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176 R. GROSS AND A. MARX Chapter 4washerspiralinputcoilSiO 2insulationlayerJosephsonjunctionsNb baseelectrodeSiO 2500 µmJosephsonjunctionsIPb topelectrodeshuntresistorFigure 4.11: Sketch of a Nb/Pb dc-SQUID using a square washer geometry and a planar spiral input coil. Thejunction area is shown on an enlarged scale on the right. Also shown is an optical micrograph of a washer-typePb/Nb dc-SQUID (by courtesy of J. Clarke).on a washer structure is still a challenge for high-T c SQUIDs. 35,36 Therefore, often so-called flip-chipstructures have been applied where the input coil is fabricated on a separate chip and then flip-chippedon the washer. 37In order to avoid complicated multilayer structures it is also common to use directly coupled high-T c dc-SQUIDs. Here, the SQUID loop is directly coupled to a parallel loop that acts as a signal pick-up loop.The big advantage of such directly coupled SQUIDs is the fact that only a single superconducting layer isrequired that can be grown with high quality on a single or bi-crystalline substrate. A schematic drawingof such a SQUID can be found in Fig. 4.22). For such directly coupled dc-SQUIDs field sensitivitiesdown to 20 fT/ √ Hz have been obtained in the white noise regime at 77 K. 384.1.5 Read-Out SchemesThe Flux-Locked Loop OperationThe 〈V 〉(Φ ext ) curves of the dc-SQUID are nonlinear. Therefore, a linear relation between an input signaland the output voltage is obtained only in the small signal limit. This problem can be solved by usingthe SQUID in a feedback circuit as a null-detector for magnetic flux. 39 One simply applies an oscillatingmagnetic flux with a peak-to-peak amplitude of about Φ 0 /2 and a frequency f mod in the 100 kHz regimeas shown in Fig. 4.12. If the quasistatic flux is exactly nΦ 0 , the resulting ac voltage is a rectified version35 J.W.M. Hilgenkamp, G.C.S. Brons, J.G. Soldevilla, R.P. Ijsselstein, J. Flokstra, H. Rogalla, Appl. Phys. Lett. 64, 3497-3499 (1994).36 B. David, D. Grundler, J.P. Krumme, O. Doessel, IEEE Trans. Appl. Supercond. AS-5, 2935-2938 (1995).37 P.A. Nilsson, Z.G. Ivanov, E.A. Stephantsov, H.K. Hemmes, J.W.M. Hilgenkamp, J. Flokstra, Inst. Phys. Conf. Ser. 148,1537-1540 (1995), D. Dew-Highes ed., Institute of Physics, Bristol.38 D. Kölle, A.H. Micklich, F. Ludwig, E. Dantsker, D.T. Nemeth, J. Clarke, Appl. Phys. Lett. 63, 2271-2273 (1993).39 J. Clarke, W.M. Goubau, M.B. Ketchen, J. Low. Temp. Phys. 25, 99 (1976).© Walther-Meißner-Institut