Chapter 7 Superconducting Photon and Particle Detectors · 2013-06-12 · 7 Superconducting Photon...

Chapter 7

Superconducting Photon and

Particle Detectors

AS-Chap. 7 - 2

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3) detector

class range signal

frequency fs (Hz)

wavelength l (mm)

example detection mechanism

modulation low fre-quency – microwave

< 1012 >1000 heterodyne detector coherent

direct detector incoherent

thermal infrared 1011 – 1015

1 – 1000 bolometers, antenna-coupled microcalorimeters

incoherent

photon visible, UV, x-ray

> 1014 < 1 STJDs, micro-calorimeters

incoherent

7 Superconducting Photon and Particle Detectors

• already discussed: sensitive magnetic flux detectors: SQUIDs

• now: sensitive detectors for em radiation and particles

• detection principle for em radiation:

coherent incoherent

classification of detectors/sensors

AS-Chap. 7 - 3

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1. modulation detector: - fast enough to follow the incoming electromagnetic signal directly low-freuqency up to microwave regime

2. thermal detector: - too slow to follow the incoming electromagnetic signal directly - measures absorbed power ∝ photon flux (photons/s) by sensitive thermometer - cannot resolve a single photon THz, far-infrared and infrared regime

3. single photon or particle detector: - is sensitive enough to measure the energy of a single absorbed photon/particle - does not measure absorbed power ∝ photon flux (photons/s) but the energy of a single photon/particle visible, UV and x-ray regime

transition between 2. and 3. depends on detector sensitivity and ranges between the near infrared and visible regime for the best detectors


AS-Chap. 7 - 4

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SIS-mixers HEMT transition edge sensor

(TES) bolometers, hot electron bolometers

superconducting tunnel junction detector (STJD)

limiting noise: quantum fluctuations:

𝑇𝑁𝑞= ℎ𝑓/2𝑘𝐵

limiting noise: phonon fluctuations:

NEP ∝ 4𝑘𝐵𝑇2𝐺

limiting noise: counting statistics:

NEP ∝ 2𝑒𝐼dark

detectors

coherent incoherent

mixers amplifiers bolometers, calorimeters

photo-conductors

direct detectors

AS-Chap. 7 - 6

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• heterodyne receivers are modulation detector

7.1 Superconducting µw Detectors: Heterodyne Receivers

• broad field of applications: - telecommunication systems (radio, mobile phones, …..) - microwave instrumentation

- radio-astronomy: receivers based on superconducting mixers

• principle of operation: - microwave signal 𝑓𝑠 mixed with local oscillator signal 𝑓𝑙𝑜

- amplification of intermediate frequancy signal 𝑓𝐼𝐹 = 𝑓𝑠 − 𝑓𝑙𝑜

- heterodyne receiver: 𝑓𝑠 ≠ 𝑓𝑙𝑜

homodyne receiver: 𝑓𝑠 = 𝑓𝑙𝑜

AS-Chap. 7 - 7

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• Noise Equivalent Power - NEP: - equivalent signal power resulting in a signal-to-noise ratio (SNR) of 1 - SNR > 1 required to detect a signal

NEP is the smallest signal power within bandwidth B of 1 Hz that can be detected

7.1.1 Noise Equivalent Power and Noise Temperature

• definition of important quantities:

• Noise Temperature TN:

𝑘𝐵𝑇𝑁 =𝑃

𝐵=

NEP

𝐵 ⇒ 𝑇𝑁 =

𝑃

𝑘𝐵 𝐵=

NEP

𝑘𝐵 𝐵 (𝑃 = power, 𝐵 = bandwidth)

example: - detector with incident power Ps generating a detector current Is

- current noise power spectral density: 𝑆𝐼 𝑓 = Δ𝐼2 /𝐵

noise current Δ𝐼 per 𝐵 power to current conversion

AS-Chap. 7 - 8

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• Quantum Limit: - in the ideal case the noise temperature 𝑇𝑁 is limited only by quantum fluctuations

7.1.1 Noise Equivalent Power and Noise Temperature

- average energy of a harmonic oscillator at temperature T:

- at T = 0: ground state energy equivalent noise power

quantum limit of noise temperature

≈ 2.5 K @ 100 GHz

quantum fluctuations

AS-Chap. 7 - 9

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7.1.2 Operation Principle of Mixers

• problem: - detect/amplify a signal at very high frequency 𝑓𝑠 - no low noise detector/amplifier available at this frequency

• solution: - down-convert the signal to a much lower frequency 𝑓𝐼𝐹 = 𝑓𝑠 − 𝑓𝑙𝑜 by superimposing it with a local oscillator signal on a nonlinear device/circuit mixer

