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Detection of Electromagnetic Radiation IV and V: Detectors and Amplifiers

Detection of Electromagnetic Radiation IV and V: Detectors and Amplifiers. Phil Mauskopf, University of Rome 21/23 January, 2004. Noise: Equations Include Bose-Einstein statistics and obtain the so-called ‘Classical’ formulae for noise correlations:

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Detection of Electromagnetic Radiation IV and V: Detectors and Amplifiers

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  1. Detection of Electromagnetic Radiation IV and V:Detectors and Amplifiers Phil Mauskopf, University of Rome 21/23 January, 2004

  2. Noise: Equations Include Bose-Einstein statistics and obtain the so-called ‘Classical’ formulae for noise correlations: Sij*() = (1-SS)ij kT  (I-SS)ij /(exp(/kT)-1) Seiej*() = 2(Z+Z)ij kT  2(Z+Z)ij /(exp(/kT)-1) Relations between voltage current and input/output waves: 1/4Z0 (Vi+Z0Ii) = ai 1/4Z0 (Vi - Z0Ii) = bi or Vi = Z0 (ai + bi) Ii = 1/Z0 (ai - bi)

  3. Noise: Derivation Quantum Mechanics II: Include zero point energy Zero point energy of quantum harmonic oscillator = /2 I.e. on the transmission line, Z at temperature, T=0 there is still energy. Add this energy to the ‘Semiclassical’ noise correlation matrix and we obtain: Seiej*() = 2  (Z+Z)ij coth(/2kT) = 2  R (2nth +1) Sij*() =  (1-SS)ij coth(/2kT) =  (2nth +1)

  4. Noise: Derivation - Quantum mechanics This is where the Scattering Matrix formulation is more convenient than the impedance method: Replace wave amplitudes, a, b with creation and annihilation operators, a, a, b, b and impose commutation relations: [a, a ] = 1 Normalized so that  a a  = number of photons [a, a ] =  Normalized so that  a a  = Energy Quantum scattering matrix: b = a + c Since [b, b ] = [a, a ] =  then the commutator of the noise source, c is given by: [c, c ] = (I - ||2)

  5. Quantum Mechanics III: Calculate Quantum Correlation Matrix If we replace the noise operators, c, c that represent loss in the scattering matrix by a set of additional ports that have incoming and outgoing waves, a, b: c i =  i a  and: (I - ||2)ij=  i j Therefore the quantum noise correlation matrix is just:  c ici = (I - ||2)ijnth = (I - SS)ijnth So we have lost the zero point energy term again...

  6. Noise: Quantum Mechanics IV: Detection operators An ideal photon counter can be represented quantum mechanically by the photon number operator for outgoing photons on port i: di =  b ibi which is related to the photon number operator for incoming photons on port j by:  b ibi =  (nS*inan)(m Simam)  +  cici = d Bii()  (nS*inan)(m Simam)  = n,mS*in Sim  anam  anam = nth(m,) nm which is the occupation number of incoming photons at port m

  7. Noise: Quantum Mechanics IV: Detection operators Therefore di= mS*imSim nth(m,) +  cici =  d Bii() Where:  cici = (I - SS)iinth The noise is given by the variance in the number of photons: ij2 =  di dj  -  di di =  d Bij() ( Bij()+ ij ) Bij() = mS*imSjm nth(m,) +  cicj = mS*imSim nth(m,) + (I - SS)ijnth(T,) Assuming that nth(m,) refers to occupation number of incoming waves, am , and nth(T,) refers to occupation number of internal lossy components all at temperature, T

  8. Noise: Example 1 - single mode detector No loss in system, no noise from detectors, only signal/noise is from port 0 = input single mode port: Sim = 0 for i, m  0 S0i = Si0  0 di=  d S*i0Si0 nth(0,) +  cici =  d Bii() ii2 =  di dji -  di di =  d Bii() ( Bii()+ ii ) For lossless system -  cici = 0 and ii2 =  d Bii() ( Bii()+ ii ) =  d Si02 nth() (Si02 nth()+ 1) Recognizing Si02 =  as the optical efficiency of the path from the input port 0 to port i we have: ii2 =  d nth() (nth()+ 1) express in terms of photon number

  9. Noise: Gain - semiclassical Minimum voltage noise from an amplifier = zero point fluctuation - I.e. attach zero temperature to input: SV() = 2  R coth(/2kT) = 2  R (2nth +1) when nth = 0 then SV() = 2  R Compare to formula in limit of high nth : SV() ~ 4 kTN R where TN Noise temperature  Quantum noise = minimum TN= /2k

