Bolometers and the CMB 1 the CMB Spectrum

BolometersCosmic Microwave and the CMB

08/07/2017 Benson | Bolometers and the CMB 1 The CMB Spectrum

10-13 77 K • CMB is a 2.725 K blackbody Rayleigh -14 • Spectrum peaks at ~150 GHz ) 10 30 K

-1 Jeans (RJ)

sr -15 • Conveniently peak of CMB “tail” 15 K -1 10 spectrum is near foreground Hz -16 -2 10 minimum (i.e., dust, synchrotron)

-17 and atmospheric windows

I (W m 10 2.725 K 10-18 • Design detector “bands” to

-19 observed within atmospheric 10 100 1000 10000 windows Freq (GHz) • Aim to design instruments where atmospheric loading dominates detector loading

08/07/2017 Benson | Bolometers and the CMB 2 Power on a Detector

Power = P (⌫)d⌫ = B(⌫,T) f(⌫) A⌦ d⌫ Z Z • B(ν,T) = Blackbody equation = [ W / m2 sr Hz ] • f(ν) = Frequency response of the detector • AΩ = Throughput (or etendue) of instrument = [m2 sr]

08/07/2017 Benson | Bolometers and the CMB 3 Power on a Detector

Power = P (⌫)d⌫ = B(⌫,T) f(⌫) A⌦ d⌫ Z Z • B(ν,T) = Blackbody equation = [ W / m2 sr Hz ] • f(ν) = Frequency response of the detector • AΩ = Throughput (or etendue) of instrument = [m2 sr] 2h⌫3 1 ⌫2 B(⌫,T)= 2k T c2 exp(h⌫/kT ) 1 B c2 RJ • In RJ limit, x = hv/kT << 1 and exp(x) ~ 1 + x, greatly simplifying the black-body equation.

08/07/2017 Benson | Bolometers and the CMB 4 Power on a Detector

• Can approximate frequency response as a band-width (Δν) times an optical efﬁciency (η), e.g., for a top-hat ﬁlter

08/07/2017 Benson | Bolometers and the CMB 5 Power on a Detector

• For a single spatial mode experiment (i.e., with a diffraction limited beam), AΩ = λ2

08/07/2017 Benson | Bolometers and the CMB 6 Power on a Detector

Power = P (⌫)d⌫ = B(⌫,T) f(⌫) A⌦ d⌫ Z Z • B(ν,T) = Blackbody equation = [ W / m2 sr Hz ] • f(ν) = Frequency response of the detector • AΩ = Throughput (or etendue) of instrument = [m2 sr] • Therefore in RJ-limit, this equation reduces to: ⌫2 P =2k T (2)(⌘⌫) RJ B c2 RJ

PRJ =2kBTRJ (⌘⌫)

08/07/2017 Benson | Bolometers and the CMB 7 Power on a Detector

PRJ =2kBTRJ (⌘⌫) • For a typical CMB experiment, one might have:

• TRJ = 20 K • Atmosphere opacity and temperature are about 0.05 and 240 K, respectively. Implies 0.05 x 240 K = 12 K of RJ loading • CMB is 2.73 K • Internal cryostat loading is ~6 K • Band-width of 30 GHz • Efﬁciency of ~0.30 • Note: For loading, the efﬁciency is how much of detector beam’s power ends up on the sky, which includes loss from spillover on optical elements, loss in optics, detectors, atmosphere, etc. (more later this week)

PRJ = 2(1.38e-23)(20 K)(40e9 Hz)(0.3) = 6.5 pW

08/07/2017 Benson | Bolometers and the CMB 8 The Bolometer

A bolometer converts a thermal Radiation (Popt) signal on the detector to an electrical signal, via the thermistor. Absorber (C)

• Popt = [pico-Watts] = The amount of optical / mm-wave power on the detector • C = [J/K] = The heat capacity of the Thermistor bolometer (P ) elec • G = [pW/K] = Thermal conductance to Thermal the heat sink. Link (G) A bolometer typically uses electrical feedback, through the thermistor, to Thermal Bath (Tbath) stabilize Tbolo

08/07/2017 Benson | Bolometers and the CMB 9 The Bolometer Power on the bolometer is the Radiation (Popt) sum of optical and electrical power, that is conducted away through the “G-link

Absorber (C) P = Popt + Pelec

Tbolo = G(T )dT Thermistor ZTbath (Pelec) For an input power, bolometer Thermal heats up and goes down with a Link (G) time constant, tau: T = P/G Thermal Bath (Tbath) ⌧ = C/G

