Lecture 10: Bolometers - Leiden Observatory

Detection of Light: Lecture 10
Detection of Light
Lecture 10: Bolometers
Matthew Kenworthy // Leiden Observatory // 2012

Overview of Course Topics
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Detection of Light: Lecture 10
Before solid state
Solid State Physics
Photodiodes and variants
Detector Arrays
Artifacts, multiplexers, readout schemes
• CCDs
• Bolometers
•
Heterodyne Receivers

Three Basic Types of Detectors
• Photon detectors
Respond directly to individual photons - releases bound charge carriers. Used from
X-ray to infrared.
Examples: photoconductors, photodiodes, photoemissive detectors, photographic
plates
• Thermal detectors
Absorb photons and thermalize their energy - modulates electrical current. Used
mainly in IR and sub-mm detectors.
Examples: bolometers
• Coherent receivers
Respond to electrical field strength and preserve phase information (but need a
reference phase “local oscillator”). Mainly used in the sub-mm and radio
regime.
Examples: heterodyne receivers
Detection of Light: Lecture 10

Detection of Light: Lecture 10
Bolometers: History
The night sky has a large thermal emission at 10 microns
SOLUTION: rapid beam switching to remove the sky background
The father of astronomical bolometers is Frank Low
Invented the Ge:Ga bolometer in 1961

A milestone in the history of bolometers
Detection of Light: Lecture 10
Many references to John C. Mather (Applied Optics 21, 1125, 1982)
The Nobel prize in Physics 2006 (with George Smoot)
PI for Far Infra Red Absolute Spectrophotometer (FIRAS) on COBE

Detection of Light: Lecture 10
State of the Art bolometers
http://www.apex-telescope.org/bolometer/laboca/technical/
LABOCA – the multichannel
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: Lecture 10
State of the Art bolometers
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 short-wave 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: Lecture 10
Basic Principle

Basic Operation of a Bolometer
T0
Wavelengths: infrared to sub-mm
Detection of Light: Lecture 10
Incoming photon’s energy.... E = hc
...is absorbed as HEAT and increases the
temperature of the material
hv to kT

Detection of Light: Lecture 10
Definitions
Thermal conductance (Watts per Kelvin):
G
Thermal heat capacity (Joules per Kelvin): C
Temperature Coefficient of Resistance (1/Kelvin): ↵

Steady State Operation of a Bolometer
Detection of Light: Lecture 10
T0
G = P0
T0 + T1
Heat sink Bolometer
T1
Thermal link
Incoming photon power flux increases Bolometer
from equilibrium temperature T0 to T0 + . T1
A thermal link with thermal conductance G transfers power to
a heat sink of temperature T0
P0
P0

Time Response of a Bolometer
Detection of Light: Lecture 10
T0
Adding an astronomical source represented as a time
varying component:
Heat sink Bolometer
Thermal link
⌘PV (t) = dQ
dt
= C dT1
dt
Where ⌘ is quantum efficiency, Q is thermal energy,
and C = dQ/dT1 is the heat capacity [J/K]
PV (t)

Bolometer Thermal Time constant
The total power absorbed by the detector is:
T1(t) = PT
G
Detection of Light: Lecture 10
PT (t) =P0 + PV (t) =GT1 + C dT1
dt
Now we turn on a signal so that: t0
The time constant is T = C/G
For t>>⇥T the temperature T1 ⇠ (P0 + P1)
...so if you measure the temperature then you can know the power

Physical Layout of Semiconductor Bolometer
Detection of Light: Lecture 10
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

Temperature Coefficient of Resistance
Detection of Light: Lecture 10
We want to talk about how the temperature of the
bolometer changes its electrical resistance, so we talk
about the temperature coefficient of resistance:
So, R depends on the temperature:
↵ = ↵(T )= 1
R
dR
dT
The sign of the Temperature Coefficient leads to very
different behaviour for a bolometer.
...where and are constants
R0
Units of K 1
B

Detection of Light: Lecture 10
The Bolometer Readout Circuit
Johnson noise is NOT the
limiting factor for bolometers
so we don’t worry about setting
high R
We can use this circuit to measure the bolometer resistance R.
Vbias
RL
R Vout
We assume so that
the current through the bolometer is
limited by RL
RL >> R

R vs T for intrinsic semiconductor
Bolometers measure the resistance R via Vout
Vbias
RL
R Vout
Detection of Light: Lecture 10
Rd =
...where the number of charge carriers is:
So, R depends on the temperature:
From previous lectures, we know that:
1 l
wd
n0 =2
= 1
qn0µn
✓ 2m ⇤ nkT
h 2
l
wd
◆ 3/2
R = R0T 3/2 e B/T
...where and are constants
R0
e (Ec EF )/kT
B

Temperature kept low for good resistivity properties
Bolometers suffer from the same fundamental noise mechanisms as photoconductors
Detection of Light: Lecture 10
PLUS the noise arising from thermal fluctuations
Keep temperature of the bolometer very low
T

Detection of Light: Lecture 10
Approximations for the temperature
coefficient of resistance
The electrical resistance for hopping can be described by:
( /T )✏
R = R0e
...where ⇡ 1/2 and is a characteristic temperature ⇡ 4 10K
The temperature coefficient of resistance is defined as:
(T )= 1
R
dR
dT =
1
R0e ( /T )1/2
d
dT
(R0e ( /T )1/2
) ⇡ 1
2
(T )= 1
R
Substituting the hopping resistance into the above equation we get:
ALTERNATIVELY
T> R = R0
For one gets empirically that
However, in both cases the point is that:
✓ T
T0
= f(T )
◆ A
and so
✓
T 3
dR
dT
◆ 1/2
(T ) ⇡ A
T
...with A = 4

