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Absolute linearity measurements
on PV HgCdTe detectors
in the infrared
E. Theocharous (Theo)
Optical Metrology Group, NPL, UK
[email protected] 24th September 2011
CONTENTS
1. Introduction
2. The NPL linearity measurement facility.
3. Results of the evaluation of PV HgCdTe detectors in the infrared.
4. The “Theo2 effect” and methods of extending the linear range of operation of HgCdTe detectors.
5. Conclusions
Why is characterisation of detectors important?
• Because it allows the uncertainty component associated with a particular detector characteristic (linearity, uniformity, temperature coefficient, etc) to be estimated (and used to calculate the combined uncertainty).
No characterisation – no uncertainty budget
• Detector suppliers exaggerate the capabilities of their products. They rely on the inability of their customers to verify their claims.
• Differences in the performance of nominally identical products.
• It allows the selection of the detector with the best performance.
Parameters determining the performance of detectors
1. The relative spectral radiant power responsivity.
2. The absolute spectral radiant power responsivity.
3. The Noise Power Spectral Density and NEP/NEI
4. Spatial uniformity of response
5. Linearity/non-linearity of response
6. Temperature coefficient of response
7. Frequency of response
8. Stability with time/ageing or fatigue
A detection system is linear If its output is directly proportional to the input
Linearity is a relatively unpopular measurement,
particularly in the infrared
Until recently there were no serious scientific
publications on the linearity of infrared detectors
(despite their widespread use)
At NPL we favour ABSOLUTE linearity measurement
methods based on power/irradiance superposition.
Accomplished by
superimposing
two beams.
detector
A
B
A+B
detector
A
B
A+B
A
B
A+B
Definition of the Linearity Factor
The linearity factor of a detector for an output of
(VA+VB)/2 is given by:
Linearity factor =
where VA, VB and VA+B represent the zero-corrected signals from the detector when apertures A, B and A+B were open, respectively, with VA set to be approximately equal to VB.
The linearity factor provides the average deviation of the responsivity from nominal over a range of 2:1 at that specific output voltage/power etc.
)( BA
BABA
VV
VVL
The “double aperture” wheel
Layout of the NPL detector linearity measurement facility
LampOAP mirror
Shutter
OAP mirror
Band-pass filter
Chopper
Pinhole
OAP mirror
OAP mirror
Detector
Filter Enclosure
Amplifier
Translation Stage
Source EnclosureDetector Enclosure
Double Aperture Wheel
ND Filter Wheel
Advantages of the NPL linearity measurement facility
• It provides an ABSOLUTE linearity measurement.
• Ensures linearity characterisation in terms of irradiance.
• Uses reflective optics so it can cover a very wide spectral range (with
ZnSe-based filters it covers the 0.6 µm to 20 µm region).
• It is fully automated.
• The use of neutral density filters to change the radiant power means
that the detector is illuminated with the same angular characteristics
for all the radiant power levels (compare with the use of apertures to
vary the radiant power/irradiance reaching the detector under test).
Linearity factor of CMT01 detector at 10.3 m
as a function of radiant power E. Theocharous et al., Applied Optics, 43, 4182-4188, 2004.
0.96
0.97
0.98
0.99
1
1.01
1.02
0.000001 0.00001 0.0001 0.001 0.01
Power / mW
Lin
eari
ty f
acto
rBlack: 1 mm
Red: 1.4 mm
Blue: 1.8 mm
Purple: 2.8 mm
Linearity of CMT01 detector as a function of photon
irradiance at 10.3 m (○) and 3.8 m (●).
0.96
0.97
0.98
0.99
1
1.01
1.00E+14 1.00E+15 1.00E+16 1.00E+17
Photon Irradiance /s-1
cm-2
Lin
earit
y f
act
or
Black: 3.8 μm
White: 10.3 μm
Is this behaviour to be expected?
• The density of the photo-generated charges is proportional to the photon irradiance.
• However, at higher charge carrier densities, there is a higher probability of recombination of charges (Auger recombination).
• Auger recombination is the dominant loss mechanism. Therefore, as the photon irradiance increases, the charge carrier lifetime decreases and therefore the non-linearity increases.
• Charge recombination is responsible for the non-linearity of PC HgCdTe detectors.
Theocharous et al.
“Absolute linearity measurements
on HgCdTe detectors in the infrared”
Applied Optics, 43, 4182-4188, 2004
E-mail [email protected] for a copy
• PV HgCdTe detectors are widely used in
FT spectrometry.
• They have superior noise characteristics
compared to PC HgCdTe detectors
• No systematic study of their linearity of
response has ever been published.
• This paper aims to rectify the situation.
PV HgCdTe detector characteristics
• 2 mm diameter active area.
• In side-looking Dewar.
• AR-coated ZnSe window.
• Cold shield limiting FoV to 60o (full angle).
• Dedicated trans-impedance amplifier with
104 and 105 V A-1 gain settings.
• Output rectified by digital lock-in amplifier.
Linearity characterisation settings
• Sources used:
– a Glowbar source (10.3 m) and
– a sapphire-windowed filament lamp (2.2 m & 4.7 m).
