IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 25, NO. 3, JUNE 2015 7501004 Trapping Flux Avalanches in Nb Films by Circular Stop-Holes of Different Size D. Carmo, F. Colauto, A. M. H. de Andrade, A. A. M. Oliveira, W. A. Ortiz, and T. H. Johansen Abstract—Dendritic flux avalanches triggered by thermomag- netic instabilities in Nb superconducting films have been limited by inclusion of circular holes of different diameters produced by opti- cal lithography. We have observed a compromise between dendrite and hole sizes, for which avalanches are effectively arrested. For holes much smaller than the dendrites, only individual branches are stopped. Large holes are not a good solution, since they change the film geometry. A noteworthy trapping is observed at the holes with diameter between the width of an individual branch and the size of a whole dendrite. The present work shows the trend to optimize stop-holes for limiting thermomagnetic avalanches in superconducting films. Index Terms—Avalanche, film, niobium, stop-hole, thermomag- netic instability. I. I NTRODUCTION S TABLE electromagnetic behavior is crucial for proper functioning of superconducting devices, including those based on thin films. However, it has been found experimentally that a large number of type-II superconducting films, e.g., Nb [1], MgB 2 [2], Pb [3], Nb 3 Sn [4], YNi 2 B 2 C [5], NbN [6], a-MoGe [7], a-MoSi [8], and recently also YBa 2 Cu 3 O x [9], become unstable when exposed to time-varying moderate mag- netic fields while cooled below a material-dependent threshold temperature [10]–[12]. The onset of unstable behavior brings forth frenetic penetration of magnetic flux, which has been pil- ing up outside of the sample due to induced shielding currents. If the film is patterned with internal non-superconducting areas, i.e. holes, the avalanches can nucleate also from points along these inner edges [9], [13]. When a magnetic field is applied perpendicular to the film plane, vortices arrange in a gradi- ent configuration with highest density at the outer edge and decreasing towards the sample center [14]. When the applied field varies with time the vortices will reconfigure, and at any Manuscript received August 12, 2014; accepted September 28, 2014. Date of publication October 24, 2014; date of current version March 13, 2015. This work was supported in part by the Brazilian funding agencies FAPESP under Contract 2013/16097-3 and CNPq, by the Brazilian program Science without Borders, and by the Norwegian Research Council. D. Carmo, F. Colauto, and W. A. Ortiz are with the Departamento de Física, Universidade Federal de São Carlos, 13565-905 São Carlos-SP, Brazil (e-mail: fcolauto@df.ufscar.br). A. M. H. de Andrade are with the Instituto de Física, Universidade Federal do Rio Grande do Sul, 91501-970 Porto Alegre-RS, Brazil. A. A. M. Oliveira is with the Instituto Federal de Educação, Ciência e Tecnologia de São Paulo—Campus Matão, 15991-502 Matão-SP, Brazil. T. H. Johansen is with the Department of Physics, University of Oslo, 0316 Oslo, Norway. He is also with the Institute for Superconducting and Electronic Materials, University of Wollongong, Wollongong, NSW 2522, Australia. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TASC.2014.2364733 location where a group of vortices moves, a local temperature increase is produced. This causes reduction in the flux pinning, and hence, even more vortices will start moving. Unless this heat production is compensated by thermal diffusion in the film or heat removal into the substrate, a thermomagnetic runaway in the form of an avalanche will take place [15], [16]. During such an event the superconductor can be heated to the flux-flow state, or above its critical temperature, and in extreme cases even above the melting point [9]. Magneto-optical imaging (MOI) experiments [1]–[9] have shown that in macroscopically homogeneous films this insta- bility leads to abrupt penetration of tree-like flux structures, rooted at a point along the edge, and often forming numerous branches. This dendritic shape is of deep concern because such an avalanche brings flux very fast and deep into the superconductor [17], [18], and is also accompanied with very large transient electrical fields [19]. Another characteristic is that the avalanches are unpredictable regarding their starting point and the path each branch will follow. This unpredictability is clearly negative for practical uses, and ways to control the propagation of these branches, which in essence are “electro- magnetic cracks” in the film, need to be developed. It is well known that mechanical cracks in plates can be stopped by drilling holes right in front of their propagation path [20]. Recently, it was shown that circular holes in a superconducting film can have a similar stabilizing effect on thermomagnetic avalanches by liming or even stopping their propagation [21]. With a circular hole one creates a region where the flux propagating in an avalanche can redistribute and relax the magnetic pressure. On the other hand, holes with sharp corners, e.g., squares and triangles, fail to have this avalanche arresting ability because flux piles up in corners and hence provoke secondary instabilities. The effective trapping ability of a circular hole obviously depends on its size relative to that of the flux dendrites. For an extremely small hole the avalanche will hardly be perturbed, whereas a large hole basically changes the film geometry. Hence, one expects there exists an optimal compromise between avalanche and hole sizes, where the im- pact of avalanches is maximally reduced. In this work, we investigate the stabilizing effect of circular holes of various diameters patterned in films of Nb, to explore which size is most efficient in arresting avalanches. We have investigated this by using MOI to observe the flux dynamics. II. MATERIAL AND METHODS Samples of Nb were prepared as films of thickness of 200 nm by magnetron sputtering in a UHV system with base pressure 1051-8223 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.