08/07/2017 Benson | Bolometers and the CMB 10 Thermistors: TES, Semiconductors

Al/Ti TES Transition Edge Sensors (TES) • Typically a metal bi-layer, superconducting transition tuned by thickness of normal / dT ~ 10 mK superconducting layers • Typical combinations (e.g., Al/Ti, Mo/Au, Al/Mn, Ti/Au) require ~20-100 nm ﬁlm thickness to achieve transitions of ~500 mK

Thermistor: TES vs NTD Germanium 12 NTD Germanium • TES ~1 Ohm, dR/dT > 0 10

) NTD ~ 2-10 MOhm, dR/dT < 0 8 • Sign of dR/dT determines if current or 6 voltage bias provides negative electrothermal feedback (ETF) 4

Resistance (M • i.e., a change in optical power, causes a change in 2 temperature and resistance, electrical power 2 2 0 changes via Joule heating (Pelec = V /R or I R) 0.30 0.35 0.40 0.45 0.50 0.55 0.60 Temperature (K) 08/07/2017 Benson | Bolometers and the CMB 11 Bolometer Saturation Power (Psat)

Turn around

• The saturation power (Psat) is a critical TES bolometer parameter: • Deﬁned as: the (optical or electrical) power required to drive the TES “normal”

• For noise reasons, typically aim for Psat ~twice the expected optical power • Characterize bolometer I-V and R-P curves, i.e., decrease the voltage bias on the bolometer and measure electrical behavior:

• As Vb decreases, TES will go into superconducting transition and exhibit a “turn- around” in IV curves where loop gain > 1 • Below “turn-around”, TES changes resistance to keep total power constant

Niemack 2008 08/07/2017 Benson | Bolometers and the CMB 12 Thermal Conductance: G(T)

• To characterize thermal-link, Increasing useful to measure Psat as a Tbath function of bath temperature

P = K(T n T n ) Current(uA) sat c bath dP n 1 G (Tc)=nKTc Voltage (uV) ⌘ dT

• For metals, n ~ 3, which shows characteristic inﬂection in P-T curve

Power (pW) Power • G ~ 100 pW/K is typical value (set by desired Tc, Psat)

Temp (K) Marriage 2007 08/07/2017 Benson | Bolometers and the CMB 13 Thermistors: TES, Semiconductors

Al/Ti TES • Electro-thermal Feedback (ETF) acts to keep total power on the bolometer constant 2 via electrical Joule heating (Pelec = V /R): dT ~ 10 mK Tbolo Popt + Pelec = G(T ) dT ZTbase d V 2 P = b dT elec R ✓ ◆ dP P 2 dR elec = elec dT R dT

If dR/dT>0, then dPelec/dT < 0

08/07/2017 Benson | Bolometers and the CMB 14 Electro-Thermal Feedback

Al/Ti TES • Strength of ETF feedback determined by slope of R(T) curve, parameterized by a “loop gain”, in analogy with electronic circuits: dT ~ 10 mK P = elec L P P (dR/R) = elec L GT Pelec↵ T dR = with ↵ L GT ⌘ R dT Resistance Electrical Thermistor (Ohms) Loop Gain NTD ~2-10 M ~1-5 Germanium TES ~1 ~20-1000

08/07/2017 Benson | Bolometers and the CMB 15 Bolometer Responsivity (dI/dP)

Al/Ti TES SI = dI/dPopt =[Amps/W atts] dR dPopt = GdT + Pelec dT ~ 10 mK R P dR d(I = V/R) dI = elec VbR

Plug into equation for Responsivity (SI):

PelecdR/VbR SI = GdT + PelecdR/R P TdR elec VbT RdT T dR SI = with ↵ Pelec TdR G(1 + GT RdT ) ⌘ R dT I 1 S = = L I P V 1+ b L 08/07/2017 Benson | Bolometers and the CMB 16 Loop Gain: Responsivity, Time Constant I 1 Al/Ti TES S = = L I P V 1+ b L dT ~ 10 mK In limit of Loop Gain >> 1, responsivity goes like -1/Vb: • Large loop gain implies a linear detector, i.e., a responsivity independent of loading or depth in the transition Similarly, it can be shown that detector “speeds-up” with increasing loop gain: ⌧ C/G ⌧ = 0 = 1+ 1+ • As detector timeL constant decreases,L its “band-width” increases. • To be stable, need to feed-back electrical signals faster than detector bandwidth.

