Low-Temperature Detector Tutorial: Development and Physics

1. Low-Temperature Detector Tutorial: Development and Physics Caroline Kilbourne NASA Goddard Space Flight Center

2. Preamble (scope and apologies) • Tutorials have opened many LTD workshops • I have some tough acts to follow! • Self-defined scope • Fundamental operating principles of low temperature detectors • of the class • of the principal examples • Real-life effects that have made life interesting • Out of scope • Mention of every type of LTD ever (or even currently) made • A complete history of every type of LTD that I do mention • Overview of all the applications • Overview of the latest and greatest results SORRY…. I’m in spaceflight-project mode (XRISM/Resolve) right now. I don’t even know the latest TES results of my own group!

3. Outline • What are low-temperature detectors? • Back to basics: equilibrium and non-equilibrium measurement of energy and power • Definitions and high-level comparison • Pair-breaking non-equilibrium detectors • Principles • Using superconductors • Thermal equilibrium detectors • Principles • Self-contained performance calculations • Coupling • Closing remarks • Closing remarks

4. What are low-temperature detectors? • LTD workshop started in 1987 as a workshop on "low temperature detectors for neutrinos and dark matter". • From the introduction to the proceedings: "The experimental investigation of these phenomena is difficult and involves unconventional techniques. These are presently under development, and bring together such seemingly disparate disciplines as astrophysics and elementary particle physics on the one hand and superconductivity and solid-state physics on the other." • Still basically true today, except we've added many more disciplines to the motivation side, and added signal processing and systems integration to the other side. “Neutrinos and dark matter" got dropped from the workshop name starting with LTD-5, in 1993. • Developers of LTDs are all interested in making measurements with unprecedented sensitivity and have realized that operating at low temperatures is required, independent of the specific sensor technology. (If it’s cold enough to talk about making a sensitive measurement of energy or power, then it’s cold enough to be an LTD.)

5. Sensitive measurements of energy and power • MEASURING ENERGY (figure of merit: energy resolution) • Impulse of time scale much shorter than measurement time • Photons • Other particles • MEASURING DOSE (figure of merit: energy resolution) • Total energy deposited over a designated integration time or from a particular phenomenon • MEASURING POWER (figure of merit: noise-equivalent power) • Energy per unit time (by definition) • Carriers of that energy not individually resolved I’m mainly going to be talking about measuring quanta of energy, as that is my background, but I will highlight implications for power measurement at several points.

6. Equilibrium and non-equilibrium methods of energy detection Non-equilibrium: • Absorbed energy goes into quantized excitations. • Each excitation has energy much greater than kT. • These excitations are then “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. • In order to improve the resolution by improving the measurement statistics, a large number of low-energy excitation quanta is required. • This, in turn, requires low-temperature operation.

7. Equilibrium and non-equilibrium methods of energy detection 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 distribution of energy in the sensor can be described by a temperature. • The ultimate energy resolution is determined by how well one can measure this change in temperature against a background of thermodynamically unavoidable temperature fluctuations. • Low-temperature operation is required in order to minimize these thermodynamic energy fluctuations. About 150 years ago, James Joule and Julius von Mayer independently determined that HEAT = ENERGY, and calorimetry was invented.

8. Superficial comparison of equilibrium or non-equilibrium scheme • Detectors based on the non-equilibrium scheme can be made faster before sacrificing resolving power. They are less sensitive to the stability of the heat-sink temperature. • Detectors based on the equilibrium scheme can achieve the best energy resolution at a given temperature in a small (low heat capacity) device, especially at higher energies. • Either way, if high spectral resolution or power sensitivity is the primary driver, low-temperature operation is required. Combining equilibrium and non-equilibrium • Some macro-bolometers are non-equilibrium/equilibrium hybrids that use the ratio of the signals in the two types as a background discriminator • In the next talk, Andrea will address massive LTDs in greater detail, so I won’t cover them here.

