Dan Swetz Quantum Sensors Group NIST Boulder, CO

1. Characterization of noise and transition shapes in superconducting transition-edge sensors using a pulsed laser diode Dan Swetz Quantum Sensors Group NIST Boulder, CO Joel Ullom Doug Bennett Randy Doriese Gene Hilton Kent Irwin Carl Reintsema Dan Schmidt

2. How to Characterize TESs? RSh RN n TC GTES CTES α β ΔE Parameters: IV vsTbath Power Law Fits Complex Z Pulses Noise Measurements: 1-Body Model 2-Body Model Models: M G2-Body C2-Body New Parameters: Goal: Develop a systematic way to combine TES measurements and optimally constrain TES models Only when we understand out detectors can we predict their behavior and optimize their performance

3. The Diode Laser: A new tool for X-ray TES characterization Vacuum Jacket 1550 nm laser: • 0.8 eV/photon (1 keV pulse = 1,200 photons) • Computer controlled Laser Variable Attenuator 3K Cold Attenuator Fiber Ferrule Flange Detector 50 mK box Collimator

4. New Capabilities using Laser Pulses Pulse Response above TC • Pulses on demand • Many trigger options • Large range of possible energies • Reliable low energy pulses 10,000 averaged pulses -8 -10 Log Detector Response (V) -12 -14 2 4 6 8 10 12 14 16 Time (ms) Detector Response vs Pulse Energy Detector Linearity 30 40 30 20 Detector Response (mV) Pulse Peak (mV) 20 10 10 0 0 0 1 2 3 4 5 0 2 4 6 8 10 12 14 Time (ms) Pulse Energy (keV)

5. The Test Detector 600 mm • 350 μm square Mo/Cu bilayer • 0.1 μm-thick Mo • 0.2 μm-thick Cu • 7 interdigitated normal Cu bars • 0.5 μm thick • 90% TES length • bismuth film absorber • 1.5 μm thick • 600 μm SiN frame • 0.5 μmthick • Overlapping perforations in SiN membrane to control GTES 350 mm Current Goal: An optimized TES for materials analysis at 7 keV* perforations Interdigitated normal bars * Doriese 1EX07

6. TES Modeling and Characterization Simple TES Hypothesis: SiN is adding a dangling 2nd body Estimate from geometry*: Cdangling ~ 0.1 pJ/K, ~ 5% of CTES Questions: Are TESs 1-body (simple) or 2-body (dangling) ? What are the effects on parameters? Can the dangling body explain (part of) the unexplained excess high-frequency noise? Dangling TES * K. Rostem, et. al, Proc. SPIE, 7020, 70200L (2008)

7. RSh Parameter Extraction Methodology RN SC Noise IV vsTbath Power Law Fits Pulses above Tc n TC RSh 260 uΩ RN 10.7 mΩ n 3.3 TC 109 mK GTES 118 pW/K CTES 1.7 pJ/K GTES CTES β Cdangling Gdangling α M ΔE

8. RSh Parameter Extraction Methodology RN SC Noise IV vsTbath Power Law Fits Pulses above Tc n TC RSh 260 uΩ RN 10.7 mΩ n 3.3 TC 109 mK GTES 118 pW/K CTES 1.7 pJ/K GTES Measurements at 10—80 % bias of Rnormal in steps of 10% CTES Complex Z β Pulses Noise β Cdangling Gdangling α M ΔE

9. RSh Parameter Extraction Methodology RN SC Noise IV vsTbath Power Law Fits Pulses above Tc n TC RSh 260 uΩ RN 10.7 mΩ n 3.3 TC 109 mK GTES 118 pW/K CTES 1.7 pJ/K GTES Measurements at 10—80 % bias of Rnormal in steps of 10% CTES Complex Za β Pulsesb β Cdangling Gdangling Cdangling GoF CZ αCZ αpulse GoF pulse Dangling Model Gdangling F α Goodness of Fit Phase Space M ΔE • a) Bennett et. al., Proc. AIP, vol. 1185. pp 737-40, (2009) b) Bennett et. al., APL submitted (2010)

10. RSh Parameter Extraction Methodology RN SC Noise IV vsTbath Power Law Fits Pulses above Tc n TC RSh 260 uΩ RN 10.7 mΩ n 3.3 TC 109 mK GTES 118 pW/K CTES 1.7 pJ/K GTES Measurements at 10—80 % bias of Rnormal in steps of 10% CTES Complex Za β Pulsesb β Cdangling Gdangling Cdangling GoF CZ αCZ αpulse GoF pulse Dangling Model Gdangling α Noise Goodness of Fit Phase Space F M M GoF noise ΔE • a) Bennett et. al., Proc. AIP, vol. 1185. pp 737-40, (2009) b) Bennett et. al., APL submitted (2010)

11. RSh Parameter Extraction Methodology RN SC Noise IV vsTbath Power Law Fits Pulses above Tc n TC RSh 260 uΩ RN 10.7 mΩ n 3.3 TC 109 mK GTES 118 pW/K CTES 1.7 pJ/K GTES Measurements at 10—80 % bias of Rnormal in steps of 10% CTES Complex Za β Pulsesb β Cdangling Gdangling Cdangling GoF CZ αCZ αpulse GoF pulse Dangling Model Gdangling α Noise Goodness of Fit Phase Space M ΔE M GoF noise ΔE • a) Bennett et. al., Proc. AIP, vol. 1185. pp 737-40, (2009) b) Bennett et. al., APL submitted (2010)

12. Pulse Fits Good Fit Why 2d GoF phase space? Exclude local minima Poor estimate of error on data • Simple model GoF = 1.58 • Dangling model achieves GoF = 14 • High Cdang, Gdang excluded Bad Fit Departure from simple model at 1.5 ms

13. Goodness of Fit: CZ and Noise Good Fit Good Fit Bad Fit Bad Fit • Simple model noise GoF = 11.3 • Dangling model achieves GoF =24 • Simple model CZ GoF = 4.5 • Dangling model achieves GoF = 6.4 Large parameter space excluded, particularly high Cdang, Gdang regions. Reasonable constraints on both Cdangling and Gdangling

14. α and M are largely unaffected by dangling parameters α M Nearly identical values from CZ fits 1-body model predicts αpulse = 310, αCZ = 314 and M = 1.52 Conclusion: Can estimate using simple model

15. Dangling Body Affects Noise and Energy Resolution ΔE bad fit region M-noise 2.28 eV = Simple model energy resolution 2.34 eV = Simple model with CTES + Cdangling 2.5—3.1eV = Dangling model energy resolution Dangling noise explains increased mid-frequency noise at ~100-1000 Hz Dangling noise degrades resolution by ~ 10--30%

16. Conclusions and Future Plans • Diode laser is a useful tool for device characterization • Device is described by a dangling two-body model • Dangling parameters have minimal affect on alpha and excess noise • Dangling body significantly degrades energy resolution • Repeat analysis on more devices Very preliminary spectrum of Mn Kα Similar 9-bar device ΔEFWHM = 3.64 eV

17. Fin

18. Energy Resolution vs Gdangling Gdangling

19. Pulse FitsEvidence for dangling models • Dangling model fits data well • Requires High S/N – 4000 pulses averaged • Simple model: • overshoots data at early times • undershoots data at late times