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Distributed transition-edge sensors for linearized position response in a phonon-mediated X-ray imaging spectrometer
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 520 (2004) 502–504
Distributed transition-edge sensors for linearized position response in a phonon-mediated X-ray imaging spectrometer Blas Cabreraa,*, Paul L. Brinka, Steven W. Lemana, Joseph P. Castlea, Astrid Tomadaa, Betty A. Youngb, Dennis S. Mart!ınez-Galarcec, Robert A. Sternc, Steve Deikerd, Kent D. Irwind a
Varian Lab 144, Department of Physics, Stanford University, Stanford, CA 94305-4060, USA b Department of Physics, Santa Clara University, Santa Clara, CA 95053, USA c Lockheed Martin Solar and Astrophysics Laboratory, Palo Alto, CA 94304, USA d National Institute of Standards & Technology, Boulder, CO 80303, USA
Abstract For future solar X-ray satellite missions, we are developing a phonon-mediated macro-pixel composed of a Ge crystal absorber with four superconducting transition-edge sensors (TES) distributed on the backside. The X-rays are absorbed on the opposite side and the energy is converted into phonons, which are absorbed into the four TES sensors. By connecting together parallel elements into four channels, fractional total energy absorbed between two of the sensors provides x-position information and the other two provide y-position information. We determine the optimal distribution for the TES sub-elements to obtain linear position information while minimizing the degradation of energy resolution. r 2003 Published by Elsevier B.V. Keywords: Transition-edge sensor; Phonon; Phonon-mediated
1. Introduction To investigate the magnetic reconnection process in the solar corona, with future solar X-ray Explorer-class satellites, one needs to image coronal flares with high spatial resolution and high-energy resolution in the 6–7 keV X-ray band of the Fe XXV and Fe XXVI complexes [1]. For a 1–2 m focal length, one needs 5–10 mm spatial resolution in the imaging plane of the X-ray telescope to obtain 1 arcsec angular resolution. An energy resolution approaching 4 eV FWHM is *Corresponding author. Tel.: +1-650-723-3395; fax: +1650-725-6544. E-mail address: [email protected] (B. Cabrera). 0168-9002/$ - see front matter r 2003 Published by Elsevier B.V. doi:10.1016/j.nima.2003.11.298
needed to obtain flow velocity resolution of about 180 km/s. An instrument with a 2 arcmin field of view requires count rates approaching 4 kHz across the entire array, allowing useful spectra in 5–10 s or less. Existing TES X-ray spectrometers have a pixel size of order 100 to 200 mm on a side, and it is difficult to see how to obtain an array of 5 mm pixels with a high fill factor by directly scaling the current TES technology.
2. Macropixel design Here, the idea is to take a single TES pixel, capable of the best energy resolution of 2–4 eV
ARTICLE IN PRESS B. Cabrera et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) 502–504
FWHM, and divide it into four subpixels each with one quarter the saturation energy of the macro pixel. Each subpixel will have a sensor noise half that of the full pixel since the noise is proportional to the square root of the heat capacity. If the amplifier noise is negligible compared to the sensor noise, then the resolution of the sum of the four sub-pixels is the same as the resolution of the original single pixel. Since the position resolution required is very coarse compared to the energy resolution, only a small portion of the available signal-to-noise need be used on the position resolution and therefore in principle the best energy resolution possible with imaging is very close to the best energy resolution without imaging. So for example, by designing small differences in the energy collected in each of the subpixels Ea ; Eb ; Ec and Ed of a square macro-pixel with edge L, we measure the position L=2oxoL=2 using x=L ¼ y using Ec & Ed : ðEa Eb Þ=E and simultaneously Then for Esat =DE one ¼ R and one xmax =Dx¼ RL & we obtain Ea;sat ¼ Esat =4 1 þ RL =Rone qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Esat =DE macro ¼ Rone = 1 þ RL =Rone : Thus if we obtain an energy resolution of 3000 with the single pixel and we want a position resolution of 300 in a macro-pixel, we increase the saturation energy by 10% which degrades the energy resolution by only 5%, to 95% of its single pixel value. We will use high purity Ge crystals as the X-ray absorber material. X-rays in the 6–7 keV band have an absorption length of 12–16 mm in Ge. Therefore a 300 mm thick Ge wafer provides highefficiency collection to well above 10 keV. After photo absorption the resulting electron rapidly produces a cloud of electron and hole pairs in the Ge which shed high energy phonons. It has been shown that charge-neutralizing cold Ge crystals allows rapid diffusion of electrons and holes to the surfaces of the crystal where the potential energy of the electron is rapidly converted into a cascade of phonons on the ms time scale [3]. We expect to use proven neutralization techniques to avoid long-lived loss of energy to the electron-hole system, which would degrade the energy resolution.
