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Design considerations for arrays of MMCs for X-ray astronomy
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 520 (2004) 407–410
Design considerations for arrays of MMCs for X-ray astronomy C. Enssa,*, A. Fleischmannb, S.R. Bandlerc,d, T.R. Stevensonc,d, G.M. Seidela b
a Department of Physics, Brown University, Box 1843, Providence, RI 02912, USA Kirchhoff-Institut fur . Physik, Universitat . Heidelberg, INF 227, Heidelberg D-69120, Germany c NASA-Goddard Space Flight Center, Code 662, Greenbelt, MD 20771, USA d Department of Astronomy, University of Maryland, College Park, MD 20742, USA
Abstract There are a number of substantially different ways of fabricating arrays of metallic magnetic calorimeters (MMCs). We discuss different designs and readout schemes and comment on the requirements, advantages and disadvantages of specific MMC arrays. In particular, we address the problems of thermal and inductive cross-talk, thermalization times, heat dissipation, layout and suitable SQUID readout techniques. r 2003 Elsevier B.V. All rights reserved. PACS: 07.85.m; 95.55.Aq; 29.46.Vj Keywords: X-ray astronomy; Calorimeters; Arrays
1. Introduction It has been recognized for some time that X-ray astronomy would greatly benefit from the availability of fast, efficient, high-energy resolution detectors fabricated into focal plane arrays containing a large number of pixels. Magnetic calorimeters have now demonstrated 3:4 eV resolution for energies up to 6:5 keV in individual pixels [1]. However, the level of technology development for producing large format MMC arrays with this high resolution is still in its infancy. In this paper we describe various different options for developing MMC arrays. The ideas presented here are based upon the properties of *Corresponding author. E-mail address: Christian [email protected] (C. Enss).
high-resolution MMCs and on what has been learned from the development of arrays using other technologies. However, these considerations are preliminary, and other designs of arrays not considered here may take advantage of the properties of MMCs in a more efficacious manner.
2. Geometries In general we assume that the basic design of an MMC pixel includes a small cylindrical disc of a paramagnetic sensor (Au with B1000 ppm Er), enclosed by a circular pickup loop, on which a much larger area absorber is supported. Other more complicated sensor geometries are possible and may have advantages in certain circumstances
0168-9002/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2003.11.346
ARTICLE IN PRESS 408
C. Enss et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) 407–410
[2]. For instance, the sensor could be in the form of a narrow and thin meander with a thin film pickup loop surrounding the meander, very close to the sensor edge. In this geometry the coupling of the magnetization of the sensor can be considerably higher than for the cylindrical shape. However, the inductance of the pickup loop is larger for the meander. Depending on the read-out scheme, this could be a desirable option. The absorber is likely to be made of bismuth with a thin underlayer of gold to enhance the thermalization of the calorimeter. This absorber should not be physically attached to anything but the sensor so as to avoid the loss of energy, e.g., the transmission of high-energy phonons to the substrate. This results in the so-called ‘‘mushroom’’ geometry with the absorber elevated above substrate on top of the sensor. In an array the thinfilm wiring for the magnetic sensors can be positioned underneath the absorbers between the mushroom stems. If the sensors are cylindrical, a large fraction of the total surface is available for wiring. Some of this area would be lost if meander strips were to be used as sensors. A typical pixel design with a heat capacity of 1012 pJ=K having a 100 ms thermal decay time requires a conductance to the thermal reservoir the order of 10 nW=K: To achieve this value, conduction via electrons is required. Thermalization via phonons is limited by the electron–phonon coupling in gold and by the Kapitza resistance. In fact, thermalization via phonons is sufficiently slow so that a silicon nitrate membrane is likely to be unnecessary. For a calorimeter having a Au volume of 2 104 mm3 the electron–phonon coupling at 50 mK; given by 5V ST 4 ; where SE0:2 109 W=ðK5 m3 Þ is E0:1 nW: The Kaptiza conductance across a Au 50 mm diameter circular interface to a Si substrate at 50 mK is approximately 0:05 nW=K: This is more than 2 orders of magnitude smaller than the conductance required. Metallic strips of the appropriate properties must be used to connect the individual pixels to the thermal reservoir, can be made negligibly small by thermally anchoring the substrate. The use of rigid substrates permits one to consider the possibility of constructing arrays by stacking layers of substrates in a step configuration