9. Use of superconductors to increase number of excitation quanta • For Si, Egap = 1.2 eV, but only 1/3 of the incident energy does into breaking pairs. The resolution is fundamentally limited to ~120 eV at 6 keV. For small gap semiconductors, an even smaller fraction of the energy goes into pair breaking. • f = “Fano factor” ~ 0.12 in Si. • The gaps of many superconductors are < 1 meV. Thus superconducting pair-breaking detectors can provide 3 – 4 orders of magnitude more excitations than semiconductors, presuming most of the energy goes into pair breaking. • As with electron-hole pairs in semiconductor ionization detectors, the resolution in superconducting non-equilibrium detectors is fundamentally limited by random fluctuation in the number of pairs generated.

10. Pair-breaking cascade • Incoming energy transferred to a single electron • Initial energetic electron loses energy to high-energy quasiparticles and phonons • Ideally, the phonons break more pairs, and the quasiparticles relax down to the energy gap D, with the energy lost mostly going into breaking more Cooper pairs • The partition of energy at the time of measurement depends on the density of phonon states with E < 2D (and thus on both the transition temperature and the Debye temperature), as well as interaction cross sections and device details affecting diffusion, trapping, and recombination. • see e.g. A Zehnder PRB 52, 12858 (1995); AG Kozorezov et al, PRB 61, 11807 (2000). • As with semiconductors, a sizable fraction of the energy goes into heat and is undetected, but the effect is not large enough to null out the starting advantage Lerch and Zehnder, in Cryogenic Particle Detectors

11. Measuring the pair-breaking as quasiparticle current • In semiconductors, a voltage is used to collect the charges • Obviously can’t do that in a superconductor; must let the quasiparticles drift • Use of thin insulating barrier with bias < 2D • Makes drifting in one direction more probable than the other • Use of a smaller-gap superconductor in the vicinity of the junction used to trap quasiparticles [NE Booth, APL 50, 293 (1987)] • Increases tunneling rate • Can result in quasiparticle multiplication • Pair breaking in small gap region by relaxation phonons from large gap • Enhanced back tunneling [DJ Goldie, et al., APL 64, 3169 (1994)] • Multiplication improves sensitivity if otherwise amplifier-noise limited, but multiplication processes increase variability in the number of excitations

12. Measuring the pair-breaking via change in kinetic inductance • The kinetic inductance results from the inertia of the Cooper pairs and increases as the Cooper-pair density decreases. • Microwave Kinetic Inductance Detectors (MKIDs) measure shift in complex impedance in microwave resonators • Same basic generation-recombination limits as tunnel junctions • Microwave readout enables scale up to very large arrays PK Day, Nature, 425, 817 (2003)

13. Non-equilibrium devices for power measurement • Non-equilibrium sensors will have a long-wavelength cut-off related to the energy of the excitations they produce and their operating temperature. This is independent of the incident power level. • E.g. HgCdTe detectors operating at 77 K rapidly degrade in performance as the wavelength is increased above 10 mm. [PL Richards, PAJ 76, 1, (1994)]

14. Equilibrium measurements • What is the fundamental limit on our knowledge of the temperature? • What is the fundamental limit on our knowledge of a change in the temperature? • System in thermodynamic equilibrium, defined by temperature, T System with heat capacity C, in thermodynamic equilibrium with infinite heat sink defined by temperature, T T

15. Thermal fluctuations – the “thermodynamic limit” • Canonical ensemble: • System in thermodynamic equilibrium, defined by temperature, T • System consists of energy states, each with probability, pn, proportional to • exp(-En/kT) • Can calculate average energy, <E>, average E2, and thus rms energy fluctuation. C is heat capacity, dE/dT. • But this is not the limiting energy resolution in an equilibrium measurement!

16. Equilibrium measurements: microcalorimeter/bolometer basics • Thermometers can be based on: resistance, capacitance, inductance, paramagnetism, electron tunneling, thermoelectric effect … • Because, in the ideal case, the dominant noise term has the same power spectrum as the signal, the measurement accuracy is controlled by the bandwidth of the measurement, which is typically set by other noise terms that dominate at high frequencies and by the detector response

17. Impulse response Time domain Frequency domain Microcalorimeter/bolometer basics Power response (both into absorber and across thermal link) To constant power Frequency response (complex); (magnitude) energy or power (E, P) absorber C thermometer thermal link G heat sink T Without feedback

18. Signal (e.g. V) Temperature fluctuations in signal units (e.g. V/sqrt(Hz)) due to thermodynamic power fluctuations of spectral density Signal/noise would be frequency-independent!

