low temperatures and exhibits a very broad tran-sition as temperature increases. This observation leads us to conclude that the electromigration process induced a pronounced gradient in the oxygen concentration which results from the variation of current density associated to
the bridge geometry.
FIG. 2. Inset: Schematic representation of current pulses of dwell time δt = 1 ms and separation ∆t = 10 s, used to mea-sure Rminand Rmax. Main panel: Representative Rmin(blue
points) and Rmax(red points) as a function of Imaxfor YBCO
at 300 K. The criterion used to determine IEM is indicated.
Region I corresponds to negligible heating effects. In region II heating effects are important although without inducing any damage in the bridge. Deterioration of the sample develops in region III.
Determining the electromigration current density JEM
based on dc drive experiments, as the one shown in Fig.1(b), is inherently inaccurate due to difficulty to sep-arate resistance changes originating as consequence of the electromigration process from those simply associ-ated to the resistance thermal coefficient. In order to overcome this technical problem, it is convenient to re-sort to pulsed current measurements where the sample resistance is monitored in between high current pulses and hence under negligible heating effects. In this case, the sample is fed with a train of pulses of δt =1 ms width, constant low value (bias) Imin= 100 µA and linearly
in-creasing high value Imax as schematically shown in the
inset of Fig.2. Consecutive pulses are separated by a long time interval, ∆t =10 s, in order to ensure thermalization of the sample to the bath temperature after each pulse. It is worth noting that the width of the pulse is much larger that the time needed for achieving a thermal sta-tionary state (∼ ns) but substantially shorter than the time evolution of the material-dependent electromigra-tion process (∼ 1 s) [12]. The sample resistance reading takes place near the end of the flat top of the pulse, be-fore the falling edge (Rmax) and in between two
consec-utive pulses (Rmin). The train of pulses is stopped once
the resistance Rmin has increased by 1 %. The main
panel of Fig.2 shows the resulting Rmin and Rmax as a
function of Imax for a typical measurement in a YBCO
microbridge. A similar measurement protocol has been adopted by Wu et al.[22] Three different regimes can be identified. For low Imax (region I) the sample resistance
does not depend on the intensity of the applied current, i.e. Rmax = Rmin. At intermediate Imax (region II),
Rmax > Rmin as consequence of Joule heating and a
non-zero resistance temperature coefficient α = dR/dT . By further increasing the applied current above a well de-fined threshold value IEM, Rminstarts to increase due to
the current-induced modifications in the material prop-erties (region III). In the particular case of YBCO, it has been suggested that at I = IEM, oxygen atoms start
to diffuse and therefore a local change of stoichiometry (and doping) is created [7–11, 21]. For even higher cur-rent values, other atoms can be displaced producing a visible damage on the structure.
For determining the superconducting critical current density Jc, voltage-current characteristics are recorded
at several temperatures (Fig.3(a)). Two critical current densities have been defined, (i) Jc1 corresponding to the
onset of dissipation is determined as the current at which a voltage threshold Vc= 50 µV is attained, and (ii) Jc2 is
the current at which a jump to a highly dissipative state is observed (vertical arrows in Fig.3(a)).
Fig.3(b-c) summarize the obtained JEM and Jc as a
function of the bath temperature Tbath. Fig.3(b) shows
the case of Al microbridges where JEM Jcfor all
tem-peratures and therefore electromigration does not repre-sent a major concern. Similar behavior is observed in La2−xCexCuO4 (not shown) where the electromigration
current at 50 K (13 MA/cm2)[11] already exceeds the maximum critical current density at zero Kelvin Jc ≈
0.02 MA/cm2[23]. Fig.3(c) shows that a different trend
is observed in YBCO. Indeed, it can be seen that the two lines JEM(Tbath) and Jc2(Tbath) intersect at T∗≈ 75
K. For temperatures T∗ < T
bath < Tc, it is possible to
access the normal state by applying sufficiently high cur-rents and without producing any damage to the sample. However, for Tbath < T∗, reaching the normal state can
be done at expenses of irreversibly modifying the proper-ties of the sample. In our case, reaching the normal state for Tbath < T∗ leads to total destruction of the sample if
no control feedback loop is implemented.
