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: S  i  j * (  ) = (1-S S) ij kT  (I-S S) ij  /(exp(  /kT)-1) S e i e j * (  ) = 2(Z+Z ) ij kT  2(Z+Z ) ij  /(exp(  /kT)-1) Relations between voltage current and input/output waves:  1/4Z 0 (V i +Z 0 I i ) = a i  1/4Z 0 (V i - Z 0 I i ) = b i or V i =  Z 0 (a i + b i ) I i = 1/  Z 0 (a i - b i )

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: S e i e j * (  ) = 2  (Z+Z ) ij coth(  /2kT) = 2  R (2n th +1) S  i  j * (  ) =  (1-S S) ij coth(  /2kT) =  (2n th +1)

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 ] = 1Normalized 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 )

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 i c i  = (I - |  | 2 ) ij n th = (I - S S) ij n th So we have lost the zero point energy term again...

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: d i =  b i b i  which is related to the photon number operator for incoming photons on port j by:  b i b i  =  (  n S * in a n )(  m S im a m )  +  c i c i  =  d B ii ( )  (  n S * in a n )(  m S im a m )  =  n,m S * in S im  a n a m   a n a m  = n th (m, )  nm which is the occupation number of incoming photons at port m

Noise: Quantum Mechanics IV: Detection operators Therefore d i =  m S * im S im n th (m, ) +  c i c i  =  d B ii ( ) Where:  c i c i  = (I - S S) ii n th The noise is given by the variance in the number of photons:  ij 2 =  d i d j  -  d i  d i  =  d B ij ( ) ( B ij ( )+  ij ) B ij ( ) =  m S * im S jm n th (m, ) +  c i c j  =  m S * im S im n th (m, ) + (I - S S) ij n th (T, ) Assuming that n th (m, ) refers to occupation number of incoming waves, a m, and n th (T, ) refers to occupation number of internal lossy components all at temperature, T

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: S im = 0 for i, m  0 S 0i = S i0  0 d i =  d S * i0 S i0 n th (0, ) +  c i c i  =  d B ii ( )  ii 2 =  d i d ji  -  d i  d i  =  d B ii ( ) ( B ii ( )+  ii ) For lossless system -  c i c i  = 0 and  ii 2 =  d B ii ( ) ( B ii ( )+  ii ) =  d S i0 2 n th ( ) (S i0 2 n th ( )+ 1) Recognizing S i0 2 =  as the optical efficiency of the path from the input port 0 to port i we have:  ii 2 =  d  n th ( ) (  n th ( )+ 1) express in terms of photon number

Noise: Gain - semiclassical Minimum voltage noise from an amplifier = zero point fluctuation - I.e. attach zero temperature to input: S V (  ) = 2  R coth(  /2kT) = 2  R (2n th +1) when n th = 0 then S V (  ) = 2  R Compare to formula in limit of high n th : S V (  ) ~ 4 kT N Rwhere T N  Noise temperature  Quantum noise = minimum T N =  /2k

Noise: Gain Ideal amplifier, two ports, zero signal at input port, gain = G: S 11 = 0 no reflection at amplifier input S 12 = G gain (amplitude not power) S 22 = 0 no reflection at amplifier output S 21 = 0 isolated output Signal and noise at output port 2: d 2 =  d S * 12 S 12 n th (1, ) +  c 2 c 2  =  d B 22 ( )  22 2 =  d 2 d 2  -  d 2  d 2  =  d B 22 ( ) ( B 22 ( )+ 1 )  c 2 c 2  = (1 - (S S) 22 )n th (T, ) What does T, n th mean inside an amplifier that has gain? Gain ~ Negative resistance (or negative temperature) n amp (T, ) = -1/ /(exp(-  /kT)-1)  -1 as T  0

Noise: Gain G 0 0 G G 2  c 2 c 2  = -(1 - (S S) 22 ) = (G 2 - 1) d 2 =  d S * 12 S 12 n th (1, ) +  c 2 c 2  =  d B 22 ( )  22 2 =  d 2 d 2  -  d 2  d 2  =  d B 22 ( ) ( B 22 ( )+ 1 ) =  d (G 2 n th (1, )+ G 2 - 1)(G 2 n th (1, )+ G 2 ) If the power gain is  = G 2 then we have:  22 2 =  d (  n th (1, )+  - 1)(  n th (1, )+  ) ~  2 (n th (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 = =

Noise: Gain vs. No gain Noise with gain should be equal to noise without gain for  = 1  22 2 =  d (  n th (1, )+  - 1)(  n th (1, )+  ) = n th (n th + 1)  for  = 1 Same as noise without gain:  ii 2 =  d  n th ( ) (  n th ( )+ 1) Difference - add (  - 1) to first term multiply ‘zero point’ energy by 

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

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

Incoherent and Coherent Sensitivity Comparison

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 - MgB 2 ? Also - PARADE’s filters work at submm (patterned copper)  180  X N Power divider

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

Implementation: Spectroscopy experiment sensitivity: (Zmuidzinas, in preparation) Each detector measures: Total power in band S(n) =  d I ( ) cos(2  x n /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  x n /c) cos(2  x n /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 !

xx “Butler Combiner” … X N Power divider Solution: Butler combiner (not pairwise) 2x2x3x3x4x4x 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

Instrumentation: Imaging interferometer: Front end OMT  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 180 

