X-ray Calorimeters

1. X-ray Calorimeters Caroline K. Stahle NASA / Goddard Space Flight Center

2. Space Astrophysics Detector Development –– 26 - 29 June 2000 • X-ray Calorimeters • Motivation • Foundations (independent of implementation) and unique considerations for x-rays • Ideal calorimeters with resistive thermometers • Performance of real semiconductor and superconductor based calorimeters • Non-resistive calorimeters • Characteristics and performance of magnetic calorimeters • Prospects and summary

3. Motivation ahigh resolution with a non-dispersive x-ray spectrometer • The 0.1 – 10 keV x-ray band corresponds to temperatures from 106 to108 K. At these temperatures the dominant radiation is collisionally-excited characteristic lines of partially ionized heavy elements. These lines provide a wealth of diagnostics on the elemental abundances and physical conditions in the gas, and measurements of Doppler shifts and line widths can give valuable information about the motion. • The good energy resolution of grating spectrometers requires optics with very high angular resolution, but the design of x-ray telescopes has involved a trade-off between angular resolution and collecting area, putting gratings at a sensitivity disadvantage. • Gratings multiplex by dispersing the spectrum across a position sensitive detector, but at the expense of confusion in spectra from spatially extended objects.

4. Direct detection: How is energy measured? Non-equilibrium: The energy produces quantized excitations each with energy much greater than kT. These are counted to determine the energy. Since, invariably, some of the energy goes elsewhere, such as into heat, the ultimate energy resolution is determined by the statistics governing the partition of energy between the system of excited states and everything else. This is how most photon and particle detectors work. Equilibrium: The energy is deposited in an isolated thermal mass and the resulting increase in temperature is measured. At the time of the measurement, all of the deposited energy has become heat and the sensor is in thermal equilibrium. The ultimate energy resolution is determined by how well one can measure this change in temperature against a background of thermodynamically unavoidable temperature fluctuations. THIS IS CALORIMETRY.

5. Calorimetry is OLD! About 150 years ago, James Joule and Julius von Mayer independently determined that HEAT = ENERGY, and calorimetry was born. But, only about 18 years ago, the power of performing calorimetric measurements at very low temperatures (< 0.1 K) was realized, independently, by Harvey Moseley and by Etorre Fiorini and Tapio Niinikoski. This is called MICROCALORIMETRY, or occasionally QUANTUM CALORIMETRY, because of its ability to measure the energy of individual photons or particles with high sensitivity.

6. Basic requirements: • • Low temperature • • Sensitive thermometer • • Thermal link weak enough that the time for restoration of the base temperature is the slowest time constant in the system yet not so weak that the device is made too slow to handle the incident flux. • • Absorber with high cross section yet low heat capacity • • Reproducible and efficient thermalization Types of thermometers: • resistive • capacitive • inductive • paramagnetic • electron tunneling

7. Thermal fluctuation noise = Signal Phonon noise

8. Signal (with thermalization time) Phonon noise White noise

9. How well can a microcalorimeter measure energy? To answer this question, we need to specify the kind of thermometer. The best energy resolution, so far, has been obtained with resistor-based calorimeters, both semiconductor thermistors and superconducting transition-edge sensors. dT ––> dR Sensitivity a = d log R / d log T Considerations for resistive thermometers: • All resistors have Johnson noise. • In order to measure the change in resistance as a change in current or voltage, the sensor must be electrically biased, resulting in Joule heating.

11. Moseley, Mather, and McCammon (1984) worked out the ultimate energy resolution attainable with an ideal resistor-based microcalorimeter. We can understand the basic dependencies simply by understanding how the signal-to-noise and bandwidth change with a, T, and C. This looks a lot like the RMS thermal fluctuation noise! But note, there is no reason why x can’t be < 1!

12. Electrothermal Feedback PJoule = I2R(T) = V2/R(T) For dP/dT < 0 (negative feedback): if dR/dT < 0, we want (nearly) constant current bias. if dR/dT > 0, we want (nearly) constant voltage bias. Negative electrothermal feedback literally speeds up the cooling of a microcalorimeter after an impulse of energy. For sensitive thermistors (large |a|), this can be a very important effect. It doesn’t change the signal-to-noise anywhere, but it does permit pushing the pulse decay times up against the limiting thermalization time, making most efficient use of the available bandwidth.

13. Illustrating effect of extreme electro-thermal feedback Signal Phonon noise Johnson noise

14. Semiconductor thermistors: • ion-implanted Si and neutron transmutation doped (NTD) Ge • doped within the metal-insulator transition • conduction proceeds via thermally activated jumps of isolated charge carriers between impurity levels. The mechanism is called variable range hopping (VRH). The average hopping distance increases as the temperature is lowered, as it becomes more probable for an electron to tunnel further to a site requiring less change in energy than to tunnel to a nearby site with a difference in energy large compared to that available in the spectrum of phonons. In doped crystalline semiconductors, which have a Coulomb gap in the density of states, VRH produces the resistance law:

15. Two non-ideal effects in semiconductor thermistors are the decrease in resistance with increasing bias power even at fixed temperature (non-Ohmic behavior) and excess noise at low frequencies (1/f noise). The former is well-modeled as a hot-electron effect (not yet clear how that conforms with VRH).