19. In reality, thermalization times or other noise will limit the high-S/N bandwidth

20. A few words about power measurement before drilling deeper into energy resolution • Responsivity to input power is equivalent of “signal” spectrum for energy impulse • Input power of an impulse contains equal power at all frequencies • But the frequency content of incident radiated power is not flat • Input modulated, thus measurement bandwidth for power is more limited • Fundamental limit in power measurement is photon-noise limit due to the statistics of the quanta that carry the power

21. Impacts on energy resolution (one variable at a time) (1) • Increasing sensitivity: increases both signal and transduced thermal noise, increasing the bandwidth. Roll off ~ 1/w, so S/N scales as sqrt of sensitivity • To benefit from increased sensitivity, need to be able to read out these higher frequencies, or to reduce the roll-off frequency • If fixed noise > thermal noise, S/N scales with sensitivity until thermal noise dominates • Reducing C (but keeping t fixed): same as increasing sensitivity, so S/N scales as 1/sqrt(C)

22. Impacts on energy resolution (one variable at a time) (2) • Reducing G (but keeping C and sensitivity fixed): • the roll off occurs at lower frequency (scales with G) • the responsivity below the roll off scales as 1/G • the thermal noise power scales as sqrt(G), but in signal units, because of the change in responsivity, it scales as sqrt(1/G) • S/N per unit frequency scales as sqrt(1/G) • bandwidth scales as sqrt(G) • From changed thermal noise level and roll-off • thus integrated S/N scales as 1/G0.25. Note Fourier transform scaling: if x(t) → X(w), then x(at) → X(w/a)/|a|

23. Calculating expected energy resolution (1) • A fundamental limit on the energy resolution can be calculated for cases in which the thermal fluctuation noise is the dominant noise term at low frequencies, and the noise term that sets the bandwidth is also intrinsic to the detector (thus above amplifier or environmental noise terms). • For an ideal resistive thermometer • the intrinsic band-limiting noise is Johnson noise • dissipation of read-out power leads to the concept of an optimal operating temperature, which changes the scaling of S/N with G • Need to apply current (voltage) to the thermistor to read the resistance change as a voltage (current) • The higher the bias, the higher the signal and thermal noise relative to the Johnson noise, but also the higher the temperature of the decoupled sensor • Decreasing G requires reducing the bias power to reach the target operating T. The responsivity scales as sqrt(G); this combined with the changes in thermal noise level results in a reduction in the bandwidth scaling with G, completely offsetting the increase in S/N per unit frequency that comes from the lower G • Thus, for ideal thermistors, resolution is independent of G.

24. Reduce G by factor of 10 S/N increases by factor of sqrt(10) Bandwidth decreases by factor of 10 S/N * sqrt(BW) doesn’t change

25. Calculating expected energy resolution (continued) • For an ideal resistive thermometer • Johnson voltage noise scales as sqrt(R), but when current bias is adjusted to reach the target T, responsivity in volts also scales as sqrt(R). • Equivalent argument for voltage bias and signal current. • Thus for ideal thermistors, resolution is independent of R. • As long as Johnson noise remains much higher than read-out noise Types of resistive sensors • Semiconductors • Ion-implanted Si and neutron-transmutation-doped (NTD) Ge • Thermally activated hopping of carriers between isolated states results in steeply increasing resistance with decreasing temperature • Superconducting Transition-Edge Sensors (TES) • Resistance rises sharply from superconducting to normal state • Sensitive thermometer within that transition • Superconductor/normal bilayers used to create lower temperature transitions

