Electromigration in the dissipative state of high temperature superconducting bridges

X. D. A. Baumans,1 A. Fernandez-Rodrıguez,2 N. Mestres,2 S. Collienne,1 J. Van de Vondel,3 A. Palau,2 and

A. V. Silhanek1

1Experimental Physics of Nanostructured Materials, Q-MAT,CESAM, Universite de Liege, B-4000 Sart Tilman, Belgium.

2Insititut de Ciencia de Materials de Barcelona, ICMAB-CSIC, Campus UAB, 08193 Bellaterra, Spain3Laboratory of Solid-State Physics and Magnetism,

KU Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium(Dated: December 8, 2018)

The current stimulated atomic diffusion in YBa2Cu3O7−δ superconducting bridges is investigated.A superconductor to insulator transition can be induced by current controlled electromigrationprocess whereas partial recovery of the superconducting state can be achieved by inverting thepolarity 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 certaintemperature T ∗. Therefore, for T < T ∗ the superconducting dissipative state cannot be accessedwithout leading to irreversible modifications of the material properties. This phenomenon could alsolead to the local deterioration of high critical temperature superconducting films abruptly penetratedby thermomagnetic instabilities.

Atomic migration is a thermally activated process thatcan be stimulated by the directional momentum transferof charge carriers [1]. Typically, this effect is only visiblein rather small devices able to sustain sufficiently largecurrent densities without triggering a thermal runawayending in melting. Electromigration (EM) has been andcontinues to be a real problem in metallic interconnectsin integrated circuits and may also play a role in thepremature wearing out of plasmonic metamaterials [2, 3]and spintronic devices requiring high current densititessuch as in domain-wall memories [4, 5].

In principle, superconducting nanocircuits are not con-cerned by atomic migration problems chiefly becausewithin the non-dissipative superconducting state there isno net momentum transfer between the carriers (Cooperpairs) and the atomic lattice. Furthermore, in low criticaltemperature superconductors, the critical current densityJc lies well below the current density JEM needed to startdisplacing atoms [6].

Interestingly, this scenario may no longer hold forcuprate superconductors. The reason is twofold, on theone hand, the atomic diffusion barrier can be relativelyweak for certain atoms like oxygen in YBa2Cu3O7−δ(YBCO) [7–10], consequently reducing JEM . On theother 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 produceirreversible damages to the material even at local tem-peratures substantially smaller than the melting point ofthe compound. This phenomenon seems to have beenlargely oversighted so far.

Motivated by these thoughts, we explored the temper-ature dependence of the electromigration current densityin cuprate superconductors and compare it with theircorresponding superconducting critical current density.We observe that for YBCO there is a temperature range

where the critical current density can exceed the currentneeded to trigger electromigration. As a consequence,within this region, surpassing the critical current densityand reaching the dissipative state might lead to severedetrimental consequences on the circuits, such as localchange of doping [11], sample deformation [12], or gener-ation of nanogaps [13]. This phenomenon could becomevisible 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 thinfilms patterned in a narrow constriction shape. A rep-resentative image of a YBCO constriction is shown inFig.1(a). The YBCO films have a thickness of 100 nmand were grown by chemical solution deposition[16] onLaAlO3 single crystal substrate. Square 300 µm × 300µm 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 werepatterned with a 4-point geometry by photolithographyfollowed by ion-beam etching. More than 10 sampleswith sharp superconducting transitions at Tc = 90 K,were analyzed in this work.

In order to induce the electromigration process, weramp up the voltage while simultaneously monitoringthe 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 havebeen presented in Ref.[17]. A typical resistance-currentcurve, R(I), obtained at T = 110 K > Tc is shown inFig.1(b). At low drives, R(I) exhibits a nearly parabolicincrease mainly due to heating effects[18]. At about 12mA, 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

2

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)

VirginEM1

EM2

EM3

EM4

EM5

(c)

(b)

5 100

150

100

R ( Ω

)

I (mA)

50

FIG. 1. (a) Scanning electron microscopy image of a YBCOconstriction. Electromigration takes place in between volt-age constants where the current density reaches its maximumvalue. (b) Evolution of the constriction resistance as a func-tion of the feedback controlled current through the deviceduring the electromigration run at 110 K. (c) Sample resis-tance versus temperature obtained at low drives (1 µA) aftera series of electromigration (EM) processes. Numbers refer tothe chronological order and the arrows indicate the currentdirection during electromigration.