08/07/2017 Benson | Bolometers and the CMB 17 Thermistors: TES, Semiconductors

Al/Ti TES TES Advantages: 1) Fab - TES’s can be fabricated on bolometer 2) Linearity - Steepness of R(T) curve dT ~ 10 mK determines strength of electrothermal response 3) Microphonics - Low-impedance = low- microphonic response • Shaking wires will cause changing capacitance to ground, large impedance implies low frequency of RC-ﬁlter

12 NTD Germanium 10 Resistance Electrical

) Thermistor

(Ohms) Loop Gain 8 NTD 6 ~2-10 M ~1-5 Germanium 4 TES ~1 ~20-1000 Resistance (M 2 0 0.30 0.35 0.40 0.45 0.50 0.55 0.60 Temperature (K) 08/07/2017 Benson | Bolometers and the CMB 18 SuZIE Bolometers (1992-1997)

Made by UC-Berkeley (1992) JPL (1998) Nylon Threads NbTi Wires

Gold Leads Bi on Sapphire Thermistor

Sapphire Substrate 1 cm

Hand-made bolometers! • Sapphire substrate with 100 nm thick bismuth absorber suspended by nylon threads • NTD Germanium thermistor, bonded to gold wires, epoxied to center • Gold is indium soldered to NbTi wires for readout • Gold wires set heat capacity (C), Nylon threads set thermal conductivity (G) • Cooled to 300 mK • NEP ~ 150 aW / Hz1/2 , Time constant ~ 150 msec 08/07/2017 Benson | Bolometers and the CMB 19 Spiderweb Bolometers (~1996-2003) Jet Propulsion Absorbing SuZIE was the ﬁrst experiment to Lab / JPL (1998) Gold Web use a “spider-web” bolometer! Thermistor • JPL design later used for ACBAR, Boomerang, Planck experiments; UC- Berkeley version used for SPT-SZ

1 cm Incorporated micro-fabrication: • Silicon-nitride (SiN) substrate, 20 nm thick gold (Au) absorber, on silicon wafer • Provides a 20x reduction in heat capacity and cosmic ray cross-section Planck Satellite (2008) • NTD Germanium thermistor indium bump bonded to web • Thermistor dominates heat capacity (C), gold leads set thermal conductivity (G) • NEP ~ 40 aW / Hz1/2 • Time constant ~ 15 msec

15 cm 08/07/2017 Benson | Bolometers and the CMB 20 SPT-SZ Detectors (2003-2009) • Made at UC-Berkeley by Erik Shirokoff, Jared Mehl, Sherry Cho • Copied JPL spider-web absorber design; - suspended 1mm thick Silicon Nitride (SiN) substrate with 12 nm thick Gold (Au) absorber 4 mm • Replaced NTD Germanium with TES bilayer of Aluminum/Titanium (Al/Ti); - Film thickness 40 nm Al, 80 nm Ti, gives a superconducting transition (Tc) of ~ 0.5 K • “G” set by gold ﬁnger to TES Si Al Cross-section m m Ti Au 30 web (Etched Silicon)

Au, G-link SiN 08/07/2017 Benson | Bolometers and the CMB 21 TES Time Constant and Stability • Bolometer has two time constants: 1) Optical time constant: How fast optical power is distributed across the bolometer 2) Electrical time constant: The electrical time constant / response of the TES • Side-TES design was too slow optically: - Optical time constant dominated by thermalization time of the spider-web Side - Changed from optical time constant from 30-40 msec to TES 10 msec by moving TES to center of the web

Center TES 08/07/2017 Benson | Bolometers and the CMB 22 TES Time Constant and Stability But Side-TES design was too fast electrically, TES stability requires: 1) Bandwidth requirement for bolometer stability: TES bandwidth < 5.8 fMUX bandwidth 2) Given fMUX ﬁlter bandwidth, this implies: 0.2 msec < tTES < 5 msec Side 3) TES speeds up as loop gain increases [tTES = t0 / (1 + L)], so assuming L ~ 10-30: TES 6 msec < t0 < 50 msec

Side-TES had a t0 < 0.1 msec! became unstable as soon as TES went into its transition.

Gold Ring added for heat Center capacity to slow down bolometer TES to t0 ~ 20 msec. 08/07/2017 Benson | Bolometers and the CMB 23 Thermal Decoupling of TES R/Rnormal = 0.70 SPT-SZ 2007 focal plane used design with center-TES and gold ring. However, design had additional instability from gold ring decoupling from the TES. Current(arb units)

R/Rnormal = 0.55

Thermal conductivity (G’) TES between gold ring and TES is too small Current(arb units)

R/Rnormal = 0.50 Gold Ring Current(arb units)

Time (msec) 08/07/2017 Benson | Bolometers and the CMB 24 Alternative Gold Coupling Designs

Good Improved TES-Gold Coupling: 1) Centered TES and increased gold connectivity, 2) Al/Ti bi-layer underlies gold, 3) Superconducting “Al” leads were narrowed, 4) Oxide layer cleaned with etch before gold (1) deposition.