with the pixels on the exposed step. While multilayer substrates are less elegant and require accurate mechanical assembly of more components, they do make it easier to bring the large number of thin-film wires out from the array and also make it easier to provide adequate thermal conduction to all parts of the array. MMCs arrays can be constructed using 1 SQUID to read out 2 pixels in loops configured as a gradiometer or in a single loop arrangement with 1 pixel per SQUID. The gradiometric pick-up has the advantage of cancelling out thermal and inductive fluctuations that couple equally into both loops. At the same time, gradiometric loops can be positioned in a way that thermal and inductive cross-talk from adjacent pixels is reduced. In fact using gradiometric pick-up loops it is conceivable that the required level of cross-talk can be achieved without any additional superconducting shielding. For non-gradiometric pickup loops this will not be the case. The use of gradiometric pick-up loops has the additional advantage that the number of electronic channels to read out the array is cut in half. However, the significant disadvantage is that the resolution of an optimal pffiffiffi detector would be reduced by a factor of 2:
3. Coupling schemes In designing an array of MMCs one must address how best to transform the change in magnetization of a sensor into a flux change in the SQUID loop. The tradeoffs and issues regarding the flux coupling for a single pixel and for a large array are different. For single pixel devices the placement of the sensor directly in the SQUID loop is the best solution for most applications, as this produces the maximum coupling. However, fabrication constraints arising from the deposition of magnetic material directly into the SQUID loop, the power dissipation associated with the operation of the SQUIDs in close proximity to the sensors and, in particular, the large number of leads present problems for this design. For arrays, the use of transformer coupling between sensor and SQUID has an advantage in that the two
ARTICLE IN PRESS C. Enss et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) 407–410
components can be physically separated, the sensor array on one substrate and the SQUIDs on another. An obvious drawback of transformer coupled SQUIDs is the reduction of signal size. The SQUID noise level must be sufficiently low that it does not degrade the signal-to-noise ratio when the signal size is reduced. For single pixel operation with a well-coupled flux transformer, the SQUID noise would have to be less than 1:5 pffiffiffiffiffiffi ffi 106 f0 = Hz in order not to contribute to the energy resolution at the 2 eV level. Since SQUIDs with a noise performance lower than this are now achievable, in principle there should be no penalty in using a well-coupled flux transformer. However, when one considers various multiplexing options, the design of the SQUID readout becomes more complex and loss from transformer coupling has consequences in other ways. In the following we discuss two different transformer coupling schemes, a direct flux transformer and a step-up flux transformer. Fig. 1 shows a simplified schematic of these different transformer schemes. In the case of a direct flux transformer the sensor is imbedded in a pick-up coil Lp ; which is part of a superconducting loop containing the input coil Li of the SQUID. For optimal coupling, Li ¼ Lp þ Ll ; the flux transfer function, the ratio of the flux change in the SQUID to that in the
pickup loop, is given by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dFs Ls : ¼ 0:5k dFp Lp þ Ll
409
ð1Þ
The parameter k is the coupling coefficient of the mutual inductance between the ffi SQUID loop and pffiffiffiffiffiffiffiffiffi the input coil, Mis ¼ k Li Ls : Obviously, the inductance of the leads should be made as small as possible. This requires that the flux transformer and the first stage SQUID are placed on the detector chip. Advantages of a direct flux transformer are that the wiring between the pixel is reduced and there is no power dissipation in the vicinity of the sensors. To separate physically the sensor array from the first stage SQUIDs by placing them on different chips requires of use of step-up transformers, Fig. 1b, because of the large inductances of the wirebond leads. The flux transfer function for an optimally designed step-up transformer ðL2 ¼ Li ; L1 ¼ Lp ; Ls oLp Þ is sffiffiffiffiffiffi dFs Ls : ð2Þ E0:35 dFp Lp It is obvious that the coupling factor in this geometry cannot exceed 0.35 and may be closer to 0.2 for practical designs. This significant loss of signal, however, might not limit the obtainable signal-to-noise ratio, if the SQUID noise can be made sufficiently low.
