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Options for an imaging array of micro-calorimeters for X-ray astronomy
Nuclear Instruments and Methods in Physics Research A 444 (2000) 260}264
Options for an imaging array of micro-calorimeters for X-ray astronomy M.P. Bruijn*, H.F.C. Hoevers, W.A. Mels, J.W. den Herder, P.A.J. de Korte Space Research Organization Netherlands, Sorbonnelaan 2, 3584 CA Utrecht, The Netherlands
Abstract A feasibility study of an imaging 32;32 pixel micro-calorimeter array, intended for the XEUS mission is presented. Three di!erent concepts, theoretically leading to an imaging spectrometer that combines an energy resolution of 5 ev for 8 keV X-rays and a count rate of at least 100 counts/s/pixel, are presented and discussed. Current progress in the "eld of single-pixel micro-calorimeters employing voltage-biased transition edge sensors forms the basis for the selection of this type of device. The design concepts originate from di!erent philosophies for the thermal design and geometrical lay-out and will use state of the art micro-machining and lithography. SQUID read-out will be the challenge and grouping of pixels might be considered, both from an electrical and a cooling point of view. 2000 Elsevier Science B.V. All rights reserved. Keywords: XEUS; X-ray astronomy; Imaging micro-calorimeter; Transition edge sensor; Electrothermal feedback
1. Introduction The X-ray Evolving Universe Spectroscopy (XEUS) mission aims to study the physics of some of the most distant and hence youngest known objects in the universe. In particular, it will measure the X-ray spectra of objects with a redshift z'4 at #ux levels below 10\ W/cm. Two narrow "eld cryogenic imaging spectrometers covering the energy range 0.05}2 and 1}10 keV with energy resolutions of about 2 eV at 1 keV and 5 eV at 8 keV, respectively, are envisioned. The very high-resolution spectra obtained from these instruments can be used to study these distant objects, while forth-
* Corresponding author. Tel.: #31-30-253-5600; fax: #3130-254-0860.
coming missions like Chandra, XMM and Astro-E will do similar science for the nearby universe. This paper discusses the Narrow Field Imaging spectrometer 2 (NFI2), which will cover the energy range between 1 and 10 keV. Currently, a closepacked array of microcalorimeters with low heat capacity absorbers and voltage-biased superconducting transition edge thermometers is considered for this spectrometer. Recent developments in this "eld indicate that this type of micro-calorimeter can ful"l the speci"cations.
2. Requirements for the XEUS NFI2 detector The scienti"c goals of the XEUS mission require a telescope of 30 m e!ective area at 1 keV with a spatial resolution of 2}5 arcsec and an imaging
0168-9002/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 9 ) 0 1 3 8 1 - 9
M.P. Bruijn et al. / Nuclear Instruments and Methods in Physics Research A 444 (2000) 260}264
sensor with a 1}2 eV energy resolution at 1 keV and 5}10 eV at 8 keV. In the 1}7 keV band the detection e$ciency should be at least 90%. This energy resolution is needed to separate and enable pro"le measurements of plasma emission lines, in particular the He-like triplets of various elements [1]. A focal length of 50 m is chosen, driven by the required e!ective area and the grazing incidence optics that are needed [2]. For a telescope with a 2 arcsec resolution and 50 m focal length a 240;240 lm pixel size of the detector leads to two times oversampling. The minimum "eld of view of the NFI instruments should be su$cient for tracking of objects with the dual spacecraft attitude control system and be a reasonable extrapolation of present day imaging micro-calorimeter technology. A sensor of 32;32 resolution elements with a "eld of view of 30 arcsec meets both requirements. To enable high-resolution spectroscopy on relatively bright sources, up to 10\ erg/cm/s, each pixel should be capable of handling a count rate of at least 100 Hz with only 1% pile up, which implies that each pixel should have a time constant smaller than 100 ls. The event fall time is selected between 50 and 100 ls, thereby setting a reasonable bandwidth requirement for the SQUID (Superconducting Quantum Interference Device) read-out, which should be able to follow approximately a 5 ls signal risetime.
3. Micro-calorimeters The recent introduction of micro-calorimeters, employing a metallic absorber and a voltage-biased superconductor to normal conductor phase transition thermometer, generally called transition edge sensor (TES), has opened a "eld of detectors that, in principle, combine high-speed, high-energy resolution and good detection e$ciency. Since these devices can be operated in extreme negative electrothermal feedback [3] (ETF), their thermal response speed can be signi"cantly increased. Extreme negative ETF also enables energy resolutions below those achievable with conventional microcalorimeters. The theory of operation and limitations for the energy resolution are described elsewhere [3].