Designs that intercepted TES improved thermal coupling to gold, but broadened Good transition and lowered loop gain BAD BAD

(2) (3)

08/07/2017 Benson | Bolometers and the CMB 25 Engineering TES Transition for TES Stability Engineer TES speed and responsivity - Palladium-Gold (PdAu) added head capacity to slow detectors (ala SPT-SZ) R(T) curve: Steeper = Faster, more linear - Tested Nb stripes and dots on TES to Broader = More stable “soften” R(T) curve and add responsivity high in the transition

Stripes Mo/Au PdAu bi-layer “BLING” TES

08/07/201Dots7 Benson | Bolometers and the CMB 26 Series Inductor with TES • A uH inductor in series with the TES can also be used to reduce response at high-frequency, typically used in time-domain SQUID multiplexing systems (more tomorrow)

Niemack 2008 08/07/2017 Benson | Bolometers and the CMB 27 Bolometers circa 2015 (SPT-3G)

Argonne National Lab (2015) mm 3

• Works like your “TV” antenna; • Antenna at center, power sent to 6 superconducting bolometers around perimeter, which measures 3-colors, 2-polarizations per pixel • Used for “SPT-3G” camera, which has 16,000 detectors. • Cooled to 0.3 degrees Kelvin above absolute zero. Bolometers circa 2015 (SPT-3G)

Argonne National Lab (2015) mm 3

• Irwin & Hilton 2005, “Transition Edge Sensors”, https:// link.springer.com/chapter/10.1007/10933596_3 • Zmuidznias & Richards 2004, “Superconducting Detectors and Mixers for mm and sub-mm Astrophysics”, http://www.submm.caltech.edu/ ~jonas/tex/papers/pdf/2004-PIEEE-Zmuidzinas.pdf • Richards 1994, “Bolometers for Infrared and millimeter waves”, http:// www.asiaa.sinica.edu.tw/~ctli/tp/bolometer.pdf • Mather 1982, “Bolometer Noise: Non-equilibrium Theory”, https:// www.osapublishing.org/ao/abstract.cfm?uri=ao-21-6-1125

08/07/2017 Benson | Bolometers and the CMB 30 08/07/2017 Benson | Bolometers and the CMB 31 Polarization Sensitive Bolometers (PSBs)

JPL modiﬁed spider-web concept to add polarization sensitivity • SiN substrate with linear crossed pattern, gold added only along one direction • NTD thermistor on edge of absorber, to minimize cross-polar response • Design used for QUAD, BICEP, Boomerang2k, and Planck experiments • Single-pixel concept needs to be scaled up for ~1000 element focal planes

(gold direction)

08/07/2017 Benson | Bolometers and the CMB 32 SPT-3G detector module assembly at Fermilab Bolometer Thermal Responsivity, SI(w)

Gold Decoupling RLC Filter Improved gold “wafﬂe” design: tTES tGold Cutoff • tGold = C/G ~ 20 msec • Stable up to loop gain ~ 50

Gold-ring

Gold-“waffle” (Red, Blue) TES

Gold Heat Capacity Evolution of Detector Sensitivity The Future CMB science has been driven by advances in detector technology; detector‘Moore’s speed has Law’ ~doubled for every Sensitivity year for 50 years! and Mapping Speed

Photon (“shot”) noise limit from ground-based observations with 0.25 Kelvin detectors BLIP – CMB Ground

BLIP – CMB Space NEP ~ 50 x10-18 W Hz-1/2

Plot from J. Zmuidzinas 08/07/2017 Benson | Bolometers and the CMB 35 ! # " /'(/"3 ,-./,01 %&'#'()* + 2 $ 6

45 ACT BICEP2 EBEX SCUBA2 !"

!"! Observational Cosmology - University of Minnesota SQUID Bolometer Readout Requirements: I I Low input impedance • Φ = nΦ0 Low power dissipation Critical • Current • High bandwidth •~100 MHz 1 Φ = (n + )Φ • Low noise. At 4 K: 2 0 • 3 pA/rtHz • 0.2 nV/rtHz V Implementation: V Lock point • Use DC SQUID as an ammeter (Superconducting Φ/Φ0 0 Quantum Interference 1 2 Device) • Current->Flux->Voltage transducer

08/07/2017 Benson | Bolometers and the CMB 37