4. Suitable multiplexing schemes
Fig. 1. Coupling schemes for MMCs. (a) Flux transformer. (b) Step-up transformer.
To meet the requirements for a sufficiently low white noise level and a sufficiently high slew rate the readout scheme and amplifier chain of MMC arrays will likely consist of a primary detector SQUID, an amplifier SQUID followed by a series array SQUID as a third stage. In principle, multiplexing can be done in either of these stages. As pointed out by Irwin [3] time division multiplexing without degradation of the signal to noise ratio is only possible if high-frequency noise is filtered out before multiplexing, because in the process of multiplexing it would be shifted to lower frequency bands. If a flux transformer is
ARTICLE IN PRESS 410
C. Enss et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) 407–410
employed, a small resistor in series with the SQUID input coil can be used to provide such a low pass filter. However, given the constraints in terms of inductances and cut-off frequency, the necessary resistor would add an intolerable contribution of Johnson noise. Therefore it is more suitable to perform the multiplexing at later stages for MMCs. After flux to voltage amplification a low pass filter can be employed with insignificant additional Johnson noise. The use of frequency domain multiplexing is also a conceivable scheme for MMC arrays. However, the biggest problem with this technique in connection with MMCs is inductive cross
talk. Without the use of complicated shielding schemes this very like roles out the possibility of frequency domain multiplexing at the first SQUID stage.
References [1] A. Fleischmann, M. Linck, T. Daniyarov, H. Rotzinger, C. Enss, G.M. Seidel, Nucl. Instr. and Meth. A (2004), these Proceedings. [2] A. Fleischmann, C. Enss, G.M. Seidel, Nucl. Instr. and Meth. A (2004), these Proceedings. [3] K.D. Irwin, Physica C 368 (2002) 203.
Nuclear Instruments and Methods in Physics Research A 520 (2004) 407–410
Design considerations for arrays of MMCs for X-ray astronomy C. Enssa,*, A. Fleischmannb, S.R. Bandlerc,d, T.R. Stevensonc,d, G.M. Seidela b
a Department of Physics, Brown University, Box 1843, Providence, RI 02912, USA Kirchhoff-Institut fur . Physik, Universitat . Heidelberg, INF 227, Heidelberg D-69120, Germany c NASA-Goddard Space Flight Center, Code 662, Greenbelt, MD 20771, USA d Department of Astronomy, University of Maryland, College Park, MD 20742, USA
Abstract There are a number of substantially different ways of fabricating arrays of metallic magnetic calorimeters (MMCs). We discuss different designs and readout schemes and comment on the requirements, advantages and disadvantages of specific MMC arrays. In particular, we address the problems of thermal and inductive cross-talk, thermalization times, heat dissipation, layout and suitable SQUID readout techniques. r 2003 Elsevier B.V. All rights reserved. PACS: 07.85.m; 95.55.Aq; 29.46.Vj Keywords: X-ray astronomy; Calorimeters; Arrays
1. Introduction It has been recognized for some time that X-ray astronomy would greatly benefit from the availability of fast, efficient, high-energy resolution detectors fabricated into focal plane arrays containing a large number of pixels. Magnetic calorimeters have now demonstrated 3:4 eV resolution for energies up to 6:5 keV in individual pixels [1]. However, the level of technology development for producing large format MMC arrays with this high resolution is still in its infancy. In this paper we describe various different options for developing MMC arrays. The ideas presented here are based upon the properties of *Corresponding author. E-mail address: Christian [email protected] (C. Enss).
high-resolution MMCs and on what has been learned from the development of arrays using other technologies. However, these considerations are preliminary, and other designs of arrays not considered here may take advantage of the properties of MMCs in a more efficacious manner.