261
In contrary to semiconductor thermistor microcalorimeters, for which arrays have been developed [4] the ETF-TES micro-calorimeters have only been demonstrated in single-pixel version to detect optical and X-ray photons. Recently, the Space Research Organization Netherlands obtained an X-ray resolution of 12.4 eV in combination with a time constant of 0.8 ms for 6 keV X-rays with a Ti/Au TES connected to a Cu absorber. This result is placed in perspective with other results [5}7] in a recent publication [8]. It is observed that the time constants directly bene"t from ETF, whereas the obtainable energy resolution pro"ts to a lesser extent. In the micro-calorimeter designs that are presented in the next section, we will conservatively assume that *E "2.355((k¹C) $5&+ can be reached, but that the time constant of the device scales with the loop gain. Here C is the pixel heat capacity and T the operating temperature.
4. Designs for the XEUS NFI2 imaging micro-calorimeter 4.1. Design alternatives Two baseline designs exist for an imaging spectrometer. One is a pixel array design, the other approach is the use of intrinsic 1-D or 2-D imaging elements [9]. As will become apparent in this paper, the margin available on the single-pixel energy resolution and the required count rate capability have led us to choose a pixel array detector as baseline design. The trade o! is more sensor and read-out complexity. So far three pixel array designs were made with the aid of a simple electrothermal model [8]. The basic di!erence among the three options is the design of the heat transport. The essential challenge for the design is to provide each pixel with an equal thermal link to the cold bath. At the same time the interpixel heat conductivity must be minimized to prevent thermal crosstalk. In Fig. 1 the three principle layouts are clari"ed. In option (a), which we call the `checker boarda, the thermal ground/heat bath is de"ned by high conductivity normal metal strips running on top of the Si N membrane, which also contains V W SECTION V.
262
M.P. Bruijn et al. / Nuclear Instruments and Methods in Physics Research A 444 (2000) 260}264
Fig. 1. Design options for a pixel array: (a) the `checkboarda, (b) the `spike beda, and (c) the `hot electron arraya. The various elements are explained in the text.
absorbers, thermometers, and electrical connections. To suppress cross talk, the packing density is reduced by dividing the detector in two (almost) identical chips, each containing half of the pixels. The pixels are placed in a checker board design and the chips are aligned to "ll the complete detection area. Part of the space between the absorbing pixels is occupied by the electrical connections, the thermal ground and the thermal connections to the thermal ground. The rest is removed in order to further decrease thermal crosstalk and enhance low-energy e$ciency. From a fabrication point of view the structure is very similar to already proven spiderweb bolometers [10,11]. The thermal ground still forms a limitation, causing the e!ective bath temperature for the pixels to change from outer to inner pixels. In option (b), the so-called `spike beda, the electrical connections run in the plane of the Si N V W membrane, while the thermal connections from each pixel to the bath are made perpendicular to that by spikes of Si N (20;20 lm wide and 4 lm V W high). Such a structure could be fabricated from
two separate chips (a chip with the pixels on a membrane and a chip with nitride spikes), which are carefully bonded together, or from a single wafer using micromachining techniques, which need considerable development. To prevent thermal cross talk in the pixel array, each pixel must have a mushroom shape, implying that there must be open space between the absorber and the wiring that runs under the absorber. This option allows for a larger heat conductance from the pixels to the bath, thereby creating more freedom in choice of the heat capacity and bath temperature. In the third option (c), the `hot electron arraya, the operating temperature is lowered such that the coupling between electrons and phonons in the absorbers becomes the dominating time constant for heat transport. The pixels can therefore be placed on a solid wafer. The thermal cross talk between the pixels is still very low because of the fast spread of the heat within the wafer. Essential in this option is a metallic contact between absorber and thermometer. The wiring needs of course to be electrically insulated from the absorbers. At this very low operating temperature (35 mK with a bath at 20 mK) the heat conductivity of Si becomes a limiting factor for the bias power that can be dissipated without increasing the e!ective bath temperature. Especially in options (b) and (c), deposition of relatively thick absorber layers and etching of pixels in it with narrow inter-pixel slits are processing challenges. 4.2. Modeling of the detector designs and their performance; the thermometer and absorber Our electrothermal model for the behavior of a pixel and one of its nearest-neighbors only includes thermal crosstalk for the moment. The design of the imaging calorimeter array is not straightforward. Many of the free design parameters have an e!ect on more than one of the performance parameters. Furthermore, not all relevant material parameters are accurately known at temperatures below 100 mK. Some trial and error is necessary in the choice of design parameters. There are however general guidelines which limit the parameter space.