It should be emphasized that for current densities exceeding Jc2, the local temperature at the
constric-tion (Tlocal) can rise substantially above the bath
tem-perature, depending on the heat removal efficiency of the cryostat and the sample specific heat. This in-duced heating will lower JEM for a given bath
tem-perature and drastically enhances the possibility that Jc2(Tbath) > JEM(Tbath). For an infinitely efficient heat
sink, Tbath= Tlocal, the maximum possible
electromigra-tion current will be obtained. In order to quantify how this will affect T∗, it is important to determine a direct re-lation between the local temperature of the constriction and the current density at the onset of EM. Tlocal can
be determined through the measured Rmax at IEM and
using the sample resistance as a thermometer. This pro-cedure has been applied to two experimental datapoints and the estimated JEM(Tlocal) along with a linear
ex-trapolation to low temperatures is indicated in Fig.3(c)
FIG. 3. (a) Current-voltage characteristics at several temper-atures used to determine the onset of dissipation, Jc1, and the
current Jc2 at which an abrupt jump in voltage is observed.
Superconducting critical current densities and electromigra-tion current density JEM for Al (b) and YBCO (c)
constric-tions, as a function of the bath temperature. The JEM(Tbath)
dependence obtained in a closed-cycle cryostation and thus reduced by Joule heating effects, is indicated with symbols. Different symbols corresponding to different samples. A sub-stantial shift of the electromigration current up to JEMM AX is
expected if heating effects are negligible, as shown by the two experimental black squares and the extrapolated dotted line.
as JEMM AX. From this analysis, one may conclude that the intersection temperature T∗ can be shifted to lower values by improving the cooling power of the cryostat. However, it should be pointed out that a better cooling power is accompanied by an increase of Jc2(Tbath), which
in turn tends to rise T∗. In the present work, the
inves-tigation has been perfomed in a Montana closed-cycle cryostat, with the sample mounted on a cold finger with a relatively poor cooling power (∼ 0.1-1 W). It would be interesting to see if by immerging the sample in liquid nitrogen, T∗ is further reduced thus extending the
tem-perature range where the normal state can be accessed without any harm. This is a highly non-trivial problem since the system can exhibit electro-thermal instabilities,
which can cause local current and temperature redistri-bution effects as discussed in Ref.[24].
To summarize, we have presented a comparative analy-sis of the temperature dependence of the electromigration current density for Al, LCCO, and YBCO microbridges. We show that for YBCO, there is a temperature range where the superconducting critical current can exceed the extrapolated electromigration current. Within this regime, accessing the dissipative state can have detrimen-tal consequences to the devices. We propose a possible way to shrink the temperature range where this harm-ful regime takes place by improving the heat evacuation and we estimate the maximum possible gain that one can expect by implementing this strategy. Possible alterna-tive approaches are (i) shunting the YBCO sample with a metallic layer deposited on top, and (ii) avoid the ther-mal runway using a feedback loop with reaction time on the order of the characteristic time scale of the heat con-duction equation, t ∼ (L/2)2ρC/κ, where L is the length
of the wire, C is its specific heat, ρ its density, and κ its thermal conductivity. This time scale can span from 10 ns to 10 µs. It would be interesting to extend this
study to Fe-based superconductors and other technolog-ically relevant superconductors such as NbN, Nb3Sn, or
MgB2. A question that deserves more experimental and
theoretical work is the possibility to achieve electromi-gration in the dissipative superconducting state.
Acknowledgments The authors acknowledge the fi-nancial support form the Fonds de la Recherche Sci-entifique - FNRS, Spanish Ministry of Economy and Competitiveness through the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2015-0496), CONSOLIDER Excellence Network (MAT2015-68994-REDC), COACHSUPENERGY project (MAT2014-51778-C2-1-R), co-financed by the European Regional Development Fund, the Research Foundation - Flanders (FWO-Vlaanderen), the COST programme NanoCoHy-bri (CA 16218), and from the Catalan Government with 2017 SGR 1519. A.F.-R. thank Spanish Ministry of Econ-omy for his FPI Spanish grant (BES-2016-077310). The work of A.V. S. is partially supported by CDR of the F.R.S.-FNRS.
asilhanek@uliege.be
[1] J. R. Loyd, Semicond. Sci. Technol. 12,1177 (1997). [2] S. P. Gurunarayanan, N. Verellen, V. S. Zharinov, F. J.
Shirley, V. V. Moshchalkov, M. Heyns, J. Van de Von-del, I. P. Radu, and P. Van Dorpe, Nano Lett. 17, 7433 (2017).
[3] V. K. Valev, D. Denkova, X. Zheng, A. I. Kuznetsov, C. Reinhardt, B. N. Chichkov, G. Tsutsumanova, E. J. Osley, V. Petkov, B. De Clercq, A. V. Silhanek, Y. Je-yaram, V. Volskiy, P. A. Warburton, G. A.E. Vanden-bosch, S. Russev, O. A. Aktsipetrov, M. Ameloot, V. V. Moshchalkov, and Th. Verbiest, Advanced Materials 24, OP29 (2012).