  10. Noise: Gain Ideal amplifier, two ports, zero signal at input port, gain = G: S11 = 0 no reflection at amplifier input S12 = G gain (amplitude not power) S22 = 0 no reflection at amplifier output S21 = 0 isolated output Signal and noise at output port 2: d2=  d S*12S12 nth(1,) +  c2c2 =  d B22() 222 =  d2 d2 -  d2 d2 =  d B22() ( B22()+ 1 )  c2c2 = (1 - (SS)22)nth(T,) What does T, nth mean inside an amplifier that has gain? Gain ~ Negative resistance (or negative temperature) namp(T,) = -1/ /(exp(-/kT)-1)  -1 as T  0

  11. Noise: Gain 0 0 0 G 0 0 G 0 0 0 0 G2  c2c2 = -(1 - (SS)22) = (G2 - 1) d2=  d S*12S12 nth(1,) +  c2c2 =  d B22() 222 =  d2 d2 -  d2 d2 =  d B22() ( B22()+ 1 ) =  d (G2 nth (1,)+ G2 - 1)(G2 nth (1,)+ G2) If the power gain is  = G2 then we have: 222 =  d (nth (1,)+  - 1)(nth (1,)+ ) ~ 2(nth (1,)+ 1)2 for  >> 1 and expressed in uncertainty in number of photons In other words, there is an uncertainty of 1 photon per unit  SS = =

  12. Noise: Gain vs. No gain Noise with gain should be equal to noise without gain for  = 1 222 =  d (nth (1,)+  - 1)(nth (1,)+ ) = nth(nth + 1) for  = 1 Same as noise without gain: ii2 =  d nth() (nth()+ 1) Difference - add ( - 1) to first term multiply ‘zero point’ energy by 

  13. Noise: Gain 22~ (nth (1,)+ 1) expressed in power referred to amplifier input, multiply by the energy per photon and divide by gain, 22~ h(nth (1,)+ 1) Looks like limit of high nth Amplifier contribution - set nth = 0 22~ h  = kTn  or Tn = h/k (no factor of 2!)

  14. Noise: Gain What happens to the photon statistics? No gain: Pin = n h and in = h n(1+n) /( ) (S/N)0 = Pin /in = n/(1+n) With gain: Pin = n h and in = h (1+n) /( ) (S/N)G = Pin /in = [n/(1+n)] (S/N)0/(S/N)G = (1+n)/n

  15. Incoherent and Coherent Sensitivity Comparison

  16. Implementation: Spectroscopy experiment: Front end Spectroscopy experiment: Back end FTS on chip Phase shifting FTS on a chip Do this in microstrip and divide all path lengths by dielectric,  Problem - signal loss in microstrip OK in mm-wave - Nb stripline, submm - MgB2? Also - PARADE’s filters work at submm (patterned copper) Power divider  X N 180

  17. Implementation: Spectroscopy experiment: Front end Spectroscopy experiment: Back end filter bank on chip Problem: Size BPF BPF BSF BPF BPF BSF

  18. Implementation: • Spectroscopy experiment sensitivity: (Zmuidzinas, in preparation) • Each detector measures: • Total power in band S(n) = d I () cos(2xn/c)/N • N = number of lags = number of filter bands • Each detector measures signal to noise ~ d I ()/N • Then take Fourier transform of signals to obtain the frequency spectrum: • R() =  i S(n)cos(2ixn/c) cos(2xn/c) • If the noise is uncorrelated • Dominated by photon shot noise (low photon occupation number) • Dominated by detector noise • Then the noise from each detector adds incoherently: • Each band has signal to noise ~ I ()/N • For filter bank (divide signal into frequency bands before detection): • Each band has signal to noise ~ I ()/ • FTS is worse by N !

  19. Solution: Butler combiner (not pairwise) Power divider … X N 2x 3x 4x x “Butler Combiner” • All lags combined on each detector: • Signals on each detector cancel except in a small band • Like a filter bank but more flexible: • Can modify phases to give different filters • Can add phase chopping to allow “stare modes” • In the correlated noise limit with phase chopping, each detector measures entire band signal - redundancy

  20. Instrumentation: Imaging interferometer: Front end  OMT 180 180  Imaging interferometer: Back end Single moded beam combiner like second part of spectrometer interferometer (e.g. use cascade of magic Tees), n=N Must be a type of Butler combiner (as spectrometer) to have similar sensitivity to focal plane array

  21. Noise: Multiple modes Case 1: N modes at entrance, N modes at detector fully filled with incoherent multimode source (I.e. CMB) Noise in each mode is uncorrelated - ii2 = N d nth() (nth()+ 1) where nth() is the occupation number of each mode Case 2: 1 mode at entrance, split into N modes that are all detected by a single multi-mode detector - must get single mode noise. Doesn’t work if we set  = 1/N ii2 = N d nth() (nth()+ 1) ~ (1/N) d nth() (nth()+ 1) Therefore noise in ‘detector’ modes must be correlated because originally we had only 1 mode

