Transcript Photon counting FIR detectors

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)
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)
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)
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)
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 nth = (I - SS)ijnth
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:
di =  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*inan )(m Simam)  +  c i ci  = d Bii()
 (n S*inan)(m Simam)  = n,m S*in Sim  an am 

 a n am  = nth(m,) nm which is the occupation number of
incoming photons at port m
Noise: Quantum Mechanics IV: Detection operators
Therefore
di = m S*imSim nth(m,) +  ci ci  =  d Bii()
Where:  ci ci  = (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() = m S*imSjm nth(m,) +  ci cj 
= m S*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
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i ci  =  d Bii()
ii2 =  di dji -  di  di  =  d Bii() ( Bii()+ ii )
For lossless system -  ci ci  = 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
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
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 2 c2  =  d B22()
222 =  d2 d2 -  d2  d2  =  d B22() ( B22()+ 1 )
 c2 c2  = (1 - (SS)22)nth(T,)
What does T, nth mean inside an amplifier that has gain?
Gain ~ Negative resistance (or negative temperature)
Noise: Gain
SS = 0
G
0
0
0
0
G
0
=0
0
0
G2
 c2 c2  = -(1 - (SS)22) = (G2 - 1)
d2 =  d S*12S12 nth(1,) +  c2 c2  =  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 
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 
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!)
Noise: Gain
What happens to the photon statistics?
No gain:
and
Pin = n h
in = h n(1+n) /( )
(S/N)0 = Pin /in = n/(1+n)
With gain:
and
Pin = n h
in = h (1+n) /( )
(S/N)G = Pin /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 - MgB2?
Also - PARADE’s filters work at submm (patterned copper)
Power divider

180
XN
Implementation:
Spectroscopy experiment: Front end
Spectroscopy experiment: Back end filter bank on chip
Problem: Size
BPF
BPF
BSF
BPF
BPF
BSF
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 !
Solution: Butler combiner (not pairwise)
Power divider
x
2x 3x 4x
…XN
“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
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
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
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 = O,p  d Bop (Bpo + op ) where o,p are mode indices
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
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
+V
Photoconductor
(Semiconductor
or superconductor
based):
Photon
Excited
electrons
Current
+V, I
Metal film
I
Thermistor
Bolometer
(Thermistor is
semiconductor
or supercondcutor
based):
EM wave
Phonons
Change in R
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
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
Time constant = C/G
C = heat capacity
Fundamentally limited by achievable
G, C - material properties, geometry
Bolometers at X-ray and IR:
X-ray
G

V BOLO ,
EXT
C
G
T BOLO
To
INT
T
To
 = C/G
IR
TIME
G
Teq
EXT
C
G
INT
To

T BOLO
To
TIME
Bolometer characteristics:
Detector
Audio Z
Readout
B-field
Coupling
-----------------------------------------------------------------------------
Absorber and thermometer independent (thermally connected)
Bolo/TES
~ 1 Ohm
SQUID
No?
CMOS
No
~ 50 Ohms HEMT
No
Bolo/Silicon ~ 1 Gohm
Bolo/KID
Absorber and thermometer the same
Antenna or
Distributed
Antenna or
Distributed
Antenna or
Distributed
HEB
~ 50 Ohms ??
No
Antenna
CEB
~ 1 kOhm
No
Antenna
??
Thermistors



Semiconductors - NTD Ge
Superconductors - single layer or bilayers
Junctions (e.g. SIN, SISe)
Superconducting thermometers: monolayers, bilayers,
multilayers
Some examples Material
Tc

Reference
---------------------------------------------------------Ti/Au
<500 mK
30
SRON
Mo/Au
<1K
300
NIST, Wisconsin,
Goddard
Al/Ti/Au
<1K
100
JPL
W
60-100 mK
UCSF
PROTOTYPE SINGLE PIXEL - 150 GHz
Schematic:
Silicon nitride
Waveguide
Absorber/
termination
Nb Microstrip
TES
Radial probe
Thermal links
Similar to JPL design, Hunt, et al., 2002 but with
waveguide coupled antenna
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 
Example - Think of it as a lossy transmission line:
R
L
C
G
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)
2
2
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 
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 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
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?
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
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
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
SIS/STJ
~ 10 kOhm FET?
Yes
Not normal
incidence
Antenna
SQPT
~ 1 kOhm
RF-SET
Yes
Antenna
KID
~ 50 Ohm
HEMT
No
Distributed
or antenna
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

e
V,I
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
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
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)
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
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