2. Geometries In general we assume that the basic design of an MMC pixel includes a small cylindrical disc of a paramagnetic sensor (Au with B1000 ppm Er), enclosed by a circular pickup loop, on which a much larger area absorber is supported. Other more complicated sensor geometries are possible and may have advantages in certain circumstances
0168-9002/$ - see front matter r 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2003.11.346
ARTICLE IN PRESS 408
C. Enss et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) 407–410
[2]. For instance, the sensor could be in the form of a narrow and thin meander with a thin film pickup loop surrounding the meander, very close to the sensor edge. In this geometry the coupling of the magnetization of the sensor can be considerably higher than for the cylindrical shape. However, the inductance of the pickup loop is larger for the meander. Depending on the read-out scheme, this could be a desirable option. The absorber is likely to be made of bismuth with a thin underlayer of gold to enhance the thermalization of the calorimeter. This absorber should not be physically attached to anything but the sensor so as to avoid the loss of energy, e.g., the transmission of high-energy phonons to the substrate. This results in the so-called ‘‘mushroom’’ geometry with the absorber elevated above substrate on top of the sensor. In an array the thinfilm wiring for the magnetic sensors can be positioned underneath the absorbers between the mushroom stems. If the sensors are cylindrical, a large fraction of the total surface is available for wiring. Some of this area would be lost if meander strips were to be used as sensors. A typical pixel design with a heat capacity of 1012 pJ=K having a 100 ms thermal decay time requires a conductance to the thermal reservoir the order of 10 nW=K: To achieve this value, conduction via electrons is required. Thermalization via phonons is limited by the electron–phonon coupling in gold and by the Kapitza resistance. In fact, thermalization via phonons is sufficiently slow so that a silicon nitrate membrane is likely to be unnecessary. For a calorimeter having a Au volume of 2 104 mm3 the electron–phonon coupling at 50 mK; given by 5V ST 4 ; where SE0:2 109 W=ðK5 m3 Þ is E0:1 nW: The Kaptiza conductance across a Au 50 mm diameter circular interface to a Si substrate at 50 mK is approximately 0:05 nW=K: This is more than 2 orders of magnitude smaller than the conductance required. Metallic strips of the appropriate properties must be used to connect the individual pixels to the thermal reservoir, can be made negligibly small by thermally anchoring the substrate. The use of rigid substrates permits one to consider the possibility of constructing arrays by stacking layers of substrates in a step configuration
with the pixels on the exposed step. While multilayer substrates are less elegant and require accurate mechanical assembly of more components, they do make it easier to bring the large number of thin-film wires out from the array and also make it easier to provide adequate thermal conduction to all parts of the array. MMCs arrays can be constructed using 1 SQUID to read out 2 pixels in loops configured as a gradiometer or in a single loop arrangement with 1 pixel per SQUID. The gradiometric pick-up has the advantage of cancelling out thermal and inductive fluctuations that couple equally into both loops. At the same time, gradiometric loops can be positioned in a way that thermal and inductive cross-talk from adjacent pixels is reduced. In fact using gradiometric pick-up loops it is conceivable that the required level of cross-talk can be achieved without any additional superconducting shielding. For non-gradiometric pickup loops this will not be the case. The use of gradiometric pick-up loops has the additional advantage that the number of electronic channels to read out the array is cut in half. However, the significant disadvantage is that the resolution of an optimal pffiffiffi detector would be reduced by a factor of 2:
3. Coupling schemes In designing an array of MMCs one must address how best to transform the change in magnetization of a sensor into a flux change in the SQUID loop. The tradeoffs and issues regarding the flux coupling for a single pixel and for a large array are different. For single pixel devices the placement of the sensor directly in the SQUID loop is the best solution for most applications, as this produces the maximum coupling. However, fabrication constraints arising from the deposition of magnetic material directly into the SQUID loop, the power dissipation associated with the operation of the SQUIDs in close proximity to the sensors and, in particular, the large number of leads present problems for this design. For arrays, the use of transformer coupling between sensor and SQUID has an advantage in that the two