• block diagram of a heterodyne receiver with a backend filter spectrometer

mixer = nonlinear circuit

AS-Chap. 7 - 10

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• simplest mixer model: the switch

- signal at: 𝑓𝐼𝐹 = 𝑓𝑠 − 𝑓𝑙𝑜 - cf. stroboscopic illumination

• Josephson junction as fast switch:

nonlinear quasiparticle IVC SIS mixer


AS-Chap. 7 - 11

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3) - we assume two sinusoidal voltages at the mixer input (signal and local oscillator):

- we form product of 𝑉𝑠 and 𝑉𝑙𝑜:

- how to achieve the multiplication? use nonlinear IVC of mixer we develop current response into Taylor series:

for V 𝑡 ∝ cos𝜔𝑡:

𝑉2 ∝ cos2𝜔𝑠𝑡 =1

2(1 − cos 2𝜔𝑠𝑡), 𝑉

3 → 3𝜔𝑠-term, …


• mathematical description of a mixer:

usually not used since sum frequency is very high IF frequency

AS-Chap. 7 - 12

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- mixer input: 𝑉 = 𝑉𝑠 + 𝑉𝑙𝑜 = 𝑎𝑠 cos𝜔𝑠𝑡 + 𝑎𝑙𝑜 cos𝜔𝑙𝑜𝑡 quadratic term 𝑉𝑠 + 𝑉𝑙𝑜2

AS-Chap. 7 - 13

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prefactor of 𝑉2-term should be large large nonlinearity !


spectrum of I(t)

in most cases not used

• schematics of a mixer

I(w)

mixer

Vs

Vlo

I0

AS-Chap. 7 - 14

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7.1.3 Noise Temperature of Heterodyne Receivers

• Dicke radiometer equation for minimal detectable input signal:

noise temperature of the receiver

observation time within bandwidth (signal averaging)

bandwidth

• example:

‐ Δ𝑓 = 1 Hz, 𝜏 = 1 𝑠 ⇒ 𝑇𝑠𝑚𝑖𝑛 = 𝑇𝑁

‐ Δ𝑓 = 1 Hz, 𝜏 < 1 𝑠 ⇒ 𝑇𝑠

𝑚𝑖𝑛 > 𝑇𝑁 we are loosing sensitivity, since Δ𝑓 ⋅ 𝜏 < 1 bandwidth is not large enough for short measuring time

‐ Δ𝑓 = 1 Hz, 𝜏 = 1 𝑠 ⇒ 𝑇𝑠𝑚𝑖𝑛 = 𝑇𝑁

we are gaining sensitivity, since Δ𝑓 ⋅ 𝜏 > 1 measuring time larger than 1/Δ𝑓 signal averaging

AS-Chap. 7 - 15

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• SNR of radiometer:

effective noise temperature 𝑇𝑁eff due

receiver, atmosphere, antenna, …

typically: Tatm + Tant ≈ 40 – 50 K @ 100 GHz

noise of Schottky diode mixers ≈ 2 000 K @ 690 - 830 GHz better mixers required SIS mixers

• important: gain of a factor two in noise temperature yields a reduction of measuring time by a factor of four

AS-Chap. 7 - 17

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• reduction of atmospheric transmission due to water vapor

atmospheric transmission at APEX, on the Llano de Chajnantor (Chile), for typical values of the precipitable water vapor (pwv).

spectral band passing through the set of filters used in SABOCA, measured at MPIfR, Bonn

AS-Chap. 7 - 18

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The Chajnantor Observatory, a facility operated by the California Institute of Technology (Caltech) in collaboration with the University of Chile and the University of Concepción, is located at an elevation of 5080 meters (16700 feet) in the Andes mountains in northern Chile. The high, dry Chajnantor plateau is one of the best sites in the world for millimeter and submillimeter astronomy.


AS-Chap. 7 - 19

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atmospheric transmission of the 800 GHz window and the coverage of MPIRE


• reduction of atmospheric transmission due to various molecules

AS-Chap. 7 - 20

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photon assisted tunneling:

7.1.4 SIS Quasiparticle Mixers

steps in IVC

AS-Chap. 7 - 21

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• IVCs of Nb/AlOx/Nb SIS mixer (two junctions in series) with the LO on and off - photon step corresponds to LO frequency of 332 GHz - inset: IF output power versus the bias voltage


-8 -4 0 4 8-100

-50

0

50

100

curr

ent

(mA

)

voltage (mV)

0 4 80.0

0.2

0.4

0.6

0.8

1.0

IF o

utp

ut

po

wer

(m

W)

voltage (mV)with LO

without LO

77 K

290 K

LO off

photon step

AS-Chap. 7 - 22

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SIS-mixers: • have conversion gain • can reach quantum limit 𝑇𝑁 = ℏ𝜔/2𝑘𝐵