Detection of Light: Lecture 11
Electrothermal feedback
For ALL semiconductors, we know that the higher the temperature,
the lower the resistivity (more charge carriers generated) :
⌧T = C
G
⌧E

Detection of Light: Lecture 10
Electrical Responsivity
Let dR, dT and dV be the changes in resistance, temperature and voltage
across the bolometer, caused by the absorbed power dP.
So, we get:
dV = IdR= I[ (T )RdT]= (T )V dT=
with Rieke p.244:
SE = dV
dP =
dT =
(T )V
G (T )PI
(T )V dP
G (T )PI
dP
G (T )PI
The responsivity is completely determined by the electrical properties of
the detector (so this is also called electrical responsivity)

Measuring Electrical Responsivity
The detector properties G and (T ) are not always known and you need to
determine them by measurement
You measure the “load curve” of I-V
by adjusting the load resistor RL
Vbias
RL
R Vout
Detection of Light: Lecture 10
Note that the local slope is
different from “the resistance”
R because of the non-linearity
of the load curve.
Slope of the load curve is: Z = dV
dI
Nominal operating point
The Load Curve

etermining responsivity at V0
The resistance at the point V0 is:
Z = R
The local slope is:
If you now rewrite Z as follows.....
Z = dV
dI
Detection of Light: Lecture 10
d(log P )
d(log R)
H +1
H 1
= R d(log V )
d(log I)
= 1
I 2
R0 = V0/I0
(dI/dV )0 =1/Z0
= R
dP
dR
so H = Z + R
Z R
d(log P )
d(log R) +1
d(log P )
d(log R) 1
...we can now find an expression for d(log P)/d (log R):
= 1
I 2
G = P
T
dP
dT
dT
dR =
(T )= 1
R
G
(T )I 2 R
dR
dT
= G
(T )P
= H
P = V ⇥ I = I 2 R
Z and R can be measured, so we can get
H, then back to determine G and a(T)

SE =
G = (T )HP
Detection of Light: Lecture 10
Different timescales
...back to the electrical responsivity:
(T )V
G (T )PI
=
(T )V
(T )HP (T )P =
On the other hand, if α(T) is known G = α(T)HP permits the determination of the thermal conductance G from
the load curve.
⇥E =
V (Z R)
2RP
...and the electrical time constant:
C
G (T )P
= V
2P
T = C
G
= C
G G
H
✓
Z
R 1
◆
= ⇥T
1 1
H
V
P (H 1) =
= 1
2I
=
✓
Z
R 1
◆
⇥T
1 Z R
Z+R
P
= ⇥T
V
⇣ Z+R
Z R
⌘
Z + R
2R
1
=

Detector responsivity from electrical responsivity
Detection of Light: Lecture 10
Mather (1982) has a derivation that includes a correction
factor of (RL + R)/(RL + Z)
So that:
E = T
✓ Z + R
2R
◆✓ RL + R
RL + Z
This equation can be used to determine the heat capacity C = T G
of the bolometer in terms of (which can be measured from S(f) )
⌧E
So, SE is electrical responsivity, but now we can derive the responsivity to
incoming radiation (where only a fraction ⌘ of the incoming energy is
absorbed) :
◆
SR = SE = 2I
✓
Z
R 1
◆

Responsivity compared to photodetectors
Photoconductor
Sphotoconductor = ⇥qG
hc
Photodiode
Sphotodiode = ⇥q
hc
Bolometer
Sbolometer = 2I
The bolometer responsivity is independent of the wavelength
(assuming QE is independent of )
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✓
Z
R 1
◆
⌘

Two sources of Bolometer Heating
T0
Detection of Light: Lecture 11
Incoming photon flux produces
AND
Electrical heating from the current
sensing in the thermometer
PV (t)
PI
PI = I 2 (Remember that ⇥ R(T ) in the thermometer)

T0
Detection of Light: Lecture 11
Two time constants
Heat flowing out of the bolometer
through the thermal link gives rise to
AND
The electrical power changes with an
electrical time constant
⌧E =
⌧T = C
G
C
G ↵(T )PI

Detection of Light: Lecture 10
Noise and NEP
There is Johnson noise, characterised by the noise voltage
VJ =< I 2 J > 1/2 R
CASE 1: if VJ is added to the bias voltage, the dissipated power P
increases and R decreases (because of the negative resistance coefficient)
so the voltage across the detector decreases
CASE 2: if VJ opposes the bias voltage, the dissipated power P decreases
and R increases, so net voltage across the detector still decreases
In both cases, the detector response opposes the ohmic voltage change
resulting from Johnson noise (negative electrothermal feedback)
=
4kT f
R
(T ) < 0

Johnson noise:
Thermal noise:
Photon noise:
TOTAL NEP NOISE:
Detection of Light: Lecture 10
The total NEP
NEPJ ⇡
NEPT = (4kT 2 G) 1/2
NEPphoton = hc
⇥
GT 2 for (T ) ⇡ T 3/2
GT 3/2 for (T ) ⇡ T 1
....due to fluctuations in the thermal motions of charge carriers
(random currents due to Brownian motion)
due to fluctuations of entropy across the thermal link that
connects the detector and the heat sink.
✓ 2⇤ ◆ 1/2
...due to fluctuations in the photon flux
NOTE: Bolometers DO NOT HAVE G-R noise
(remember: no particle pairs created/destroyed)
NEP = p (NEP 2 photon + NEP 2 + NEP 2 J + ...)