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3. Linear position response In Fig. 1, we show the design of our Ge imaging spectrometer, a 1.5 mm 1.5 mm square macropixel with four segmented TES sensors covering in total about 25% of the area. With this coverage and a 0.3 absorption probability when phonons are incident on the W films, it takes about eight attempts for each phonon to be absorbed. Most phonons will spread throughout the (1.5 mm)2 crystal. The collection time into the TESs will be about 2–3 ms. We have obtained fall times as short as 7 ms with the optical detectors [2] and here our target is 20 ms, for a count rate of B4 kHz. The Ge crystal substrate is isolated from the remaining Ge substrate with a SiN membrane to prevent escape of athermal phonons. In order to obtain the highest resolutions we adjust the total area of the 4 TES sensors for a saturation energy B10% above 7 keV. The design allows simultaneous x and y position determination of individual events. The segments for each channel are connected electrically in
Fig. 1. Schematic diagram of chip design. The inner black square is the edge of the (1.5 mm)2 absorber. The region between the two black squares is etched through the entire 300 mm thick wafer and suspended with 1 mm thick SiN. Each of the four channels (shadings) is wired in parallel. The wiring layer goes along the diagonals and requires no crossovers within the absorber area.
ARTICLE IN PRESS 504
B. Cabrera et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) 502–504
Fig. 2. One dimensional energy distribution at each of eight TES sub-elements for 4 different event locations (5–8 symmetric to 1–4).
parallel using 2 mm wide Al/W rails—a photolithographic technology well developed for optical detectors [2]. Here we demonstrate a linear position response along one axis, with a 1D Monte Carlo calculation. Fig. 2 shows the total energy collected in each of 8 sub-elements of two combined TES sensors, which together form a uniform area coverage all along the length of the detector. We have one degree of freedom left, which is the percentage of each sub-element connected to one versus the other TES. In Fig. 3, we calculate the total energy absorbed in left most of the two TESs for two different sensor distributions. The first is the standard 100% fill of half the subelements by each TES, producing the nonlinear ‘‘S’’ shaped response curve. To improve the linearity in the second example, each TES is distributed all along the detector length, with one TES concentrated towards one end and tapering off towards the other end, and the other TES done symmetrically the other way. A linear response is evident with this distributed TES. In conclusion, for applications requiring mm scale pixels, an effective 2D array of pixels can be obtained in a phonon-mediated Ge absorber using four distributed TES sensors. The position response can be made linear, and simultaneously the
Fig. 3. Comparison of total energy absorbed in left most TES for two different sensor distributions, one for side by side sensors and the second for the new distributed sensor designed to linearize and homogenize the response across the crystal absorber.
variations in pulse shape can be made very small. Before a practical detector can be made, however, we must demonstrate both the full collection of electron-hole potential energy from Ge, and 20 ms recovery times.
Acknowledgements This research was supported in part by the Department of Energy under Grant No. DEFG03-90ER40569, and by NASA Grants NAG53775 and NAG5-3263. RAS & DMG were supported by the Lockheed Martin Independent Research Program.
References [1] J.T. Mariska, G.A. Doschek, Astrophys. J. 485 (1997) 904. [2] A.J. Miller, B. Cabrera, R.M. Clarke, E. FigueroaFeliciano, S. Nam, R.W. Romani, IEEE Trans. Appl. Supercond. 9 (1999) 4205. [3] T. Shutt, J. Emes, E.E. Haller, J. Hellmig, B. Sadoulet, D. Seitz, B.A. Young, S. White, LTD8, Nucl. Instr. and Meth. A 444 (2000) 340.