M.P. Bruijn et al. / Nuclear Instruments and Methods in Physics Research A 444 (2000) 260}264
The demand for the absorption e$ciency sets the minimum thickness for any chosen absorber material. With the selected pixel size of 240;240 lm the minimum temperature-dependent heat capacity is known. Combining these data with the required energy resolution, assuming *E " $5&+ 2.355((k¹C(¹)), brings the operating temperature for all designs below about 70 mK. The main factors determining the fall time are the pixel heat capacity, its thermal link to the bath and the amount of ETF, which depends on the sensitivity of the thermometer at the set point as well as the bath and set point temperatures. As elementary superconductor with a transition temperature in the range of 35}70 mK only thin sputtered tungsten "lms can be used [7]. Proximity bi-layers, consisting of a thin layer of superconducting material (e.g. Al, Ti, Mo, Ir) and a layer of normal metal (e.g. Au, Ag, Cu) are an alternative, where the layer thicknesses can be used to tune the transition temperature. Stability against corrosion and interdi!usion are important issues. In order to prevent a temperature excursion, after impact of a photon, which is larger than the transition width, either this width or the total pixel heat capacity has to be enlarged. Since larger heat capacities degrade the energy resolution and problems exist with operation at large loop gains, present in case of thermometers with steep transitions, it seems best to #atten the thermometer response either by changing its geometry, or by di!erential doping, or by applying a magnetic "eld. (We conservatively assume here again no practical gain in resolution by the ETF, but a steepness (a"¹/R dR/d¹) high enough not to cause a theoretical resolution *E '2.355((k¹C)). A too large temper$5&+ ature excursion increases the fall time and causes non-linearity of response and non-uniformity of fall time constant. As absorber material high-Z materials are chosen for their X-ray absorption cross section. The semi-metal Bi is favorable in designs (a) and (b) since it has a much lower heat capacity than a normal metal. Combination with a thin Au coating reduces the thermalization time of the pixel. Investigation of superconducting absorbers could be relevant as well, given the low heat capacity in the superconducting phase. In option (c) Au is prefer-
263
red, because the electron-phonon coupling time is better matched to the required time constant. More details of the design and performance characteristics of the three options can be found elsewhere [8]. 4.3. Comparison of the three design options With the aid of the electrothermal modeling results, and the ideas on fabrication feasibility, we can make up a list of advantages and disadvantages of the three presented designs. The `checker boarda fabrication process needs few developments, thick absorbers can be patterned more easily and cross talk can be minimized. On the contrary, the uniformity of response is poor, it is a fragile structure, cannot be used with single-pixel read-out and the detection e$ciency is impaired at the low-energy end of the spectrum. The `spike beda design has in principle a uniform response and allows for the highest bath temperature. It is a fragile structure for which the fabrication process needs the most developments. Disadvantageous is also the rather large thermal cross talk. The `hot electron arraya inherently has a uniform response, the thermal cross talk is very low for a substrate with a good heat conductivity and it can also be designed with individual pixel read-out if required. The fabrication process is by far the least complicated and the structure is rugged. The main disadvantage is the low operation temperature: The time constants are very sensitive to the operating temperature and the design is most dependent on the heat conductivity of the substrate. In this regime of operation there are no published X-ray performance data available yet for normal metal absorbers on a solid substrate, read out by a ETFTES. For optical wavelengths good performance was demonstrated [7] without normal metal absorbers. NIS-junction microcalorimeters [12] were fabricated on a membrane. Other experiments utilize large crystalline absorbers (phonon-mediated detection) [13}15]. A problem area could be substrate events: X-ray photons which pass the absorbers into the substrate (about 10%) will generate small signals in more than one pixel simultaneously.
SECTION V.