  22. Noise: Multiple modes Resolution: Depending on mode expansion, either noise is fully correlated from one mode to another or it is uncorrelated. General formula: Mode scattering matrix 2 =   d Bop (Bpo + op ) where o,p are mode indices O,p

  23. Two types of mm/submm focal plane architectures: Bare array Antenna coupled IR Filter Filter stack Bolometer array Antennas (e.g. horns) X-misson line SCUBA2 PACS SHARC2 Microstrip Filters Detectors BOLOCAM SCUBA PLANCK

  24. Mm and submm planar antennas: Quasi-optical (require lens): Twin-slot Log periodic Coupling to waveguide (require horn): Radial probe Bow tie

  25. Pop up bolometers: Also useful as modulating mirrors...

  26. SAFIR BACKGROUND

  27. +V Photoconductor (Semiconductor or superconductor based): Photon Excited electrons Current +V, I Bolometer (Thermistor is semiconductor or supercondcutor based): Metal film I EM wave Thermistor Phonons Change in R

  28. Basic IR Bolometer theory: S (V/W) ~ IR/G R=R(T) is 1/R(dR/dT) I~constant G=Thermal conductivity NEP = 4kT2G + eJ/S Time constant = C/G C = heat capacity Fundamentally limited by achievable G, C - material properties, geometry Silicon nitride “spider web” bolometer: Absorber and thermal isolation from a mesh of 1 mx4 m wide strands of Silicon Nitride Thermistor = NTD Germanium or superconducting film

  29. Bolometers at X-ray and IR:  V , T G BOLO EXT X-ray C T BOLO T T G o INT o  = C/G TIME  G EXT T IR eq C T T BOLO G o INT T o TIME

  30. Bolometer characteristics: Detector Audio Z Readout B-field Coupling ----------------------------------------------------------------------------- Absorber and thermometer independent (thermally connected) Bolo/TES ~ 1 Ohm SQUID No? Antenna or Distributed Bolo/Silicon ~ 1 Gohm CMOS No Antenna or Distributed Bolo/KID ~ 50 Ohms HEMT No Antenna or Distributed Absorber and thermometer the same HEB ~ 50 Ohms ?? No Antenna CEB ~ 1 kOhm ?? No Antenna

  31. Thermistors • Semiconductors - NTD Ge • Superconductors - single layer or bilayers • Junctions (e.g. SIN, SISe)

  32. Superconducting thermometers: monolayers, bilayers, multilayers Some examples - Material Tc  Reference ---------------------------------------------------------- Ti/Au <500 mK 30 SRON Mo/Au < 1 K 300 NIST, Wisconsin, Goddard Al/Ti/Au < 1 K 100 JPL W 60-100 mK UCSF

  33. PROTOTYPE SINGLE PIXEL - 150 GHz Schematic: Silicon nitride Waveguide Absorber/ termination Nb Microstrip TES Thermal links Radial probe Similar to JPL design, Hunt, et al., 2002 but with waveguide coupled antenna

  34. PROTOTYPE SINGLE PIXEL - 150 GHz Details: TES Thermal links Radial probe Absorber - Ti/Au: 0.5 / - t = 20 nm Need total R = 5-10  w = 5 m  d = 50 m Microstrip line: h = 0.3 m,  = 4.5  Z ~ 5 

  35. Example - Think of it as a lossy transmission line: R L G C R represents loss along the propagation path can be surface conductivity of waveguide or microstrip lines G represents loss due to finite conductivity between boundaries = 1/R in a uniform medium like a dielectric Z = (R+iL)/(G+iC) For a section of transmission line shorted at the end: G= 1/R Z= (R+iL)/(1/R+iC) = (R2+iRL)/(1+iRC) Z = (R2+iLR)/(1+iRC) = (R2+ZLR)/(1+R/ZC)

  36. Example - impedances of transmission lines Z = (R2+iLR)/(1+iRC) = (R2+ZLR)/(1+R/ZC) So we want ZL < R and ZC > R for good matching Calculate impedance of C, L for 50 m section of microstrip w = 5 m, h = 0.3 m,  = 4.5  Z ~ (h/2w) 377/  ~ 5  0 is magnetic permeability: free space = 4  10-7 H m-1 0 is the dielectric constant: free space = 8.84  10-12 F m-1 d = 50 m L ~ 0(d  h)/2w ~ 1.5 m ×  ~ 2 × 10-12 H C ~ (d  2w)/h ~ 9 mm × 0 ~ 8 × 10-14 F ZL = L = 2(150 GHz) 2  10-12 H ~ 2  ZC = 1/C = 1/2(150 GHz) 8  10-14 F ~ 13 