Nuclear Instruments and Methods in Physics Research A 520 (2004) 502–504
Distributed transition-edge sensors for linearized position response in a phonon-mediated X-ray imaging spectrometer Blas Cabreraa,*, Paul L. Brinka, Steven W. Lemana, Joseph P. Castlea, Astrid Tomadaa, Betty A. Youngb, Dennis S. Mart!ınez-Galarcec, Robert A. Sternc, Steve Deikerd, Kent D. Irwind a
Varian Lab 144, Department of Physics, Stanford University, Stanford, CA 94305-4060, USA b Department of Physics, Santa Clara University, Santa Clara, CA 95053, USA c Lockheed Martin Solar and Astrophysics Laboratory, Palo Alto, CA 94304, USA d National Institute of Standards & Technology, Boulder, CO 80303, USA
Abstract For future solar X-ray satellite missions, we are developing a phonon-mediated macro-pixel composed of a Ge crystal absorber with four superconducting transition-edge sensors (TES) distributed on the backside. The X-rays are absorbed on the opposite side and the energy is converted into phonons, which are absorbed into the four TES sensors. By connecting together parallel elements into four channels, fractional total energy absorbed between two of the sensors provides x-position information and the other two provide y-position information. We determine the optimal distribution for the TES sub-elements to obtain linear position information while minimizing the degradation of energy resolution. r 2003 Published by Elsevier B.V. Keywords: Transition-edge sensor; Phonon; Phonon-mediated
1. Introduction To investigate the magnetic reconnection process in the solar corona, with future solar X-ray Explorer-class satellites, one needs to image coronal flares with high spatial resolution and high-energy resolution in the 6–7 keV X-ray band of the Fe XXV and Fe XXVI complexes [1]. For a 1–2 m focal length, one needs 5–10 mm spatial resolution in the imaging plane of the X-ray telescope to obtain 1 arcsec angular resolution. An energy resolution approaching 4 eV FWHM is *Corresponding author. Tel.: +1-650-723-3395; fax: +1650-725-6544. E-mail address: [email protected] (B. Cabrera). 0168-9002/$ - see front matter r 2003 Published by Elsevier B.V. doi:10.1016/j.nima.2003.11.298
needed to obtain flow velocity resolution of about 180 km/s. An instrument with a 2 arcmin field of view requires count rates approaching 4 kHz across the entire array, allowing useful spectra in 5–10 s or less. Existing TES X-ray spectrometers have a pixel size of order 100 to 200 mm on a side, and it is difficult to see how to obtain an array of 5 mm pixels with a high fill factor by directly scaling the current TES technology.
2. Macropixel design Here, the idea is to take a single TES pixel, capable of the best energy resolution of 2–4 eV
ARTICLE IN PRESS B. Cabrera et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) 502–504
FWHM, and divide it into four subpixels each with one quarter the saturation energy of the macro pixel. Each subpixel will have a sensor noise half that of the full pixel since the noise is proportional to the square root of the heat capacity. If the amplifier noise is negligible compared to the sensor noise, then the resolution of the sum of the four sub-pixels is the same as the resolution of the original single pixel. Since the position resolution required is very coarse compared to the energy resolution, only a small portion of the available signal-to-noise need be used on the position resolution and therefore in principle the best energy resolution possible with imaging is very close to the best energy resolution without imaging. So for example, by designing small differences in the energy collected in each of the subpixels Ea ; Eb ; Ec and Ed of a square macro-pixel with edge L, we measure the position L=2oxoL=2 using x=L ¼ y using Ec & Ed : ðEa Eb Þ=E and simultaneously Then for Esat =DE one ¼ R and one xmax =Dx¼ RL & we obtain Ea;sat ¼ Esat =4 1 þ RL =Rone qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Esat =DE macro ¼ Rone = 1 þ RL =Rone : Thus if we obtain an energy resolution of 3000 with the single pixel and we want a position resolution of 300 in a macro-pixel, we increase the saturation energy by 10% which degrades the energy resolution by only 5%, to 95% of its single pixel value. We will use high purity Ge crystals as the X-ray absorber material. X-rays in the 6–7 keV band have an absorption length of 12–16 mm in Ge. Therefore a 300 mm thick Ge wafer provides highefficiency collection to well above 10 keV. After photo absorption the resulting electron rapidly produces a cloud of electron and hole pairs in the Ge which shed high energy phonons. It has been shown that charge-neutralizing cold Ge crystals allows rapid diffusion of electrons and holes to the surfaces of the crystal where the potential energy of the electron is rapidly converted into a cascade of phonons on the ms time scale [3]. We expect to use proven neutralization techniques to avoid long-lived loss of energy to the electron-hole system, which would degrade the energy resolution.