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4.4. Multi-pixel read-out using SQUIDs The signal of the voltage-biased TES is a current change originating from a low impedance source and the only suitable current ampli"er is a lownoise DC-SQUID with su$cient bandwidth. If each pixel is to be read out with its own SQUID, 1024 SQUIDs are needed for a 32;32 array. The present experimental work on single-pixel microcalorimeters indicates that the SQUID read-out is a critical component, because of the SQUID itself and because of the required feedback electronics. For this reason and limitations on the available cooling power it might be advantageous to have a read-out system with a smaller number of SQUIDs. The number of SQUIDs can, in principle, be reduced if pixel rows and columns are grouped together. The position of impact can be determined by a coincidence technique between row- and column SQUID's. If m pixels are grouped together, the energy resolution will be a factor (m worse than in case of a single-pixel read-out and the count rate capability will reduce to 1/m. Since the margins in the performance parameters are limited, the number of pixels that can be connected is rather limited, typically 4 or 8. As a result the number of SQUIDs reduces with a factor up to 6.
5. Conclusion We have presented here our ideas about the design of a high-energy resolution imaging spectrometer for the XEUS mission. The state of the design is still very preliminary. Based on the current experimental status of single-pixel micro-calorimeters, three fundamentally di!erent designs for an imaging spectrometer, that will meet most of the requirements from the astronomical community, have been presented. Future e!orts should be directed in three "elds: The performance of single pixel versions in the temperature regime proposed here must be proven. Secondly, processing developments are essential to investigate the di!erent de-
sign options. Finally, development is needed of multi-pixel read-out schemes using SQUIDs.
Acknowledgements This work is supported by the Nederlandse organisatie voor Wetenschappelijk Onderzoek (NWO).
References [1] P.A.J. de Korte, M. Bavdaz, L. Duband, A.D. Holland, A.J. Peacock, L. StruK der, SPIE Proc. 3766 (1999) 09. [2] M. Bavdaz, B.R. Aschenbach, M.W. Beijersbergen, H.W. BraK uninger, A.J. Peacock, R. Willingale, SPIE Proc. 3766 (1999) 08. [3] K.D. Irwin 1995, Appl. Phys. Lett. 66 (1998). [4] C.K. Stahle, R.L. Kelly, D. McCammon, S.H. Moseley, A.E. Szymkowiak, Nucl. Instr. and Meth. A 370 (1996) 266. [5] D.A. Wollman, K.D. Irwin, G.C. Hilton, L.L. Dulcie, P.E. Newbury, J.M. Martinis, J. Microscopy 188 (1997) 196. [6] G.C. Hilton, D.A. Wollman, K.D. Irwin, L.L. Dulcie, N.P. Bergren, J.M. Martinis, IEEE Trans. Appl. Supercond. (1998), to be published. [7] B. Cabrera, R.M. Clarke, P. Colling, A.J. Miller, S.W. Nam, R.W. Romani, Appl. Phys. Lett. 73 (1998) 735. [8] P.A.J. de Korte, H.F.C. Hoevers, M.P. Bruijn, A.C. Bento, W.A. Mels, J.A.M. Bleeker, A.D. Holland, M.J.T. Turner, SPIE Proc. 3766 (1999) 12. [9] H. Kraus, F. von Feilitzsch, J. Jochum, R.L. Mossbauer, Th. Peterreins, F. ProK bst, Phys. Lett. B 231 (1989) 195. [10] J.J. Bock, D. Chen, P.D. Mauskopf, A.E. Lange et al., Space Sci. Rev. 74 (1995) 229. [11] F.B. Kiewiet, M.P. Bruijn, H.F.C. Hoevers, A.C. Bento, W.A. Mels, P.A.J. de Korte, IEEE Trans. Appl. Supercond. (1998), to be published. [12] M. Nahum, J.M. Martinis, Appl. Phys. Lett. 66 (23) (1995) 3203. [13] K.D. Irwin, S.W. Nam, B. Cabrera, B. Chugg, G.S. Park, R.P. Welty, J.M. Martinis, IEEE Trans. Appl. Supercond. 5 (1995) 2690. [14] R.M. Clarke, P.L. Brink, S.W. Nam, A.K. Davies, B. Chugg, B.A. Young, B. Cabrera, S. Cooper (Ed.), Proceedings LTD-7, Munich, 1997 p. 229. [15] M. Sisti, C. Bucci, M. BuK hler, S. Cooper, F. v. Feilitzsch, J. HoK hne, V. JoK rgens, M. Loidl, O. Meier, U. Nagel, F. ProK bst, A. Rulofs, M.L. Sarsa, J. Schnagl, W. Seidel, L. Stodolsky, A. Stolovits, L. Zerle, S. Cooper (Ed.), Proceedings LTD-7, Munich, (1997) p. 232.