  37. MULTIPLEXED READ-OUTTDM and FDM

  38. Why TES are good: 1. Durability - TES devices are made and tested for X-ray to last years without degradation 2. Sensitivity - Have achieved few x10-18 W/Hz at 100 mK good enough for CMB and ground based spectroscopy 3. Speed is theoretically few s, for optimum bias still less than 1 ms - good enough 4. Ease of fabrication - Only need photolithography, no e-beam, no glue 5. Multiplexing with SQUIDs either TDM or FDM, impedances are well matched to SQUID readout 6. 1/f noise is measured to be low 7. Not so easy to integrate into receiver - SQUIDs are difficult part 8. Coupling to microwaves with antenna and matched heater thermally connected to TES - able to optimize absorption and readout separately

  39. Problems: • Saturation - for satellite and balloons. • Excess noise - thermal and phase transition? • High sensitivity (NEP<10-18) requires temperatures < 100 mK Solutions: • Overcome saturation by varying the thermal conductivity of detector - superconducting heat link • Thermal modelling and optimisation • Reduce slope of superconducting transition • Better sensitivity requires reduced G - HEBs?

  40. Problems: Excess Noise - Physics Width of supercondcuting transition depends on mean free path of Cooper pair and geometry of TES Centre of transition = RN/2 = 1 Cooper pair with MFP = D/2 Derive equivalent of Johnson noise using microscopic approach with random variation in mean free path of Cooper pair Gives a noise term proportional to dR/dT

  41. Problems: Sensitivity - Requires very low temperature Fundamentally - a bolometer is a square-law detector Therefore, it is a linear device with respect to photon flux Response (dR) is proportional to change in input power (dP) In order to count photons, it is better to have a non-linear device (I.e. digital) - photoconductor

  42. Hot Electron Bolometer (HEB) -Tiny superconducting strip across an antenna (sub micron) - DC voltage biases the strip at the superconducting transition -RF radiation heats electrons in the strip and creates a normal hot spot -Can be used as a mixer or as a direct detector Minimum C (electrons only) Sensitivity limited by achievable G

  43. Photoconductor characteristics: Detector Audio Z Readout B-field Coupling ----------------------------------------------------------------------------- BIB Ge > 1012 Ohm CIA No Distributed QD phot. ~ 1 Gohm QD SET Yes/No Antenna QWIP ~ 1 Gohm CIA No Not normal incidence SIS/STJ ~ 10 kOhm FET? Yes Antenna SQPT ~ 1 kOhm RF-SET Yes Antenna KID ~ 50 Ohm HEMT No Distributed or antenna

  44. Detectors: Semiconductor Photoconductor Pure crystal - Si, Ge, HgCdTe, etc. Low impurities Low level of even doping Achieve - ‘Freeze out’ of dopants Incoming radiation excites dopants into conduction band They are then accelerated by electric field and create more quasiparticles  measure current  e V,I

  45. Detectors: Semiconductor BIB Photoconductor Method of controlling dark current while increasing doping levels to increase number of potential interactions Take standard photoconductor and add undoped part on end Achieve - ‘Freeze out’ of dopants Incoming radiation excites dopants into conduction band They are then accelerated by electric field and create more quasiparticles  measure current  e V,I

  46. Detectors: Quantum Well Infrared Photoconductor Easier method of controlling dark current and increasing the number of potential absorbers - use potential barriers Thin sandwich of amorphous semiconductor material with low band gap Create 2-d electron gas Energy levels are continuous in x, y but have steps in z AlGaAs AlGaAs GaAs

  47. Detectors: Quantum Well Infrared Photoconductor Solve for energy levels using Schrodinger: Particle in a box - H = E, H = p/2m + V V = 0  x, y and for 0<z<a (I.e. within well) V = V  x, y and for z<a or z<0 (I.e. outside well) Solve for wavefunctions within well: Simple solution:  = A ei(kxx+ kyy) sin(nz/a) Has continuous momentum in x, y, discrete levels in z

  48. Detectors: Quantum Well Infrared Photoconductor Advantages over standard bulk photoconductor - 1. Can have large carrier density within quantum well with low dark current due to well barriers - high quantum efficiency 2. Can engineer energy levels within well to suit wavelength of photons - geometry determined rather than material

  49. Detectors: Quantum Dots Confinement in 3 dimensions gives atomic-like energy level structure:  = A sin(lx/a) sin(my/b) sin(nz/c) E2 = (22/2m*)(l2/a2 + m2/b2 + n2/c2) Useful for generation of light in a very narrow frequency band - I.e. quantum dot lasers Also could be useful for absorption of light in narrow frequency band

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