26. Resistive thermometers

27. About that optimal bias • Given a practical heat-sink temperature and thermistor, we can ask what bias gives the best resolution in the ideal case • Given a TES with a certain Tc, obviously that’s its optimal bias temperature (neglecting current dependence), and the lowest practical heat sink temperature is the best choice • But starting with a heat-sink temperature, we can determine the optimal Tc to aim for • Nonetheless, there is a practical reason to bias higher than this ideal-case optimum • Increasing the strength of the electrothermal feedback • Reducing the impact of temperature instability of the heat sink

28. P sink 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. • ETF reduces the thermal noise, Johnson noise, and signal at low-frequencies, which results in pushing the roll-off frequency close to the high-S/N bandwidth. • ETF also improves stability, allowing stable operation in the superconducting transition. [KD Irwin, APL, 66, 1998 (1995)] I V V2/R(T) TES Heat Sink

29. Calculating expected energy resolution (2) • A fundamental limit on the energy resolution can be calculated for cases in which the thermal fluctuation noise is the dominant noise term at low frequencies, and the noise term that sets the bandwidth is also intrinsic to the detector (thus above amplifier or environmental noise terms). • For an ideal paramagnetic thermometer • The intrinsic band-limiting noise is the thermal fluctuation noise from energy exchange between the spin and electron systems. • Similar to case of changing G in generic calorimeter, but in this case one can specify the t of both sensor-to-heat-sink and the internal links. • The integrated S/N scales, not just as 1/G0.25, but as (t1 /t0) 0.25, where t1 and t0 are the external and internal time constants, respectively. A Fleischmann, et al., RSI, 74, 3947 (2003)

30. More about inductive thermometers • No heat dissipated • could be real advantage over resistive calorimeters for large arrays • but dissipation allows electrothermal feedback, which stabilizes the operating temperature, relaxing temperature stability required at heat sink

31. Coupling in the signal: absorbers, lenses, and antennae Example: absorbers for calorimeters • Low specific heat • High absorption of photons (particles) to be sensed • Good thermalization • Energy lost or trapped before it can become heat will not be measured. If the amount lost is not always the same, the energy resolution will be degraded. • The time required for the whole absorber to reach the same temperature must be faster than the time for the heat to flow from the absorber to the thermometer, or the signal will depend on the location of energy deposition • Decoupling the absorber to allow it to equilibrate makes the signal roll off faster than the thermal fluctuation noise to the heat sink and introduces thermal fluctuations between the absorber and the thermometer. • There is no single ideal absorber material. We need to balance heat capacity, absorption efficiency, and thermalization according to the needs of the experiment. • The thermometer is not necessarily well suited for collecting the signal. Thus absorbers, lenses, or antennae are used to couple the signal.

32. A sensitive detector can see thermalization non-uniformity Low-energy shoulder and slow secondary time constant were recently found to correlate with surface discoloration on recently tested HgTe. Such non-Gaussian response would need to be calibrated.

33. A sensitive detector can see thermalization non-uniformity CAUTION: NON-IDEAL EFFECT Low-energy shoulder and slow secondary time constant were recently found to correlate with surface discoloration on recently tested HgTe. Such non-Gaussian response would need to be calibrated.

34. A sensitive detector can see thermalization non-uniformity CAUTION: NON-IDEAL EFFECT (oops!) Low-energy shoulder and slow secondary time constant were recently found to correlate with surface discoloration on recently tested HgTe. Such non-Gaussian response would need to be calibrated.

35. Ideal devices are lovely; reality is more complicated • Non-linearity • Particularly interesting for TESs, due to limited dynamic range and voltage bias • Additional sources of noise, both intrinsic, environmental, and associated with the read out • Equilibrium devices often need complicated thermal models with multiple disconnected thermal masses. • Non-equilibrium devices with thermal elements • Thermal MKIDs • Equilibrium devices with non-equilibrium features • Position sensitive calorimeters • Issues with arraying • Crosstalk • Gradients • Not to mention uniformity, reproducibility, interconnects…

36. I look forward to hearing about the great performance of the latest non-idealdevices, and all the applications that are benefiting from using them!