Options for an imaging array of micro-calorimeters for X-ray astronomy M.P. Bruijn*, H.F.C. Hoevers, W.A. Mels, J.W. den Herder, P.A.J. de Korte Space Research Organization Netherlands, Sorbonnelaan 2, 3584 CA Utrecht, The Netherlands
Abstract A feasibility study of an imaging 32;32 pixel micro-calorimeter array, intended for the XEUS mission is presented. Three di!erent concepts, theoretically leading to an imaging spectrometer that combines an energy resolution of 5 ev for 8 keV X-rays and a count rate of at least 100 counts/s/pixel, are presented and discussed. Current progress in the "eld of single-pixel micro-calorimeters employing voltage-biased transition edge sensors forms the basis for the selection of this type of device. The design concepts originate from di!erent philosophies for the thermal design and geometrical lay-out and will use state of the art micro-machining and lithography. SQUID read-out will be the challenge and grouping of pixels might be considered, both from an electrical and a cooling point of view. 2000 Elsevier Science B.V. All rights reserved. Keywords: XEUS; X-ray astronomy; Imaging micro-calorimeter; Transition edge sensor; Electrothermal feedback
1. Introduction The X-ray Evolving Universe Spectroscopy (XEUS) mission aims to study the physics of some of the most distant and hence youngest known objects in the universe. In particular, it will measure the X-ray spectra of objects with a redshift z'4 at #ux levels below 10\ W/cm. Two narrow "eld cryogenic imaging spectrometers covering the energy range 0.05}2 and 1}10 keV with energy resolutions of about 2 eV at 1 keV and 5 eV at 8 keV, respectively, are envisioned. The very high-resolution spectra obtained from these instruments can be used to study these distant objects, while forth-
* Corresponding author. Tel.: #31-30-253-5600; fax: #3130-254-0860.
coming missions like Chandra, XMM and Astro-E will do similar science for the nearby universe. This paper discusses the Narrow Field Imaging spectrometer 2 (NFI2), which will cover the energy range between 1 and 10 keV. Currently, a closepacked array of microcalorimeters with low heat capacity absorbers and voltage-biased superconducting transition edge thermometers is considered for this spectrometer. Recent developments in this "eld indicate that this type of micro-calorimeter can ful"l the speci"cations.
2. Requirements for the XEUS NFI2 detector The scienti"c goals of the XEUS mission require a telescope of 30 m e!ective area at 1 keV with a spatial resolution of 2}5 arcsec and an imaging
0168-9002/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 9 ) 0 1 3 8 1 - 9
M.P. Bruijn et al. / Nuclear Instruments and Methods in Physics Research A 444 (2000) 260}264
sensor with a 1}2 eV energy resolution at 1 keV and 5}10 eV at 8 keV. In the 1}7 keV band the detection e$ciency should be at least 90%. This energy resolution is needed to separate and enable pro"le measurements of plasma emission lines, in particular the He-like triplets of various elements [1]. A focal length of 50 m is chosen, driven by the required e!ective area and the grazing incidence optics that are needed [2]. For a telescope with a 2 arcsec resolution and 50 m focal length a 240;240 lm pixel size of the detector leads to two times oversampling. The minimum "eld of view of the NFI instruments should be su$cient for tracking of objects with the dual spacecraft attitude control system and be a reasonable extrapolation of present day imaging micro-calorimeter technology. A sensor of 32;32 resolution elements with a "eld of view of 30 arcsec meets both requirements. To enable high-resolution spectroscopy on relatively bright sources, up to 10\ erg/cm/s, each pixel should be capable of handling a count rate of at least 100 Hz with only 1% pile up, which implies that each pixel should have a time constant smaller than 100 ls. The event fall time is selected between 50 and 100 ls, thereby setting a reasonable bandwidth requirement for the SQUID (Superconducting Quantum Interference Device) read-out, which should be able to follow approximately a 5 ls signal risetime.
3. Micro-calorimeters The recent introduction of micro-calorimeters, employing a metallic absorber and a voltage-biased superconductor to normal conductor phase transition thermometer, generally called transition edge sensor (TES), has opened a "eld of detectors that, in principle, combine high-speed, high-energy resolution and good detection e$ciency. Since these devices can be operated in extreme negative electrothermal feedback [3] (ETF), their thermal response speed can be signi"cantly increased. Extreme negative ETF also enables energy resolutions below those achievable with conventional microcalorimeters. The theory of operation and limitations for the energy resolution are described elsewhere [3].