503
3. Linear position response In Fig. 1, we show the design of our Ge imaging spectrometer, a 1.5 mm 1.5 mm square macropixel with four segmented TES sensors covering in total about 25% of the area. With this coverage and a 0.3 absorption probability when phonons are incident on the W films, it takes about eight attempts for each phonon to be absorbed. Most phonons will spread throughout the (1.5 mm)2 crystal. The collection time into the TESs will be about 2–3 ms. We have obtained fall times as short as 7 ms with the optical detectors [2] and here our target is 20 ms, for a count rate of B4 kHz. The Ge crystal substrate is isolated from the remaining Ge substrate with a SiN membrane to prevent escape of athermal phonons. In order to obtain the highest resolutions we adjust the total area of the 4 TES sensors for a saturation energy B10% above 7 keV. The design allows simultaneous x and y position determination of individual events. The segments for each channel are connected electrically in
Fig. 1. Schematic diagram of chip design. The inner black square is the edge of the (1.5 mm)2 absorber. The region between the two black squares is etched through the entire 300 mm thick wafer and suspended with 1 mm thick SiN. Each of the four channels (shadings) is wired in parallel. The wiring layer goes along the diagonals and requires no crossovers within the absorber area.
ARTICLE IN PRESS 504
B. Cabrera et al. / Nuclear Instruments and Methods in Physics Research A 520 (2004) 502–504
Fig. 2. One dimensional energy distribution at each of eight TES sub-elements for 4 different event locations (5–8 symmetric to 1–4).
parallel using 2 mm wide Al/W rails—a photolithographic technology well developed for optical detectors [2]. Here we demonstrate a linear position response along one axis, with a 1D Monte Carlo calculation. Fig. 2 shows the total energy collected in each of 8 sub-elements of two combined TES sensors, which together form a uniform area coverage all along the length of the detector. We have one degree of freedom left, which is the percentage of each sub-element connected to one versus the other TES. In Fig. 3, we calculate the total energy absorbed in left most of the two TESs for two different sensor distributions. The first is the standard 100% fill of half the subelements by each TES, producing the nonlinear ‘‘S’’ shaped response curve. To improve the linearity in the second example, each TES is distributed all along the detector length, with one TES concentrated towards one end and tapering off towards the other end, and the other TES done symmetrically the other way. A linear response is evident with this distributed TES. In conclusion, for applications requiring mm scale pixels, an effective 2D array of pixels can be obtained in a phonon-mediated Ge absorber using four distributed TES sensors. The position response can be made linear, and simultaneously the
Fig. 3. Comparison of total energy absorbed in left most TES for two different sensor distributions, one for side by side sensors and the second for the new distributed sensor designed to linearize and homogenize the response across the crystal absorber.
variations in pulse shape can be made very small. Before a practical detector can be made, however, we must demonstrate both the full collection of electron-hole potential energy from Ge, and 20 ms recovery times.
Acknowledgements This research was supported in part by the Department of Energy under Grant No. DEFG03-90ER40569, and by NASA Grants NAG53775 and NAG5-3263. RAS & DMG were supported by the Lockheed Martin Independent Research Program.
References [1] J.T. Mariska, G.A. Doschek, Astrophys. J. 485 (1997) 904. [2] A.J. Miller, B. Cabrera, R.M. Clarke, E. FigueroaFeliciano, S. Nam, R.W. Romani, IEEE Trans. Appl. Supercond. 9 (1999) 4205. [3] T. Shutt, J. Emes, E.E. Haller, J. Hellmig, B. Sadoulet, D. Seitz, B.A. Young, S. White, LTD8, Nucl. Instr. and Meth. A 444 (2000) 340.