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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 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] • 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 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] • 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 (λ2)(⌘∆⌫) 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) • 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 δP = − elec L δP P (dR/R) = elec L GδT 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 δI 1 S = = − L I δP V 1+ b L 08/07/2017 Benson | Bolometers and the CMB 16 Loop Gain: Responsivity, Time Constant δI 1 Al/Ti TES S = = − L I δP 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);
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