261
In contrary to semiconductor thermistor microcalorimeters, for which arrays have been developed [4] the ETF-TES micro-calorimeters have only been demonstrated in single-pixel version to detect optical and X-ray photons. Recently, the Space Research Organization Netherlands obtained an X-ray resolution of 12.4 eV in combination with a time constant of 0.8 ms for 6 keV X-rays with a Ti/Au TES connected to a Cu absorber. This result is placed in perspective with other results [5}7] in a recent publication [8]. It is observed that the time constants directly bene"t from ETF, whereas the obtainable energy resolution pro"ts to a lesser extent. In the micro-calorimeter designs that are presented in the next section, we will conservatively assume that *E "2.355((k¹C) $5&+ can be reached, but that the time constant of the device scales with the loop gain. Here C is the pixel heat capacity and T the operating temperature.
4. Designs for the XEUS NFI2 imaging micro-calorimeter 4.1. Design alternatives Two baseline designs exist for an imaging spectrometer. One is a pixel array design, the other approach is the use of intrinsic 1-D or 2-D imaging elements [9]. As will become apparent in this paper, the margin available on the single-pixel energy resolution and the required count rate capability have led us to choose a pixel array detector as baseline design. The trade o! is more sensor and read-out complexity. So far three pixel array designs were made with the aid of a simple electrothermal model [8]. The basic di!erence among the three options is the design of the heat transport. The essential challenge for the design is to provide each pixel with an equal thermal link to the cold bath. At the same time the interpixel heat conductivity must be minimized to prevent thermal crosstalk. In Fig. 1 the three principle layouts are clari"ed. In option (a), which we call the `checker boarda, the thermal ground/heat bath is de"ned by high conductivity normal metal strips running on top of the Si N membrane, which also contains V W SECTION V.
262
M.P. Bruijn et al. / Nuclear Instruments and Methods in Physics Research A 444 (2000) 260}264
Fig. 1. Design options for a pixel array: (a) the `checkboarda, (b) the `spike beda, and (c) the `hot electron arraya. The various elements are explained in the text.
absorbers, thermometers, and electrical connections. To suppress cross talk, the packing density is reduced by dividing the detector in two (almost) identical chips, each containing half of the pixels. The pixels are placed in a checker board design and the chips are aligned to "ll the complete detection area. Part of the space between the absorbing pixels is occupied by the electrical connections, the thermal ground and the thermal connections to the thermal ground. The rest is removed in order to further decrease thermal crosstalk and enhance low-energy e$ciency. From a fabrication point of view the structure is very similar to already proven spiderweb bolometers [10,11]. The thermal ground still forms a limitation, causing the e!ective bath temperature for the pixels to change from outer to inner pixels. In option (b), the so-called `spike beda, the electrical connections run in the plane of the Si N V W membrane, while the thermal connections from each pixel to the bath are made perpendicular to that by spikes of Si N (20;20 lm wide and 4 lm V W high). Such a structure could be fabricated from
two separate chips (a chip with the pixels on a membrane and a chip with nitride spikes), which are carefully bonded together, or from a single wafer using micromachining techniques, which need considerable development. To prevent thermal cross talk in the pixel array, each pixel must have a mushroom shape, implying that there must be open space between the absorber and the wiring that runs under the absorber. This option allows for a larger heat conductance from the pixels to the bath, thereby creating more freedom in choice of the heat capacity and bath temperature. In the third option (c), the `hot electron arraya, the operating temperature is lowered such that the coupling between electrons and phonons in the absorbers becomes the dominating time constant for heat transport. The pixels can therefore be placed on a solid wafer. The thermal cross talk between the pixels is still very low because of the fast spread of the heat within the wafer. Essential in this option is a metallic contact between absorber and thermometer. The wiring needs of course to be electrically insulated from the absorbers. At this very low operating temperature (35 mK with a bath at 20 mK) the heat conductivity of Si becomes a limiting factor for the bias power that can be dissipated without increasing the e!ective bath temperature. Especially in options (b) and (c), deposition of relatively thick absorber layers and etching of pixels in it with narrow inter-pixel slits are processing challenges. 4.2. Modeling of the detector designs and their performance; the thermometer and absorber Our electrothermal model for the behavior of a pixel and one of its nearest-neighbors only includes thermal crosstalk for the moment. The design of the imaging calorimeter array is not straightforward. Many of the free design parameters have an e!ect on more than one of the performance parameters. Furthermore, not all relevant material parameters are accurately known at temperatures below 100 mK. Some trial and error is necessary in the choice of design parameters. There are however general guidelines which limit the parameter space.