• low LO power required

calculated optimum

noise temperature 𝑇𝑁𝑜𝑝𝑡


quantum theory of SIS mixers: J.R. Tucker, Quantum limited detection in tunnel junction mixers, IEEE J. Quantum Electron 15, 1234-1258 (1979)

0.1 1 2

101

102

Top

t

N (

K)

fs / f

g

gap frequency: fg = 2𝚫/eh

AS-Chap. 7 - 23

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100 500 1000

0.1

1

5

DSB

no

ise

tem

per

atu

re (

K/G

Hz)

frequency (GHz)

noise temperature of Nb based SIS quasiparticle mixers developed at different laboratories

3 − 5 ℏ𝜔𝑠/𝑘𝐵


SRON Caltech Univ. of Cologne CFA&SMA IRAM NRO NRAO

3h/kB

AS-Chap. 7 - 24

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gap frequencies fg: Nb: 700 GHz NbN: 1.2 THz HTS: several THz ( problem: no sharp QP IVC!)

• frequency limitations:

junction capacitance 𝑪𝑱: tends to short out the high-frequency signal current

embed junctions into tuning circuit compensating for 𝐶𝐽

optimum situation (empirically): 𝜔𝑠𝑅𝑁𝐶𝐽 ≃ 2 − 4

with BCS expression: 𝐽𝑐 =𝜋

4

2Δ

e

1

RNA we obtain (Nb/AlOx/Nb)

𝐽𝑐 ≃𝜋

16

2Δ

𝑒

𝐶

𝐴 𝜔𝑠 ≃ 8 000

A

cm2

50 fF/µm² 500 GHz

small junctions with high Jc

2.9 meV 𝐴 ≃ 1 𝜇𝑚2

𝜔𝑠𝑅𝑁𝐶𝐽 ≃ 2 − 4

AS-Chap. 7 - 25

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high frequency design: - junction size « free-space wavelength, 3 mm @ 100 GHz) - lumped element circuit


AS-Chap. 7 - 26

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AS-Chap. 7 - 27

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The integrated MPIfR/SRON 800 GHz system in the Cassegrain focus cabin of the JCMT.

“With a diameter of 15 m the James Clerk Maxwell Telescope (JCMT) is the largest astronomical telescope in the world designed specifically to operate in the submillimeter wavelength region of the spectrum. The JCMT is used to study our Solar System, interstellar dust and gas, and distant galaxies. It is situated close to the summit of Mauna Kea, Hawaii, at an altitude of 4092m.”


AS-Chap. 7 - 28

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Cologne Observatorium for Submillimeter Astronomy Gornergrat, Zermatt


AS-Chap. 7 - 29

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Fully assembled flight model of the HIFI (Heterodyne Instrument for the Far Infrared: 480-1280 GHz and 1410-1910 GHz) focal plain unit: for each frequency band one mixer for horizontal and one mixer for vertical

polarization processes the signal. One mixer band will operate at a time selected by switching the respective IF-amplifiers to operation (source: SRON, NL, April 2006)


AS-Chap. 7 - 30

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Noise temperature data for HIFI frequency bands (Heterodyne Instrument for the Far Infrared (480-1280 GHz and 1410-1910 GHz). The lower five bands are realized as SIS-mixers. Frequency bands 6L and 6H use HEB devices as mixers. The green line shows the mixer performance baseline. For band 2 the data, acquired in the FPU (filled points) confirm the data, presented in this thesis (open points, compare Fig. 4.29). Source: G. de Lange, SRON, NL


AS-Chap. 7 - 31

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square-law detector: - convert incoming signal power into change of dc current Δ𝐼 - use of QP nonlinearity of SIS junction to rectify the signal

7.2 Superconducting µw Detectors: Direct Detectors

AS-Chap. 7 - 32

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• principle of operation:

- Taylor series:

- input signal:

- dc current response corresponds to time average (classical treatment):

- time average of input power:

Rd = diff. resistance at I0

= numerical factor ≤ 1 (finite absorption thickness, reflectivity, etc.)

- detector efficiency: (power-to-current conversion)

AS-Chap. 7 - 33

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- quantum mechanical treatment:

- sharp onset of qp tunneling current @ 𝑉 = 2Δ/𝑒 for 𝑉0 < 2Δ/𝑒

each photon is transformed into an additional electron tunneling across the barrier

J.R. Tucker and M.J. Feldman, Quantum detection at millimeter wavelength, Rev. Mod. Phys. 57, 1055 (1985).