ARTICLE IN PRESS C. Enss et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) 407–410
components can be physically separated, the sensor array on one substrate and the SQUIDs on another. An obvious drawback of transformer coupled SQUIDs is the reduction of signal size. The SQUID noise level must be sufficiently low that it does not degrade the signal-to-noise ratio when the signal size is reduced. For single pixel operation with a well-coupled flux transformer, the SQUID noise would have to be less than 1:5 pffiffiffiffiffiffi ffi 106 f0 = Hz in order not to contribute to the energy resolution at the 2 eV level. Since SQUIDs with a noise performance lower than this are now achievable, in principle there should be no penalty in using a well-coupled flux transformer. However, when one considers various multiplexing options, the design of the SQUID readout becomes more complex and loss from transformer coupling has consequences in other ways. In the following we discuss two different transformer coupling schemes, a direct flux transformer and a step-up flux transformer. Fig. 1 shows a simplified schematic of these different transformer schemes. In the case of a direct flux transformer the sensor is imbedded in a pick-up coil Lp ; which is part of a superconducting loop containing the input coil Li of the SQUID. For optimal coupling, Li ¼ Lp þ Ll ; the flux transfer function, the ratio of the flux change in the SQUID to that in the
pickup loop, is given by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dFs Ls : ¼ 0:5k dFp Lp þ Ll
409
ð1Þ
The parameter k is the coupling coefficient of the mutual inductance between the ffi SQUID loop and pffiffiffiffiffiffiffiffiffi the input coil, Mis ¼ k Li Ls : Obviously, the inductance of the leads should be made as small as possible. This requires that the flux transformer and the first stage SQUID are placed on the detector chip. Advantages of a direct flux transformer are that the wiring between the pixel is reduced and there is no power dissipation in the vicinity of the sensors. To separate physically the sensor array from the first stage SQUIDs by placing them on different chips requires of use of step-up transformers, Fig. 1b, because of the large inductances of the wirebond leads. The flux transfer function for an optimally designed step-up transformer ðL2 ¼ Li ; L1 ¼ Lp ; Ls oLp Þ is sffiffiffiffiffiffi dFs Ls : ð2Þ E0:35 dFp Lp It is obvious that the coupling factor in this geometry cannot exceed 0.35 and may be closer to 0.2 for practical designs. This significant loss of signal, however, might not limit the obtainable signal-to-noise ratio, if the SQUID noise can be made sufficiently low.
4. Suitable multiplexing schemes
Fig. 1. Coupling schemes for MMCs. (a) Flux transformer. (b) Step-up transformer.
To meet the requirements for a sufficiently low white noise level and a sufficiently high slew rate the readout scheme and amplifier chain of MMC arrays will likely consist of a primary detector SQUID, an amplifier SQUID followed by a series array SQUID as a third stage. In principle, multiplexing can be done in either of these stages. As pointed out by Irwin [3] time division multiplexing without degradation of the signal to noise ratio is only possible if high-frequency noise is filtered out before multiplexing, because in the process of multiplexing it would be shifted to lower frequency bands. If a flux transformer is
ARTICLE IN PRESS 410
C. Enss et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) 407–410
employed, a small resistor in series with the SQUID input coil can be used to provide such a low pass filter. However, given the constraints in terms of inductances and cut-off frequency, the necessary resistor would add an intolerable contribution of Johnson noise. Therefore it is more suitable to perform the multiplexing at later stages for MMCs. After flux to voltage amplification a low pass filter can be employed with insignificant additional Johnson noise. The use of frequency domain multiplexing is also a conceivable scheme for MMC arrays. However, the biggest problem with this technique in connection with MMCs is inductive cross
talk. Without the use of complicated shielding schemes this very like roles out the possibility of frequency domain multiplexing at the first SQUID stage.
References [1] A. Fleischmann, M. Linck, T. Daniyarov, H. Rotzinger, C. Enss, G.M. Seidel, Nucl. Instr. and Meth. A (2004), these Proceedings. [2] A. Fleischmann, C. Enss, G.M. Seidel, Nucl. Instr. and Meth. A (2004), these Proceedings. [3] K.D. Irwin, Physica C 368 (2002) 203.