M.P. Bruijn et al. / Nuclear Instruments and Methods in Physics Research A 444 (2000) 260}264
The demand for the absorption e$ciency sets the minimum thickness for any chosen absorber material. With the selected pixel size of 240;240 lm the minimum temperature-dependent heat capacity is known. Combining these data with the required energy resolution, assuming *E " $5&+ 2.355((k¹C(¹)), brings the operating temperature for all designs below about 70 mK. The main factors determining the fall time are the pixel heat capacity, its thermal link to the bath and the amount of ETF, which depends on the sensitivity of the thermometer at the set point as well as the bath and set point temperatures. As elementary superconductor with a transition temperature in the range of 35}70 mK only thin sputtered tungsten "lms can be used [7]. Proximity bi-layers, consisting of a thin layer of superconducting material (e.g. Al, Ti, Mo, Ir) and a layer of normal metal (e.g. Au, Ag, Cu) are an alternative, where the layer thicknesses can be used to tune the transition temperature. Stability against corrosion and interdi!usion are important issues. In order to prevent a temperature excursion, after impact of a photon, which is larger than the transition width, either this width or the total pixel heat capacity has to be enlarged. Since larger heat capacities degrade the energy resolution and problems exist with operation at large loop gains, present in case of thermometers with steep transitions, it seems best to #atten the thermometer response either by changing its geometry, or by di!erential doping, or by applying a magnetic "eld. (We conservatively assume here again no practical gain in resolution by the ETF, but a steepness (a"¹/R dR/d¹) high enough not to cause a theoretical resolution *E '2.355((k¹C)). A too large temper$5&+ ature excursion increases the fall time and causes non-linearity of response and non-uniformity of fall time constant. As absorber material high-Z materials are chosen for their X-ray absorption cross section. The semi-metal Bi is favorable in designs (a) and (b) since it has a much lower heat capacity than a normal metal. Combination with a thin Au coating reduces the thermalization time of the pixel. Investigation of superconducting absorbers could be relevant as well, given the low heat capacity in the superconducting phase. In option (c) Au is prefer-
263
red, because the electron-phonon coupling time is better matched to the required time constant. More details of the design and performance characteristics of the three options can be found elsewhere [8]. 4.3. Comparison of the three design options With the aid of the electrothermal modeling results, and the ideas on fabrication feasibility, we can make up a list of advantages and disadvantages of the three presented designs. The `checker boarda fabrication process needs few developments, thick absorbers can be patterned more easily and cross talk can be minimized. On the contrary, the uniformity of response is poor, it is a fragile structure, cannot be used with single-pixel read-out and the detection e$ciency is impaired at the low-energy end of the spectrum. The `spike beda design has in principle a uniform response and allows for the highest bath temperature. It is a fragile structure for which the fabrication process needs the most developments. Disadvantageous is also the rather large thermal cross talk. The `hot electron arraya inherently has a uniform response, the thermal cross talk is very low for a substrate with a good heat conductivity and it can also be designed with individual pixel read-out if required. The fabrication process is by far the least complicated and the structure is rugged. The main disadvantage is the low operation temperature: The time constants are very sensitive to the operating temperature and the design is most dependent on the heat conductivity of the substrate. In this regime of operation there are no published X-ray performance data available yet for normal metal absorbers on a solid substrate, read out by a ETFTES. For optical wavelengths good performance was demonstrated [7] without normal metal absorbers. NIS-junction microcalorimeters [12] were fabricated on a membrane. Other experiments utilize large crystalline absorbers (phonon-mediated detection) [13}15]. A problem area could be substrate events: X-ray photons which pass the absorbers into the substrate (about 10%) will generate small signals in more than one pixel simultaneously.
SECTION V.