less and less current is needed to increase the resistance.In order to investigate the effect of electromigration onthe electrical properties of the YBCO, we performed sev-eral electromigration runs in the very same sample andmeasure the R(T ) characteristics in between consecutiveruns. The results presented in Fig.1(c) show a systematicdecrease of Tc and an increase of the normal state resis-tance after electromigration. The fact that the criticaltemperature Tc of YBCO is related to the oxygen dop-ing level[19, 20] suggests that the observed modificationafter electromigration can be associated to a selectiveelectromigration process mainly leading to the displace-ment of oxygen atoms and hence to a local change ofdoping[10, 11, 21]. Note that the EM takes place onlyat the isthmus of the structure where current crowdingis maximum. In other words, part of the structure inbetween the voltage contacts remains unchanged. Thisnaturally 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 thebias current it is possible to partially heal the constric-tion as evidenced by a reduction of the normal state resis-tance and the reappearance of a superconducting tran-sition (curve EM4). This initial healing is followed bya deterioration of the superconducting properties and alowering of the normal state resistance, as shown by thecurve EM5. Further electromigration leads to simultane-ous degradation of both the superconducting and normalstate properties of the bridges. Note that at intermedi-ate electromigration stages the sample resistance remainsfinite at low temperatures and exhibits a very broad tran-sition as temperature increases. This observation leadsus to conclude that the electromigration process induceda pronounced gradient in the oxygen concentration whichresults from the variation of current density associated to

the bridge geometry.

FIG. 2. Inset: Schematic representation of current pulses ofdwell time δt = 1 ms and separation ∆t = 10 s, used to mea-sure Rmin and Rmax. Main panel: Representative Rmin (bluepoints) and Rmax (red points) as a function of Imax for YBCOat 300 K. The criterion used to determine IEM is indicated.Region I corresponds to negligible heating effects. In region IIheating effects are important although without inducing anydamage in the bridge. Deterioration of the sample developsin region III.

Determining the electromigration current density JEMbased on dc drive experiments, as the one shown inFig.1(b), is inherently inaccurate due to difficulty to sep-arate resistance changes originating as consequence ofthe electromigration process from those simply associ-ated to the resistance thermal coefficient. In order toovercome this technical problem, it is convenient to re-sort to pulsed current measurements where the sampleresistance is monitored in between high current pulsesand 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 theinset of Fig.2. Consecutive pulses are separated by a longtime interval, ∆t =10 s, in order to ensure thermalizationof the sample to the bath temperature after each pulse.It is worth noting that the width of the pulse is muchlarger that the time needed for achieving a thermal sta-tionary state (∼ ns) but substantially shorter than thetime evolution of the material-dependent electromigra-tion process (∼ 1 s) [12]. The sample resistance readingtakes 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 oncethe resistance Rmin has increased by 1 %. The mainpanel of Fig.2 shows the resulting Rmin and Rmax as afunction of Imax for a typical measurement in a YBCOmicrobridge. A similar measurement protocol has beenadopted by Wu et al.[22] Three different regimes can beidentified. For low Imax (region I) the sample resistance

3

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 anon-zero resistance temperature coefficient α = dR/dT .By further increasing the applied current above a well de-fined threshold value IEM , Rmin starts to increase due tothe current-induced modifications in the material prop-erties (region III). In the particular case of YBCO, ithas been suggested that at I = IEM , oxygen atoms startto 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 avisible damage on the structure.

For determining the superconducting critical currentdensity Jc, voltage-current characteristics are recordedat several temperatures (Fig.3(a)). Two critical currentdensities have been defined, (i) Jc1 corresponding to theonset of dissipation is determined as the current at whicha voltage threshold Vc = 50 µV is attained, and (ii) Jc2 isthe current at which a jump to a highly dissipative stateis observed (vertical arrows in Fig.3(a)).