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 -  ii 2 = N  d  n th ( ) (  n th ( )+ 1) where n th ( ) 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  ii 2 = N  d  n th ( ) (  n th ( )+ 1) ~ (1/N)  d n th ( ) (n th ( )+ 1) Therefore noise in ‘detector’ modes must be correlated because originally we had only 1 mode

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 B op (B po +  op ) where o,p are mode indices O,p

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

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

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

SAFIR BACKGROUND

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

Basic IR Bolometer theory: S (V/W) ~  IR/G R=R(T) is 1/R(dR/dT) I~constant G=Thermal conductivity NEP =  4kT 2 G + e J /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

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

Conventional Bolometers with semiconducting thermistors: Best ones: 300 mK - NEP~  W/Hz  ~10 ms 100 mK - NEP~  W/Hz  ~10 ms Sensitivity limited by G Time constant limited by C TES, HEB bolometers-faster

DetectorAudio ZReadoutB-fieldCoupling Absorber and thermometer independent (thermally connected) Bolo/TES~ 1 OhmSQUIDNo?Antenna or Distributed Bolo/Silicon~ 1 GohmCMOSNoAntenna or Distributed Bolo/KID~ 50 OhmsHEMTNoAntenna or Distributed Absorber and thermometer the same HEB~ 50 Ohms??NoAntenna CEB~ 1 kOhm??NoAntenna Bolometer characteristics:

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

Superconducting thermometers: monolayers, bilayers, multilayers Some examples - MaterialTc  Reference Ti/Au<500 mK30SRON Mo/Au< 1 K300NIST, Wisconsin, Goddard Al/Ti/Au< 1 K100JPL W mKUCSF

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

PROTOTYPE SINGLE PIXEL GHz Details: 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  TES Thermal links

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 ) =  ( R 2 +i  RL )/(1+i  RC ) Z =  (R 2 +i  LR)/(1+i  RC) =  (R 2 +Z L R)/(1+R/Z C ) Example - Think of it as a lossy transmission line: C R G L

Example - impedances of transmission lines Z =  (R 2 +i  LR)/(1+i  RC) =  (R 2 +Z L R)/(1+R/Z C ) So we want Z L 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   H m -1  0 is the dielectric constant: free space = 8.84  F m -1 d = 50  m L ~  0 (d  h)/2w ~ 1.5  m ×  ~ 2 × H C ~  (d  2w)/h ~ 9 mm ×  0 ~ 8 × F Z L =  L = 2  (150 GHz)  2  H ~ 2  Z C = 1/  C = 1/2  (150 GHz)  8  F ~ 13 

MULTIPLEXED READ-OUT TDM and FDM

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 x 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

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

Problems: Excess Noise - Physics Width of supercondcuting transition depends on mean free path of Cooper pair and geometry of TES Centre of transition = R N /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

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

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

DetectorAudio ZReadoutB-fieldCoupling BIB Ge> OhmCIANoDistributed QD phot.~ 1 GohmQD SETYes/NoAntenna QWIP~ 1 GohmCIANoNot normal incidence SIS/STJ~ 10 kOhmFET?YesAntenna SQPT~ 1 kOhmRF-SETYesAntenna KID~ 50 OhmHEMTNoDistributed or antenna Photoconductor characteristics:

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

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 V,I  e

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 GaAs AlGaAs

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 e i(k x x+ k y y) sin(n  z/a) Has continuous momentum in x, y, discrete levels in z

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

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) E 2 = (  2  2 /2m * )(l 2 /a 2 + m 2 /b 2 + n 2 /c 2 ) 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

Superconducting Tunnel Junctions: X-ray-IR Two slabs of superconductor separated by an insulator photons excite quaiparticles that tunnel through the junction n(e - )/  ~ h /E  Superconducting photoconductor! With band gap = 1 meV vs. 1 eV for semiconductors (or 100 meV for donor level) Sensitivity limited by: 1. Quantum efficiency 2. Dark current Speed generally not a concern

Readout for superconducting junctions: SETs? RF-SET (e.g. Schoelkopf) Work for - SIS and SINIS - Antenna coupled photodetectors SQPT - Antenna coupled photoconductors read out with SETs > 1 e - /photon but are delicate and require e-beam lithography

Types of antennas/absorbers: 1. Twin-slot - planar quasi optical - JPL, Berkeley 2. Finline - wide band coupling to waveguide - Cam 3. Radial probe - wideband coupling to waveguide - Cam, JPL 4. Spider-web - Low cosmic ray cross section, large area absorber - JPL 5. Silicon PUDs - Filled area arrays - SCUBA2, NIST/Goddard

The readout problem - low noise multiplexing technologies: 1. SQUIDs - noise temperature < 1 nK Inductively coupled amplifier 10s of MHz bandwidth 2. FETs - noise temperature < 0.1 K Capacitively coupled amplifier 10s of kHz bandwidth 3. SETs - noise temperature < 1 uK Capacitively coupled amplifier GHz bandwidth 4. HEMTs - noise temperatures < 1 K Capacitively coupled amplifier 10s GHz bandwidth

Conclusions: Many possible new technologies around Multiplexable bolometers already satisfy criteria for imaging missions New photoconductors (semiconductor or superconductor) or HEBs probably needed for higher sensitivity instruments, probably antenna coupled