2 500 A/W @ 100 GHz

replace derivatives in the classical expression by the second difference of the unpumped IVC computed for the three points 𝑉 = 𝑉0 and 𝑉 = 𝑉0 ± ℏ𝜔𝑠/𝑒, divided by the first difference computed between and 𝑉 = 𝑉0 ± ℏ𝜔𝑠/𝑒

AS-Chap. 7 - 34

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7.2.1 NEP of Direct Detectors

• example: SIS direct detector operated at low T Nyquist noise:

shot noise: dominates due to low T and high R

- for 𝐼0 → 0: ≈ 10-22 W/ Hz @ 100 GHz, Ns = 1 and B = 1Hz

𝐼 = 𝑁𝑒𝐵: number of electrons tunneling through barrier per time

- measured values: 10-16 W/ Hz @ few 10 GHz corresponds to Ns ≈ 1014 @ B = 1Hz equivalently ≈ 1014 ph/s for SNR = 1

far from single photon detection

AS-Chap. 7 - 35

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• infrared regime:

detector cannot follow the em signal directly measure average power dissipated by signal: photon flux (photons/s) thermal detector: measure T due to absorbed power

- sensitive thermometer required, eg. transition edge sensor (TES) TES bolometers

7.3 Thermal Detectors

• quasi-thermal detectors:

sometimes thermal equilibrium is not strictly achieved (e.g. electrons not in equilibrium with phonons - use of effective temperature T* (e.g. for electrons)

AS-Chap. 7 - 36

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• incoming radiation power 𝑃𝑠 + thermal background radiation 𝑃𝑏 ≃ 𝑏 𝐴 𝜎 𝑇𝑏4

A = absorber area, b = geometry factor s = 5.67 x 10-8 W/m²K4: Stefan-Boltzmann constant) Tb = background temperature

heat up sensor with heat capacity C and mass M measure 𝛿𝑇 by thermometer

7.3.1 Principle of Thermal Detectors

• loss of absorbed power by radiative emission ≃ 𝑎 𝜖𝐴 𝜎 𝑇4 𝜖 = emissivity, a = geometry factor

direct thermal coupling to heat sink, transferred heat ∝ 𝐺 𝑇 ⋅ 𝛿𝑇 G = thermal conductance [W/K]

fs

incident power Ps

C(T) M

thermometer: T absorber: e

heat sink: TS

G(T)

T0 T0 G(T)

TS

fs

C(T) M

heat sink

AS-Chap. 7 - 37

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𝜏𝑡ℎ = 𝐶/𝐺: thermal time constant large 𝛿𝑇/𝑃𝑠 small G fast detector small C (thin membrane)

T


• heat balance equation:

can be neglected for large Ps

• for time varying field: Ps = P0 + Ps eiwt dc + ac detector response

dc

ac

(Pb and radiative loss neglected)

AS-Chap. 7 - 38

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• antenna-coupled micro-bolometer: - radiation wavelength > absorber size

- collect radiation power by antenna - electric power is dissipated in a few µm- sized thermally active element


Two detector types:

• bolometer: - radiation wavelength << absorber size

- absorbed radiation power is determined by 𝛿𝑇 measurement

- thermometer is a T-dependent resistance

AS-Chap. 7 - 39

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7.3.2 Bolometers: the thermometer

• irradiation temperature rise 𝛿𝑇 resistance change 𝛿𝑅 =𝑑𝑅

𝑑𝑇𝛿𝑇

increase of heat dissipation due to bias current

𝐼2𝛿𝑅 𝑒𝑖𝜔𝑡

• time varying part of heat balance equation (Pb and radiative loss neglected):

R(T) I

Ps

T0

R0

R

T

2DT

2R

0

T0

dR

T Tc0

• Transition Edge Sensor (TES): make use of narrow sc transition large 𝑑𝑅/𝑑𝑇

AS-Chap. 7 - 40

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3) • responsivity S (V/W):

large dR/dT small G and C are required

7.3.2 Bolometers

AS-Chap. 7 - 41

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7.3.2 Bolometers

NEP of 1.6 × 10−16 W/ Hz @ 0.45 K

Transition Edge Sensors (TES) consisting of bilayers of Mo and a Au/Pd alloy, deposited on a SiN membrane

SABOCA ( Submillimeter APEX Bolometer Camera) Max-Planck-Institut für Radioastronomie (MPIfR), Bonn

AS-Chap. 7 - 42

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The Large APEX BOlometer CAmera (LABOCA)

7.3.2 Bolometers

NTD thermistor

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Transition edge sensor (TES) bolometers sense small temperature changes that occur when photons are absorbed and converted to heat. The use of TESs enables

arrays with a much larger number of pixels than is practical with spider-web bolometers. Sustaining its leading role in superconducting TES array technology,

MDL developed and continues to improve a process to create arrays of thousands of TESs with high yield (>90 percent). These arrays are being employed on three

major astrophysics projects, all with the same goal: generating detailed maps of the polarization of the cosmic microwave background (CMB).

