XI. Bolometers Principle XII. Bolometers Response. This lecture course follows the textbook Detection of

Transcription

1 Detection of Light XI. Bolometers Principle XII. Bolometers Response This lecture course follows the textbook Detection of Light by George Rieke, Detection Cambridge of Light Bernhard Brandl University Press 1

2 Detection of Light Bernhard Brandl 2

3 Two Fundamental Principles of Detection Respond to individual photon energy Photons Waves Respond to electrical field strength and preserve phase Detection of Light Bernhard Brandl 3

4 Two Types of Direct Detection Based on photoelectric effect (release of bound charges) Thermalize photon energy Detection of Light Bernhard Brandl 4

5 Detection of Light Bernhard Brandl 5

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7 The Beginnings The father of astronomical bolometers is Frank Low ( ). He invented the Ge:Ga bolometer in Detection of Light Bernhard Brandl 7

8 A milestone in the History of Bolometers See John C. Mather (Applied Optics 21, 1125, 1982); PI of the Far Infra Red Absolute Spectrophotometer (FIRAS) on COBE and Nobel prize winner in Physics 2006 (with George Smoot) Detection of Light Bernhard Brandl 8

9 Detection of Light Bernhard Brandl 9

10 A simple thermal Model (1) Thermal link Heat sink Bolometer A detector is connected by a weak thermal link to a heat sink at T 0 From its environment, the detector absorbs a constant power P 1 so that T 0 T 0 + T 1 The thermal link has a thermal conductance which counteracts that temperature increase Detection of Light Bernhard Brandl 10

11 For Reference: P 0 : zero-point heat load of the bolometer (analogous to dark current in photoconductors) P 1 : constant (generic) external power on the bolometer. P V : time-variable power, due to the absorbed photon flux (i.e., the signal we want to detect) P T : total power of all components P I : power due to the sensing current through the bolometer Detection of Light Bernhard Brandl 11

12 A simple thermal Model (2) Heat sink Thermal link Thermal conductance G [W / K] Now we introduce a time-variable power component P V (t) the photon flux we want to detect where is the quantum efficiency, and is the thermal energy Detection of Light Bernhard Brandl 12

13 A simple thermal Model (3) The total power absorbed by the detector is then: We switch the signal on/off so that: Then the solution is: PP 0 + ηηpp 1 GG GG 1 ee tt/ CC/GG for t > 0 The signal response changes exponentially with the thermal time constant Detection of Light Bernhard Brandl 13

14 Electrical Time Constant Besides the thermal time constant there is also the electrical heating from the current sensing in the thermometer P I : The electrical power changes with an electrical time constant < Since α(t) < 0 *, this term is always positive: *see slide # Detection of Light Bernhard Brandl 14

15 Conclusion For t >> τ T and τ T > τ E, the temperature T 1 is proportional to (P 0 + ηp 1 ). In other words, if you measure the temperature then you know the power, and, after calibration, you know the source brightness Detection of Light Bernhard Brandl 15

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17 General Layout of Semiconductor Bolometer A chip of doped silicon or germanium acts both as bolometer detector and thermometer. High input impedance amplifier measures the voltage voltage depends on resistance resistance depends on temperature Detection of Light Bernhard Brandl 17

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19 Bolometer Readout Circuit We can use this circuit to measure V out to derive the bolometer resistance R. Johnson noise is usually not the limiting factor for bolometers so we don t need a very high resistance R for the bolometer. We assume that R L >> R so that the current through the bolometer is limited by R L Detection of Light Bernhard Brandl 19

20 Temperature Coefficient of Resistance (1) Bolometer temperature electrical resistance temperature coefficient of resistance α: ( in units of Kelvin 1 ) The sign of α leads to very different behavior for a bolometer. A positive/negative temperature coefficient (PTC/NTC) refers to materials that experience an increase/decrease in electrical resistance when their temperature is raised. Material α/ K Silicon Germanium Carbon Manganin Constantan Nichrome Mercury Copper Aluminum Tungsten Iron Lithium Detection of Light Bernhard Brandl 20

21 Temperature Coefficient of Resistance (2) To make sure that there are good electrical properties for this very low temperature, the doping is so heavy that hopping is the dominant mode. If T << Δ, and the semiconductor is heavily doped, the electrical resistance for hopping can be described by: where ϵ ½ and Δ 4 10 K is a characteristic temperature. Substituting the hopping resistance into the above equation yields: Detection of Light Bernhard Brandl 21

22 Detection of Light Bernhard Brandl 22

23 Frequency Response The frequency response of a classical RC-circuit is given by (Rieke 1.38): v0 Vout ( f ) = 2 + 2πfτ 1/ [ ( ) ] 2 1 RC Similarly, the frequency response of a bolometer is given by: where S(0) is the low frequency responsivity in [V / W] and the electrical time constant. is Detection of Light Bernhard Brandl 23