Fig.3(b-c) summarize the obtained JEM and Jc as afunction of the bath temperature Tbath. Fig.3(b) showsthe case of Al microbridges where JEM � Jc for all tem-peratures and therefore electromigration does not repre-sent a major concern. Similar behavior is observed inLa2−xCexCuO4 (not shown) where the electromigrationcurrent at 50 K (13 MA/cm2)[11] already exceeds themaximum critical current density at zero Kelvin Jc ≈0.02 MA/cm2[23]. Fig.3(c) shows that a different trendis observed in YBCO. Indeed, it can be seen that thetwo lines JEM (Tbath) and Jc2(Tbath) intersect at T ∗ ≈ 75K. For temperatures T ∗ < Tbath < Tc, it is possible toaccess 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 canbe done at expenses of irreversibly modifying the proper-ties of the sample. In our case, reaching the normal statefor Tbath < T ∗ leads to total destruction of the sample ifno control feedback loop is implemented.

It should be emphasized that for current densitiesexceeding Jc2, the local temperature at the constric-tion (Tlocal) can rise substantially above the bath tem-perature, depending on the heat removal efficiency ofthe cryostat and the sample specific heat. This in-duced heating will lower JEM for a given bath tem-perature and drastically enhances the possibility thatJc2(Tbath) > JEM (Tbath). For an infinitely efficient heatsink, Tbath = Tlocal, the maximum possible electromigra-tion current will be obtained. In order to quantify howthis will affect T ∗, it is important to determine a direct re-lation between the local temperature of the constrictionand the current density at the onset of EM. Tlocal canbe determined through the measured Rmax at IEM andusing the sample resistance as a thermometer. This pro-cedure has been applied to two experimental datapointsand 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 thecurrent 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 thusreduced by Joule heating effects, is indicated with symbols.Different symbols corresponding to different samples. A sub-stantial shift of the electromigration current up to JMAX

EM isexpected if heating effects are negligible, as shown by the twoexperimental black squares and the extrapolated dotted line.

as JMAXEM . From this analysis, one may conclude that

the intersection temperature T ∗ can be shifted to lowervalues by improving the cooling power of the cryostat.However, it should be pointed out that a better coolingpower is accompanied by an increase of Jc2(Tbath), whichin turn tends to rise T ∗. In the present work, the inves-tigation has been perfomed in a Montana closed-cyclecryostat, with the sample mounted on a cold finger witha relatively poor cooling power (∼ 0.1-1 W). It would beinteresting to see if by immerging the sample in liquidnitrogen, T ∗ is further reduced thus extending the tem-perature range where the normal state can be accessedwithout any harm. This is a highly non-trivial problemsince the system can exhibit electro-thermal instabilities,

4

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 electromigrationcurrent density for Al, LCCO, and YBCO microbridges.We show that for YBCO, there is a temperature rangewhere the superconducting critical current can exceedthe extrapolated electromigration current. Within thisregime, accessing the dissipative state can have detrimen-tal consequences to the devices. We propose a possibleway to shrink the temperature range where this harm-ful regime takes place by improving the heat evacuationand we estimate the maximum possible gain that one canexpect by implementing this strategy. Possible alterna-tive approaches are (i) shunting the YBCO sample witha metallic layer deposited on top, and (ii) avoid the ther-mal runway using a feedback loop with reaction time onthe order of the characteristic time scale of the heat con-duction equation, t ∼ (L/2)2ρC/κ, where L is the lengthof the wire, C is its specific heat, ρ its density, and κits thermal conductivity. This time scale can span from10 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, orMgB2. A question that deserves more experimental andtheoretical 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 andCompetitiveness through the Severo Ochoa Programmefor 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 RegionalDevelopment Fund, the Research Foundation - Flanders(FWO-Vlaanderen), the COST programme NanoCoHy-bri (CA 16218), and from the Catalan Government with2017 SGR 1519. A.F.-R. thank Spanish Ministry of Econ-omy for his FPI Spanish grant (BES-2016-077310). Thework of A.V. S. is partially supported by CDR of theF.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, andT. 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, andL. 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 deVondel, 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, andB. 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.

5

L. Greene Phys. Rev. B 83, 060511(R) (2011). [24] A. V. Gurevich and R. G. Mints, Rev. Mod. Phys. 59,941 (1987).

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)

VirginEM1

EM2

EM3

EM4

EM5

(c)

(b)

5 100

150

100

R ( Ω

)

I (mA)

50

http://dx.doi.org/10.1063/1.5063797

http://dx.doi.org/10.1063/1.5063797