7.3.2 Bolometers

AS-Chap. 7 - 44

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Next-Generation CERES Instrument Will Enhance Climate Forecasts MDL is furthering development of the next-generation CERES-C, a continuation of the Earth Radiation Budget Experiment/Clouds and the Earth’s Radiant Energy System (ERBE/CERES)

climatological experiment, to measure both solar-reflected and Earth-emitted radiation from the top of the atmosphere to Earth’s surface. CERES-C requires detectors that are broadband

(absorptivity >90 percent between 0.3–50 µm) with an absorber area of 1.5x1.5 mm, a baseline noise equivalent power (NEP) below 7x10–9 W (goal: 2x10–9 W) between 0.3–30 Hz bandwidth, a

response time between 8–9 ms, a responsivity of at least 65 V/W, and a dynamic range of 0–60 µW. We recently completed a wafer of thermopile detectors and demonstrated that the detectors

exceed all the requirements of CERES-C.

7.3.2 Bolometers

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Noise Equivalent Power (NEP) determined by:

7.3.2 Bolometers

• phonon noise (thermal fluctuations): thermodynamic energy fluctuations in the detector due to the random exchange of phonons (or electrons) through the thermal link

• photon noise (random emission of photons) NEPBLIP (background limited infrared detectors)

plausibility:

- number of phonons in absorber ∼𝐶

𝑘𝐵, phonon energy ∼ 𝑘𝐵𝑇0 Δ𝐸𝑟𝑚𝑠

2 ∼ 𝑘𝐵2𝑇0

2𝑁 = 𝑘𝐵𝑇02𝐶

- ⟨Δ𝑇⟩ =Δ𝐸𝑟𝑚𝑠

𝐶 Δ𝑇2 =

𝑘𝐵𝑇02

𝐶= 𝑆𝑇 𝜔 𝑑𝜔 (𝑆𝑇 𝑓 = Δ𝑇2 𝑓 /𝐵)

AS-Chap. 7 - 46

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• 1/f noise (various sources)

7.3.2 Bolometers

thermal noise dominates for large S, T0, and G

• Nyquist noise (voltage fluctuations in resistor)

- voltage noise power spectral density 𝑆𝑉 = 4𝑘𝐵𝑇𝑅0 V2

Hz

- responsivity 𝑆 𝑉

𝑊

ratio of thermal noise and Nyquist noise

• amplifier noise

AS-Chap. 7 - 47

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T0 , G should be small make response time small, t = C/G C as small as possible

7.3.2 Bolometers

BILP: Background Limited Infrared Photodetector

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high temperature superconductor bolometer

7.3.2 Bolometers

Si

Si3N4

absorber

YBa2Cu3O7 film

• small mass (C), • small thermal coupling to heat sink (G), • sensitive temperature sensor (TES) • broad band absorption (advantage compared to semiconducting sensors)

AS-Chap. 7 - 49

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100

101

102

103

108

109

1010

1011

1012

D*

(cm

Hz1

/2/W

)

wavelength (mm)

HgCdTe

HgCdTe 77 K

InSb PtSi

YBCO/YSZ/Si3N4

YBCO/YSZ/Si

photon noise (300 K, 0.02 sr)

PC PV

specific detectivity 𝐷∗ = 𝐴/NEP vs. Wavelength (𝐴 = detector area)

7.3.2 Bolometers

1012 Hz 1014 Hz

AS-Chap. 7 - 50

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Nonequilibrium Effects: relaxation processes in a superconducting film after absorption of em radiation

𝐺𝑖 = 𝐶𝑖/𝜏𝑖

𝑇𝑒𝑓𝑓𝑒𝑙 depends on PS and Cel

𝑇0 depends on C

7.3.2 Bolometers

• not discussed so far: physics of absorption process and relaxation to thermal equilibrium complex process, only brief qualitative discussion

AS-Chap. 7 - 51

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• far infrared to millimeter radiation long wavelength - radiation collected via antenna

- induced electrical power dissipated in absorber ≪ wave length - keep absorber mass/heat capacity small

- measure 𝛿𝑇 by µm-sized thermometer

7.3.3 Antenna-Coupled Micro-Bolometers

(a) Transition-Edge Micro-bolometers (b) Hot Electron Microbolometer (c) Hot Electron Bolometer Mixer

• main detector types:

absorber/thermometer

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(a) Transition-Edge Micro-bolometers

7.3.3 Antenna-Coupled Micro-bolometers

• example: YBCO transition edge sensor on YSZ membrane - S > 1000 V/W @ 85 K

- NEP ≈ 3 x 10-12 W / Hz - t = 2 µs

AS-Chap. 7 - 53

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Left: 2" silicon wafer after microfabrication of more than a hundered antenna-coupled bolometer devices. Top right: Optical micrograph of niobium bolometer with log spiral antenna for terahertz detection. Bottom right: Measured frequency response of device with log spiral antenna (source: Yale University).