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4.4. Multi-pixel read-out using SQUIDs The signal of the voltage-biased TES is a current change originating from a low impedance source and the only suitable current ampli"er is a lownoise DC-SQUID with su$cient bandwidth. If each pixel is to be read out with its own SQUID, 1024 SQUIDs are needed for a 32;32 array. The present experimental work on single-pixel microcalorimeters indicates that the SQUID read-out is a critical component, because of the SQUID itself and because of the required feedback electronics. For this reason and limitations on the available cooling power it might be advantageous to have a read-out system with a smaller number of SQUIDs. The number of SQUIDs can, in principle, be reduced if pixel rows and columns are grouped together. The position of impact can be determined by a coincidence technique between row- and column SQUID's. If m pixels are grouped together, the energy resolution will be a factor (m worse than in case of a single-pixel read-out and the count rate capability will reduce to 1/m. Since the margins in the performance parameters are limited, the number of pixels that can be connected is rather limited, typically 4 or 8. As a result the number of SQUIDs reduces with a factor up to 6.
5. Conclusion We have presented here our ideas about the design of a high-energy resolution imaging spectrometer for the XEUS mission. The state of the design is still very preliminary. Based on the current experimental status of single-pixel micro-calorimeters, three fundamentally di!erent designs for an imaging spectrometer, that will meet most of the requirements from the astronomical community, have been presented. Future e!orts should be directed in three "elds: The performance of single pixel versions in the temperature regime proposed here must be proven. Secondly, processing developments are essential to investigate the di!erent de-
sign options. Finally, development is needed of multi-pixel read-out schemes using SQUIDs.
Acknowledgements This work is supported by the Nederlandse organisatie voor Wetenschappelijk Onderzoek (NWO).
References [1] P.A.J. de Korte, M. Bavdaz, L. Duband, A.D. Holland, A.J. Peacock, L. StruK der, SPIE Proc. 3766 (1999) 09. [2] M. Bavdaz, B.R. Aschenbach, M.W. Beijersbergen, H.W. BraK uninger, A.J. Peacock, R. Willingale, SPIE Proc. 3766 (1999) 08. [3] K.D. Irwin 1995, Appl. Phys. Lett. 66 (1998). [4] C.K. Stahle, R.L. Kelly, D. McCammon, S.H. Moseley, A.E. Szymkowiak, Nucl. Instr. and Meth. A 370 (1996) 266. [5] D.A. Wollman, K.D. Irwin, G.C. Hilton, L.L. Dulcie, P.E. Newbury, J.M. Martinis, J. Microscopy 188 (1997) 196. [6] G.C. Hilton, D.A. Wollman, K.D. Irwin, L.L. Dulcie, N.P. Bergren, J.M. Martinis, IEEE Trans. Appl. Supercond. (1998), to be published. [7] B. Cabrera, R.M. Clarke, P. Colling, A.J. Miller, S.W. Nam, R.W. Romani, Appl. Phys. Lett. 73 (1998) 735. [8] P.A.J. de Korte, H.F.C. Hoevers, M.P. Bruijn, A.C. Bento, W.A. Mels, J.A.M. Bleeker, A.D. Holland, M.J.T. Turner, SPIE Proc. 3766 (1999) 12. [9] H. Kraus, F. von Feilitzsch, J. Jochum, R.L. Mossbauer, Th. Peterreins, F. ProK bst, Phys. Lett. B 231 (1989) 195. [10] J.J. Bock, D. Chen, P.D. Mauskopf, A.E. Lange et al., Space Sci. Rev. 74 (1995) 229. [11] F.B. Kiewiet, M.P. Bruijn, H.F.C. Hoevers, A.C. Bento, W.A. Mels, P.A.J. de Korte, IEEE Trans. Appl. Supercond. (1998), to be published. [12] M. Nahum, J.M. Martinis, Appl. Phys. Lett. 66 (23) (1995) 3203. [13] K.D. Irwin, S.W. Nam, B. Cabrera, B. Chugg, G.S. Park, R.P. Welty, J.M. Martinis, IEEE Trans. Appl. Supercond. 5 (1995) 2690. [14] R.M. Clarke, P.L. Brink, S.W. Nam, A.K. Davies, B. Chugg, B.A. Young, B. Cabrera, S. Cooper (Ed.), Proceedings LTD-7, Munich, 1997 p. 229. [15] M. Sisti, C. Bucci, M. BuK hler, S. Cooper, F. v. Feilitzsch, J. HoK hne, V. JoK rgens, M. Loidl, O. Meier, U. Nagel, F. ProK bst, A. Rulofs, M.L. Sarsa, J. Schnagl, W. Seidel, L. Stodolsky, A. Stolovits, L. Zerle, S. Cooper (Ed.), Proceedings LTD-7, Munich, (1997) p. 232.