24 Electrical Responsivity Let dr, dt and dv be the changes in resistance, temperature and voltage across the bolometer, caused by the absorbed power dp. with Rieke p.244 So, we get for the electrical responsivity: with Rieke p.245 S E is completely determined by the electrical properties of the detector. S E electrical responsivity α(t) temperature coefficient of resistance [K -1 ] V voltage [V] G thermal conductance [W/K] P I power from sensing current [W] Detection of Light Bernhard Brandl 24

25 Measuring Electrical Responsivity The detector properties G and α are not always known need to determine them by measurement. The Load Curve Measure the load curve of I-V by adjusting the load resistor RL Nominal operating point Note that the local slope is different from a constant resistance R because of the non-linearity of the load curve Detection of Light Bernhard Brandl 25

26 Bolometer Detector Responsivity S E is only the electrical responsivity. If we want to get the responsivity to incoming radiation we need to multiply S E with the absorbed fraction η of the incoming radiation: Unlike photoconductors, the bolometer responsivity is independent of the wavelength λ (assuming the QE η is independent of λ). Photoconductors and photodiodes: Detection of Light Bernhard Brandl 26

27 Detection of Light Bernhard Brandl 27

28 The total NEP (1) Bolometers suffer from the same fundamental noise mechanisms as photoconductors plus the noise from thermal fluctuations: Johnson noise can be characterized by the noise voltage : where Johnson noise:...due to fluctuations in the thermal motions of charge carriers (random currents due to Brownian motion) Detection of Light Bernhard Brandl 28

29 The total NEP (2) Thermal noise: due to fluctuations of entropy across the thermal link that connects the detector and the heat sink. Photon shot noise:...due to fluctuations in the photon flux. (Note: Bolometers do not have G-R noise since no particle pairs are being created or destroyed). Total NEP noise: Detection of Light Bernhard Brandl 29

30 NEP Performance of Bolometers bad NEP good Conclusions: the colder, the better the smaller, the better D T (from Puget & Coron 1994 for the SAMBA mission) Detection of Light Bernhard Brandl 30

31 Detection of Light Bernhard Brandl 31

32 Composite Bolometers (1) In some cases, Si bolometers with high impurity concentrations can be very efficient absorbers. In many cases, however, the QE is too low. Quick solution: enhance absorption with black paint but this will also increase the heat capacity. A high QE bolometer for far-ir and sub-mm would have too much heat capacity hence composite bolometers. low heat capacity high QE low QE high heat capacity The heat capacity of the blackened sapphire plate is only 2% of that of Ge Detection of Light Bernhard Brandl 32

33 Composite Bolometers (2) Detection of Light Bernhard Brandl 33

34 Etched Bolometers Etching physical designs in Si means that you can make bolometer arrays and really reduce the thermal timescales Detection of Light Bernhard Brandl 34

35 Detection of Light Bernhard Brandl 35

36 Hot Electron Bolometers Bolometers for sub-mm/mm wavelengths can use highly doped (n-type) InSb: Impurity levels ~ conduction band ev sufficient to create free electrons leading to a sea of free electrons. Incident photons are absorbed by the free electrons so absorption raises their energies above thermal equilibrium: "hot electrons. Lattice interaction is weak de-excitation takes long time. Hot electrons significantly affect the mobility (and thus the conductivity) so measuring the resistance means monitoring the photon signal. Example: thermal conductance G = W/K typical n ~ cm -3 typical τ ~ s typical NEP ~ W (Hz) -1/2 fast! low! Detection of Light Bernhard Brandl 36

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38 Hot Electron Nano-Bolometers Titanium and Niobium metals, about 500nm long and 100nm wide at 0.1K Photons heat the electrons in the Ti section, which is thermally isolated by superconducting Nb leads. These devices can detect as little as a single photon of FIR light! Detection of Light Bernhard Brandl 38

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40 LABOCA LABOCA the multi-channel bolometer array for APEX operating in the 870 μm (345 GHz) atmospheric window. The signal photons are absorbed by a thin metal film cooled to about 280 mk. The array consists of 295 channels in 9 concentric hexagons. The array is under-sampled, thus special mapping techniques must be used Detection of Light Bernhard Brandl 40

41 Herschel/PACS Detection of Light Bernhard Brandl 41

42 Herschel/PACS Herschel/PACS bolometer: a cut-out of the 64x32 pixel bolometer array assembly. 4x2 monolithic matrices of 16x16 pixels are tiled together to form the shortwave focal plane array. The 0.3 K multiplexers are bonded to the back of the sub-arrays. Ribbon cables lead to the 3K buffer electronics Detection of Light Bernhard Brandl 42