(a) Transition-Edge Micro-bolometers


AS-Chap. 7 - 54

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(b) Hot Electron Micro-bolometer - superconducting antenna + normal metal load of antenna + thermometer - thermometer measures effective T of electron system of normal metal


• very low T operation is advantageous:

efficient thermal decoupling of absorber from environment (thermal conductivity of insulator T3)

e-p scattering time increases 1/T3

electron system decoupled from lattice hot electrons (trapped for long time)

• thermometer: S/I/N junction (N: absorber) - magnitude of QP tunneling current electron T - low NEP and high sensitivity for T ≈ 0.1 K and N volume ≈ 1 µm³

NEP ≈ few 10-18 W / Hz S ≈ few 109 V/W

AS-Chap. 7 - 55

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A scanning electron micrograph of the antenna-coupled Nb bridge bolometer. The inset at upper right shows a detailed image of the feed region taken at a steep angle to show the separation between the bridge and the substrate. The diagram at lower left shows the model used in the theoretical treatment with S indicating the superconducting regions, and the shaded area in the middle of the bridge marking the normal region extending from −𝑙𝑛/2 to +𝑙𝑛/2.

A superconducting antenna-coupled hot-spot microbolometer A. Luukanen and J. P. Pekola, Appl. Phys. Lett. 82, 3970 (2003)

𝑆 = −1430 A/W

NEP = 1.4 × 10−14 W/ Hz @ 4.2 K

AS-Chap. 7 - 56

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Superconducting Hot Spot Micro-bolometer

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A superconducting hot-spot air-bridge bolometer (SHAB) consisting of a niobium (Nb) air bridge (1 μm wide and 15 μm long) suspended between the feed points of a logarithmic spiral antenna. Below the superconducting critical temperature Tc ≈ 8.2 K, a DC current bias produces a normal-state region (called a hot spot), where the local temperature is higher than Tc at the center of the bridge.


M.S. Vitiello et al., "Terahertz quantum cascade lasers with large wall-plug efficiency," Appl. Phys. Lett., 90, 191115 (2007).

AS-Chap. 7 - 58

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(c) Hot Electron Bolometer Mixer

small heat capacity, good thermal coupling short thermal time constant 𝜏𝑡ℎ = 𝐶/𝐺 large 𝑓𝐼𝐹 ∼ 1/𝜏𝑡ℎ possible

mixing up to 𝑓𝑠 > 2Δ/𝑒, i.e. several THz possible low LO power required for 𝑓𝑠 > 2Δ 𝑇 /ℎ no harmonics of signal and LO no magnetic field to suppress SC

7.3.3 Antenna-Coupled Microbolometers

V

I

antenna

phonon escape

superconducting microbridge

quasiparticle diffusion

Ps Plo

AS-Chap. 7 - 59

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• power coupled into the microbridge:

• bolometer cannot follow the fast power variation at 𝑓𝑠 or 𝑓𝑙𝑜, but at 𝑓𝐼𝐹 = 𝑓𝑙𝑜 − 𝑓𝑠 :

• IF voltage amplitude:

S: responsivity

• absorption of photons heating measure 𝜹𝑻 at 𝒇𝑰𝑭 by fast thermometer (𝝉𝒕𝒉 < 𝟏𝒏𝒔) no upper frequency limit by energy gap as for SIS mixers!

• cooling down by: phonon emission (phonon cooling) diffusion of hot electrons (diffusion cooling)


AS-Chap. 7 - 60

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NbN hot electron bolometer mixer (SRON, The Netherlands)


AS-Chap. 7 - 61

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• with increasing quantum energy, the signal due to individual photons may become detectable (e.g. in visible to UV range)

• time interval between single photon events must be larger than detector response time single photon counting possible (photon counting mode) averaging over long time (photon integrating mode)

• if we can resolve the signal height as a function of the photon energy single photon spectroscopy

7.4 SC Particle and Single Photon Detectors

• detector types:

(a) superconducting tunnel junction detector (STJD): non-thermal detector (counting of excess qp generated by single photon)

(b) micro-calorimeter: thermal detector (bolometer with single photon resolution)

• applications:

- e.g. superconducting spectrometers for astronomical imaging (optical to soft x-ray) - particle detectors (electrons, -particles, …

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7.4.1 Thermal Photon and Particle Detectors: Micro-calorimeters

• energy resolution of a detector can be derived from NEP

example: NEP of thermal detectors can be as low as 10-18 W/ Hz if thermal time constant 𝜏 ≈ 1 ms corresponding to B ≈ 1 kHz Δ𝐸 = NEP ⋅ 𝜏 ≈ 10−19 J ≈ 1 eV corresponds to energy of single photon of visible light !!

