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2. Experimental details

2.1 Fabrication

Two 2D-arrays were fabricated using standard e-beam technique. The mask layout was created with a CAD program and then transferred to an e-beam lithography machine. A two layer e-beam resist was used with a thick bottom layer and a thin, hard top layer. The bottom layer was 400 nm 10% copolymer (spin: 2000 rpm) baked on a hot plate for 5 min. in 170°C. The top layer was 40 nm 1.8% 350k PMMA (spin: 3000 rpm) baked on a hot plate for 5 min. at 170°C. The exposure dose was 270 µC/cm2. After exposure the chips were developed in a mixture of isopropanol (CH3-CHOH-CH3) and water (H2O) with the ratio 84:3 in an ultrasonic bath for about 1 min. The advantage of this recipe was that both layers were developed in a single stage in a non-toxic developer. However, the development time seemed to be rather sensitive to the ultrasonic bath power. While developing several chips, one at a time, the noise from the ultrasonic bath increased audibly. After that the development time was decreased by half.

A two layer resist was used to create bridges of e-beam resist over the chip surface. During development the bottom layer was developed quicker than the top layer and an undercut was created under the edge of the top layer. From an SEM image the undercut to was estimated to be approximately 130 nm at the chip surface. This undercut was enough to create bridges in the top layer where the distance between exposed areas was smallest. After development, Al was evaporated from two angles. During evaporation the pressure was about 10-4 Pa (10-6 mbar). A 200Å layer was evaporated from an angle of 10° from perpendicular. Oxygen was then let into the evaporation chamber to a pressure of about 2 Pa (0.02 mbar). The first chip, H7#43, was oxidized for 5 min. and the second chip, H9#44, for 2 min. Then the oxygen was pumped out again and a second layer of Al, 350Å, was evaporated from an angle of -10°. This angle evaporation procedure was developed by Dolan8 (figure 1). The resulting normal state resistance per junction was 33 k and 7.6 k for the two chips respectively.

2.2 Chip layout

The measured chips contained 2D tunnel junction arrays with 168x168 junctions. At the top and bottom the array was connected to a long solid bar extending along the entire side. At the sides were four Hall probes on each side at positions 1/6, 1/3, 1/2 and 5/6 of the distance from the top to the bottom bar. These Hall probes were connected through three tunnel junctions to the array. The size of the tunnel junctions were 100x200 nm. There were also tunnel junctions on the islands in series with the junctions between the islands, which were approximately 25 times larger than the small junctions and being strongly Josephson coupled they could generally be ignored. Figures 2 and 3 show SEM pictures of the entire array and close-ups of individual islands, a Hall probe and the top solid bar. Because the e-beam machine gives some stray exposure around the focus point, some unconnected islands were created near the left and right edges of the array to make sure that the exposure dose would be the same at the edge and inside the array. These are clearly seen as the bright areas at the left and right sides of the array.


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