[4] S. Parkin, M. Hayashi, and L. Thomas, Science 320, 190 (2008).
[5] C.-Y. You, I. M. Sung, and B.-K. Joe, Appl. Phys. Lett. 89, 222513 (2006).
[6] D. Staudt and R. Hoffmann-Vogel, J. Phys. D: Appl. Phys. 50, 185301 (2017).
[7] K. Govinda Rajan, P. Parameswaran, J. Janaki, and T. S. Radhakrishnan, J. Phys. D: Appl. Phys. 23, 694 (1990).
[8] S. Vitta, M. A. Stan, J. D. Warner, and S. A. Alterovitz, Appl. Phys. Lett. 58, 759 (1991).
[9] G. N. Mikhailova, A. M. Prokhorov, A. V. Troitskii, and L. Yu. Shchurova, Inorganic Materials 36, 807 (2000). [10] B. H. Moeckly, D. K. Lathrop, and R. A. Buhrman, Phys.
Rev. B 47, 400 (1993); B. H. Moeckly, R. A. Buhrman, and P. E. Sulewski, Appl. Phys. Lett. 64, 1427 (1994). [11] X. D. A. Baumans, J. Lombardo, J. Brisbois, G. Shaw,
V. S. Zharinov, G. He, H. Yu, J. Yuan, B. Zhu, K. Jin, R. B. G. Kramer, J. Van de Vondel and A. V. Silhanek, Small 13, 1700384 (2017).
[12] J. Lombardo, Z. L. Jelic, X. D. A. Baumans, J. E. Scheerder, J. P. Nacenta, V. V. Moshchalkov, J. Van de Vondel, R. B. G. Kramer, M. V. Milosevic and A. V.
Silhanek, Nanoscale 10, 1987 (2018).
[13] G. Esen and M. S. Fuhrer, Appl. Phys. Lett. 87, 263101 (2005); D. R. Strachan, D. E. Smith, D. E. Johnston, T.-H. Park, M. J. Therien, D. A. Bonnell, and A. T. Johnson, Appl. Phys. Lett. 86, 043109 (2005); M. L. Trouwborst, S. J. v. d. Molen, B. J. v. Wees, J. Appl. Phys. 99, 114316 (2006).
[14] M. Baziljevich, E. Baruch-El, T. H. Johansen, and Y. Yeshurun, Appl. Phys. Lett. 105, 012602 (2014). [15] A. J. Kerman, E. A. Dauler, J. K. W. Yang, K. M.
Ros-fjord, V. Anant, K. K. Berggren, G. N. Goltsman, and B. M. Voronov, Appl. Phys. Lett. 90, 101110 (2007). [16] X. Obradors, T. Puig, S. Ricart, M. Coll, J. Gazquez,
A. Palau, and X Granados, Supercond. Sci. Technol. 25, 123001 (2012).
[17] V. S. Zharinov, X. D.A. Baumans, A. V. Silhanek, E. Janssens, and J. Van de Vondel, Rev. Sci. Instrum. 89, 043904 (2018).
[18] X. D. A. Baumans, D. Cerbu, O.-A. Adami, V. S. Zhari-nov, N. Verellen, G. Papari, J. E. Scheerder, G. Zhang, V. V. Moshchalkov, A. V. Silhanek, and J. Van de Vondel, Nat. Commun. 7, 10560 (2016).
[19] B. Wuyts, V. V. Moshchalkov, and Y. Bruynseraede, Phys. Rev. B 53, 9418 (1996).
[20] Kouichi Semba and Azusa Matsuda, Phys. Rev. Lett. 86, 496 (2001).
[21] A. Palau, A. Fernandez-Rodriguez, J. C. Gonzalez-Rosillo, X. Granados, M. Coll, B. Bozzo, R. Ortega-Hernandez, J. Sune, N. Mestres, X. Obradors, and T. Puig, ACS Appl. Mater. Interfaces 10, 30522 (2018). [22] Zheng Ming Wu, M. Steinacher, R. Huber, M. Calame,
S. J. van der Molen, and C. Schnenberger, Appl. Phys. Lett. 91, 053118 (2007).
[23] K. Jin, P. Bach, X. H. Zhang, U. Grupel, E. Zohar, I. Diamant, Y. Dagan, S. Smadici, P. Abbamonte, and R.
L. Greene Phys. Rev. B 83, 060511(R) (2011). [24] A. V. Gurevich and R. G. Mints, Rev. Mod. Phys. 59, 941 (1987).