AS-Chap. 7 - 63

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• incident single photon/particle heats up sensor - thermometer: transition edge bolometer transition edge sensor (TES)

• energy resolution:

with 𝜖 = 1, 𝜏 = 𝐶/𝐺, 𝐵 =1

𝜏 ⇒ Δ𝐸 = NEP ⋅ 𝜏


• dominating NEP at low T: thermal noise

low T0, low C required

example: reduce heat capacity by fabricating thin absorber layers (e.g. Bi, Au) on Si3N4 membrane

AS-Chap. 7 - 65

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- SC: Mo/Cu or Ti/Au: Tc < 1 K - energy resolution few eV - counting rate 1000/s at 1 keV photon energy - collecting area 4 mm2 at T = 0.1K


micrographs curtesy of SRON, The Netherlands

AS-Chap. 7 - 66

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example: - 𝑇0 = 0.1 K - 𝐶 = 10−12 J/K - 𝑉 = 100 µm³ - 𝑐𝑉 = 1 J/m³K

Δ𝐸FWHM ≈ 10 eV

converts from one standard deviation to FWHM

AS-Chap. 7 - 67

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x-ray spectrum of a 55Fe source recorded by Mo/Cu TES energy resolution of 4.5 0.1 eV FWHM @ 5.9 keV photon energy


improved sensors: 2.4 eV FWHM @ 5.9 keV photon energy, 30 times better than Si(Li) semiconductor sensors

AS-Chap. 7 - 68

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• Principle of operation: - incoming radiation generates excess number N of QPs:

measure 𝛿𝐼 of excess QP tunneling current

𝛿𝑄 = 𝛿𝐼 𝑑𝑡 ∝ 𝑁 ∝ 𝐸

• electronic readout:

FET-based charge amplifier

7.4.2 Superconducting Tunnel Junction Photon and Particle Detectors

AS-Chap. 7 - 69

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• energy resolution:

limited by statistical fluctuations of N given by 𝐹 ⋅ 𝑁 (F = Fano factor)


𝜖 = average energy required for a single excess qp F = 1 for Poisson process, Monte Carlo simulations yield F ≈ 0.2

• other noise contributions:

tunneling is statistical

process

inhomogeneities diffusion losses of

qp

amplifier noise

*2.355 = 2 2 ln 2 converts from one standard deviation to FWHM

AS-Chap. 7 - 70

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detector type excitation e

gas proportional counter electron-hole pair 25-35 eV

scintillator photon ~ 3 eV

semiconductor detector electron-hole pair 3.65 eV (Si), 2.85 eV (Ge)

STJD quasiparticle 2.6 meV (Nb), 1.3 meV (Ta)

superfluid 4He roton 0.75 meV

superfluid 3He quasiparticle 0.14 meV


energy 𝜖 required for generating elementary excitations should be as small as possible

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calculated energy resolving power 𝑹 = 𝑬/𝚫𝑬


AS-Chap. 7 - 72

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• QP counting by tunneling STJD count excess QPs


DOS electrode 1

DOS electrode 2

Fermi distribution in electrode 1 and 2

density of states: 𝑑𝐹 = 𝐷𝐹/𝑉

AS-Chap. 7 - 73

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• main tunneling processes:

Note: once qp has tunneled to SC2 (process A), it can tunnel back again to SC1 (process B) QPs can be counted several times increase of signal !!!