43 MAMBO Detection of Light Bernhard Brandl 43

44 MUSTANG Detection of Light Bernhard Brandl 44

45 ACBAR The Arcminute Cosmology Bolometer Array Receiver (ACBAR) produces high-resolution images of the CMB. The receiver is an array of 16 detectors in 3-millimeter wavelength bands near the CMB peak ACBAR is installed at the 2.1-meter Viper telescope at the South Pole Station in Antarctica Detection of Light Bernhard Brandl 45

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47 Wikipedia: Superconductivity Superconductivity is a phenomenon of exactly zero electrical resistance and expulsion of magnetic fields occurring in certain materials when cooled below a characteristic critical temperature. It was discovered by Dutch physicist Heike Kamerlingh Onnes on April 8, 1911 in Leiden Detection of Light Bernhard Brandl 47

48 Wikipedia: Cooper Pairs (1) a Cooper (or BCS) pair is a pair of electrons bound together at low temperatures in a certain manner. In 1956, Leon Cooper showed that an arbitrarily small attraction between electrons in a metal can cause a paired state of electrons to have a lower energy than the Fermi energy, which implies that the pair is bound Detection of Light Bernhard Brandl 48

49 Cooper Pairs (2) The energy to break Cooper pairs is very small ( long wavelength detectors), and their range is many 100 times the lattice spacing. This is the classical superconductor theory, called BCS theory. (It does not explain high T C superconductors.) Detection of Light Bernhard Brandl 49

50 Wikipedia: Magnetic Fields In 1933 Meissner and Ochsenfeld discovered that when a superconductor is placed in a weak external magnetic field H, and cooled below T C the magnetic field is ejected. (Actually, the Meissner effect does not cause the field to be completely ejected but instead the field penetrates the superconductor but only to a very small distance.) Detection of Light Bernhard Brandl 50

51 Detection of Light Bernhard Brandl 51

52 Superconducting Bolometers Superconducting films are suitable as bolometers. The steep gradient in R = f{t} around T C makes them very sensitive devices. Resistance of a superconducting bolometer with a heat sink at 0.3K Superconducting bolometers can be much faster than semiconducting bolometers Detection of Light Bernhard Brandl 52

53 Superconducting Hot Electron Bolometers The best of both HEB and superconductivity! Make them small, so its a microbolometer. Superconducting thin film HEB extend to higher frequencies! Detection of Light Bernhard Brandl 53

54 Detection of Light Bernhard Brandl 54

55 Josephson (SIS) Junctions Consider the following junction: Insulator Superconductor Superconductor Cooper pair wave functions can extend across the insulator: With a bias voltage applied, they tunnel across the junction. The insulator must be thinner than the tunneling distance of a Cooper pair Detection of Light Bernhard Brandl 55

56 Biased SIS Junctions Superconductor Insulator Superconductor (SIS): NO VOLTAGE: Cooper pairs can flow and carry small currents (Josephson effect) SMALL VOLTAGE: Energy states shifted, but insulator still blocks normal currents. LARGER VOLTAGE: Voltage just exceeds the energy gap and you get nonlinear behaviour Detection of Light Bernhard Brandl 56

57 Problem of high Capacitance SIS junctions typically have 10 times higher capacitance than Schottky diodes. Cancel out the capacitance with an inductance This inductance is provided with a superconducting stripline Schematics: R n = normal mixer resistance C j = junction capacitance L t = stripline tuning inductance Detection of Light Bernhard Brandl 57

58 SQUIDs (1) Superconducting QUantum Interference Devices (SQUIDs) are based on the Josephson effect. In SQUIDs two Josephson junctions are connected in a loop. The output voltage of a biased SQUID is: where R is the resistance of the junctions, Φ is the magnetic flux, and I 0 the maximum current through the junctions at zero voltage. If the SQUID is biased close to 2I 0, very small changes in I can be detected at the SQUID output. It acts as a low input impedance amplifier Detection of Light Bernhard Brandl 58

59 SQUIDs (2) Two Josephson junctions in parallel with a current flowing through them. Current is split evenly between them Detection of Light Bernhard Brandl 59

60 SQUIDs (3) A SQUID is essentially a very, very sensitive magnetometer: A magnetic field passing through the hole will generate an opposite circulating current Detection of Light Bernhard Brandl 60

61 Transition Edge Sensors A transition edge sensor (TES) is based on the strongly temperaturedependent resistance of the superconducting phase transition. Detected photons heat up the SIS current pulse goes through an inductor generates magnetic field sensed by SQUID. TES require one SQUID per pixel. TES are fiddly and tricky to manufacture and operate. TES are very difficult to multiplex in the 1000 s Detection of Light Bernhard Brandl 61