16. Absorbers for use with semiconductor thermistors: • low heat capacity (< 0.1 pJ/K if limited to a< 6 and needing few eV resolution) • high Z constituents (for X-ray opacity) • good thermalization Insulators and semiconductors impurity levels in their bandgaps on which electrons can become trapped before thermalizing, leading to incomplete and noisy thermalization Normal metals thermalize well, but the electronic specific heat is prohibitive Narrow gap semiconductors / semimetals (HgTe) thermalize well, but have low Debye temperatures High Z superconductors Thermalization in a superconductor can be delayed by slow quasiparticle recombination times at temperatures far below the critical temperature. One factor in whether a superconductor thermalizes well is how much energy goes into phonons with energy less than the superconducting gap. One expects a greater proportion of sub-gap phonons the lower the Debye temperature. Thus we may have with superconductors the same situation that we have with semiconductors, that good thermalization requires a high specific heat. HgTe and Sn have been good compromises.

17. State of the art in NTD-based x-ray calorimeters: Milan: Sn absorber SAO: Comparable results with similar materials

18. State of the art in astrophysical instrumentation using x-ray calorimeter arrays: XRS (Astro-E) and XQC (sounding rocket) • • micromachined arrays of ion-implanted Si with HgTe absorbers optimized for the 0.3 - 10 keV and < 1 keV x-ray bands respectively • • Goddard 36-pixel array flown on Wisconsin/GSFC XQC sounding rocket experiment, had an energy resolution ranging from 5 to about 12 eV over the 0.05 - 1 keV band. • • Goddard 32-pixelXRSarray: • 8 - 9 eV baseline and low energies • 9 - 10 eV at 3.3 keV • 11 - 12 eV at 5.9 keV

19. The dominant noise term in the XRS devices is excess 1/f noise; however, preliminary results from experiments with a novel implanation procedure indicate that it will soon be possible to combine the advantages of working with silicon for array fabrication with the uniform doping and lower excess noise associated with the NTD thermistors. Diffusing implanted dopants confined in a “silicon-on-insulator” layer has already yielded deeper and more uniform implant density than had previously been possible. Preliminary results from the GSFC/Wisconsin groups show that the excess 1/f noise per volume is at least a factor of 4 better than our current thermistors, and this is just a lower limit.

20. Superconducting Transition-Edge Sensors in Calorimeters What causes the resistance in the transition? • thermal gradient leads to “phase separation” OR • flux flow (e.g. nucleation of phase-slip lines)

21. • TES thermometers provide ~100 times more sensitivity than practical semiconductor thermistors. • Increase a, increase the measurement bandwidth. • Except, this a is only good over a small temperature range. • We need to increase C to stay within the transition. This C is set by a and the required saturation energy. C = E/dT ~ aE/T • Thus we can no longer improve resolution by increasing sensitivity. • For 6 keV x-rays, the predicted resolution works out to be nearly the same as that originally anticipated for semiconductor calorimeters. • But the large heat capacity budget eases absorber selection and has other practical advantages. • And the large a, through electrothermal feedback, permits the falltime to be shortened to match the measurement bandwidth, reducing pile-up • And for lower saturation energies, such as for an optical detector, the full advantage of the higher sensitivity can be exploited K. Irwin (1995)

22. Just as semiconductor-based calorimeters are still being optimized in view of their non-ideal properties, excess noise in TES x-ray calorimeters is presently under investigation: • NIST low G, low bias bolometers show no excess noise • excess current noise seen in “fast” x-ray devices • indication that it results at least in part from the nature and quality of the TES boundary conditions • still a long way away from being able to discuss quantitatively the tradeoffs between resolution and speed

23. 120 100 Instrument Resolution: 2.0  0.1 eV FWHM Al Ka1,2 80 Counts per 0.25 eV bin 450 counts/sec 60 40 Al Ka3,4 20 0 1480 1485 1490 1495 1500 1505 Bismuth absorber Energy (eV) TES Al/Ag bilayer

24. MnKa1 MnKa2 Mo/Cu TES

25. Al Ka1,2 Goddard Mo/Au TES results at different bias points: 2.9 +/- 0.2 eV at 1.5 keV and 3.6 +/- 0.1 eV at 3.3 keV. Al Ka3,4 K Ka1,2

26. Thermometers not based on changing resistance: • no dissipation, but also no electrothermal feedback • no Johnson noise tied directly to the thermometric property of the sensor • Paramagnetic calorimeters (< 1eV resolution at 6 keV predicted) • spin system of isolated ions of d and f transition elements in a non-magnetic matrix. • in a weak magnetic field there exists a small Zeeman splitting between the spin-up and spin-down energy states, thus atemperature change results in a change in magnetization, which can be sensed by a SQUID • metallic matrix provides best coupling of phonons to spins, at expense of exchange interaction between spins • • because the sensitivity increases with the heat capacity of the spin system, the predicted resolution of an optimized magnetic calorimeter degrades more slowly with heat capacity than resistive calorimeters • • What ends up being the bandwidth limiting noise without Johnson noise? SQUID noise, pick-up from Johnson noise currents in absorber and nearby metal, phonon noise between weakly coupled systems

27. Au:Er Heidelberg/Brown 13 eV FWHM at 5.9 keV

28. Overview and Prospects: • 18 years ago, the potential advantages of calorimetric measurement of astrophysical x-ray spectra were first realized. • In that time we have moved from proofs-of-concept to space-flight instruments and from ideal theoretical detectors to a better understanding of the additional characteristics not present in the ideal detector models. • The loss of Astro-E has delayed the start of the era of high-resolution, high-efficiency, astrophysical x-ray spectroscopy. The questions Astro-E would have answered are now differed to future microcalorimeter-based missions. • Demonstrations of next-generation microcalorimeters and novel arraying schemes bode well for mission concepts such as Constellation-X and XEUS.