• process A: qp tunnels from SC1 to SC2, large probability due to large DOS of empty states in SC2

• process B: CP in SC 1 is broken up, one qp tunnels to SC2 and recombines with qp of SC2, effectively charge e is transferred from SC2 to SC1 tunneling of hole from SC1 to SC2

• process C and D are analogue to A and B but with much smaller probabilities

AS-Chap. 7 - 74

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• tunneling current:

with

• extra tunneling current due to photon/particle absorption:

𝜏𝐷: signal decay time

• first order approximation of collected charge:

𝜏𝐷 ≫ 𝜏tun to maximize 𝛿𝑄𝑠

make 𝜏tun ∝ 𝑑, 𝐽𝑐−1

small JJs with high 𝐽𝑐 and small 𝑑

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QP trapping

QP trapping close to tunneling barrier makes tunneling time shorter total collected charge increases significantly improving the energy resolution


S1 I eV

µ1

(i)

(ii)

(iii)

(iv)

ħW

= D

-D´

ħW

= 2D´

tR

tep

(v)

E

𝑺𝟏′

𝚫′

𝚫

absorber layer trapping layer trapping layer

ba

rrier

𝑺𝟐′

µ1

AS-Chap. 7 - 76

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3) lateral QP trapping

no QP diffusion into leads

large-gap absorber


lead

𝚫𝟑

tunnel junction

𝚫𝟏 lead

𝚫𝟑

tunnel junction

𝚫𝟏

absorber

𝚫𝟐

qp diffusion

lead

𝚫𝟑

𝚫𝟑 > 𝚫𝟐 > 𝚫𝟏

tunnel junction

𝚫𝟏

AS-Chap. 7 - 77

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AS-Chap. 7 - 78

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energy resolution of a Nb/Al/AlOx/Al/Nb STJD vs photon energy

counting rates up to 104/s per pixel operation at 0.1 K


S. Friedrich et al., IEEE Trans. Appl. Supercond. AS-9, 3330 (1999)).

AS-Chap. 7 - 79

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Close-up of the 100 pixel array detector with 200-µm-square superconducting-tunnel-junctions (STJs). Because of the better energy resolution (ΔE), an array detector of 100-µm-square pixels with the same arrangement was used to measure XANES of N in SiC. (b) Histogram of ΔE values for the 80 operating 100-µm-square STJs. The solid line shows a Gaussian fit with a mean value of 14.2 eV and a standard deviation of 2.8 eV.

X-ray absorption near edge spectroscopy with a superconducting detector for nitrogen dopants in SiC M. Okubo et al., Scientific Reports 2, 831 (2012)


resolution: 2.8 eV @ 14.2 keV

AS-Chap. 7 - 80

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single photon charge spectrum at (a) 350 nm and (b) 250 nm wavelength


A. Peacock et al., Nature 381, 135 - 137 (09 May 1996) Single optical photon detection with a superconducting tunnel junction

AS-Chap. 7 - 81

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• antenna coupled STJD for sub-millimeter-wave single photons

R.J. Schoelkopf et al., IEEE Trans. Appl. Supercond. 9, 2935 (1999)

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(a) Microscope photograph of a transmission-line STJ detector. The long junctions of 4 µm x 27 µm in size are symmetrically integrated on both wings of a Nb log-periodic antenna. A Nb antenna and an impedance transformer were used in this prototype fabrication, although Nb is a high-loss material above 𝑓𝑔 ≃ 0.7 THz. (b) Typical I–V curve of the STJ

detector at 4.2 K.

S. Ariyoshi et al., Supercond. Sci. Technol. 25, 075011 (2012) Terahertz detector with transmission-line type superconducting tunnel junctions

AS-Chap. 7 - 83

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Detector types: (i) modulation detectors: heterodyne receivers, direct detectors (ii) thermal detectors: without antenna for absorber mass > wave length with antenna for absorber mass < wave length (iii) single photon/particle detectors:

Summary

Noise equivalent power (NEP):

Noise temperature: 𝑇𝑁 =𝑃

𝑘𝐵 𝐵=

NEP

𝑘𝐵 𝐵 (𝑃 = power, 𝐵 = bandwidth)

quantum limit:

Dicke radiometer equation for minimal detectable input signal:

Heterodyne receiver: frequency down-conversion by nonlinear element –> SIS tunnel junction

mixer input: 𝑉(𝑡) = 𝑎𝑠 cos𝜔𝑠𝑡 + 𝑎𝑙𝑜 cos𝜔𝑙𝑜𝑡

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Summary (2)

Direct detector: „rectification“ by nonlinear element (SIS tunnel junction

(quantum limit) detector efficiency:

thermal detector: responsivity

Hot electron bolometer mixer:

make T0 , G small, make C small for short response time t = C/G

small 𝜏eff ∼ 𝐶/𝐺eff to allow for large IF bandwidth, large 𝑑𝑅/𝑑𝑇, small 𝐺eff

Micro-calorimeter:

small T, G and C, 𝜖 ≃ 1

STJ photon detector:

small average energy 𝜖 per excess quasiparticle

Chapter 7 Superconducting Photon and Particle Detectors · 2013-06-12 · 7 Superconducting Photon...

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Transcript of Chapter 7 Superconducting Photon and Particle Detectors · 2013-06-12 · 7 Superconducting Photon...