• Source output was spectrally filtered by dielectric
bandpass filters.
• Used different area pinholes which illuminated
different areas on the active area of the test detector.
• Incident radiation modulated at 70 Hz.
Absolute spectral responsivity of PV HgCdTe
detector, 1.5 mm diameter spot
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2 4 6 8 10 12 14
Wavelength (μm)
DC
Eq
uiv
ale
nt
Re
sp
on
siv
ity
(A
/W)
Noise Equivalent Power of PV HgCdTe detector
0.0
0.5
1.0
1.5
2.0
2 4 6 8 10 12 14
Wavelength/μm
No
ise E
qu
ivale
nt
Po
wer/
(nW
Hz
-1/2
)
Linearity characteristics of the PV CMT detector
0.99
0.992
0.994
0.996
0.998
1
1.002
1.004
0 5 10 15 20 25
Lock-in output/V
Lin
eari
ty f
acto
r
10.3 μm
4.7 μm
2.2 μm,
Linearity characteristics of the PV CMT detector
0.98
0.99
1
1.01
1.02
1.03
1.04
0.01 0.1 1 10 100Lock-in output/V
Lin
eari
ty f
acto
r
10.3 μm
4.7 μm
2.2 μm,
Plots of the linearity data as a function of total radiant
power incident on the test detector. The plots
corresponding to different wavelengths do not overlap.
0.98
0.985
0.99
0.995
1
1.005
0 50 100 150 200 250 300
Power/μW
Lin
eari
ty F
acto
r
10.3 μm
4.7 μm
2.2 μm
When the same data are plotted as a function of photon
irradiance the resulting plots show good overlap.
0.988
0.99
0.992
0.994
0.996
0.998
1
1.002
0.E+00 2.E+20 4.E+20 6.E+20 8.E+20
Photon irradiance/(photons s-1
m-2
)
Lin
eari
ty f
acto
r
10.3 μm
4.7 μm
2.2 μm
The linearity factor of the PV HgCdTe detector measured at 2.2 m,
with a 0.4 mm, 0.6 mm, 1.0 mm diameter spots, as well as with the
active area of the test detector overfilled.
0.975
0.98
0.985
0.99
0.995
1
0 10 20 30 40 50
Lock-in output/V
Lin
eari
ty f
acto
r
no aperture
1 mm diam.
0.6 mm diam.
0.4 mm diam.
The linearity factor measured at 2.2 m
as a function of the DC equivalent irradiance
0.975
0.98
0.985
0.99
0.995
1
0 50 100 150 200
DC Equiv. irradiance at 2.2 μm/(μW mm-2
)
Lin
ea
rity
fa
cto
r
no aperture
1 mm diam.
0.6 mm diam.
0.4 mm diam.
Spatial uniformity of response of the PV HgCdTe detector at
2.2 m, measured using a 100 m diameter probe spot.
0
0.5
1
1.5
2
0
0.5
1
1.5
2
00.10.20.30.40.50.60.70.80.91
Relative
response
Position/mm
Position/mm
0.9-1
0.8-0.9
0.7-0.8
0.6-0.7
0.5-0.6
0.4-0.5
0.3-0.4
0.2-0.3
0.1-0.2
0-0.1
Linearity factor as a function of lock-in output measured at the
centre and near the edge of the active area of the test detector.
0.982
0.984
0.986
0.988
0.99
0.992
0.994
0.996
0.998
1
0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2
Lock-in output/V
Lin
eari
ty F
acto
r
centre
edge
The non-linearity of a photodetection system can be
due to the detector itself, the amplifier itself, or BOTH.
• It can also arise due to the lock-in amplifier
(E. Theocharous, “Absolute linearity characterisation of lock-in
amplifiers” Applied Optics, 47, 1090-1096, 2008). Deviation from
linearity limited to less than 0.1%.
• The linearity of the trans-impedance amplifier
was checked with a current source.
• The fact that the linearity characteristics
depend on the area of illuminated spot
confirms that the non-linearity originates
within the PV HgCdTe detector.
Contribution due to the thermal background
• All measurements correspond to an ambient
temperature background.
• This is how the test detector will be used
normally.
• This is not an issue with “visible” detectors
but it is an issue for infrared detectors.
The Theo2 effect
NPL’s detector stability measurement facility
The responsivity of a HgCdTe detector depends
on the temperature of objects in its Field of View.
21
22
23
24
25
26
27
28
29
30
0 1 2 3 4 5 6
Time (h)
Te
mp
era
ture
(oC
)
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
No
rm
alis
ed
ou
tpu
t
temperature
Normalised output
• The responsivity of the HgCdTe detector
was dependent on the temperature inside
the chamber.
• It is not a “Temperature coefficient of
response” effect because the detector
wafer was maintained at “77 K”.
• What was causing the drift?
The
soldering
iron
test
Change in the responsivity of a PC HgCdTe detector
0.75
0.8
0.85
0.9
0.95
1
0 2 4 6 8 10 12 14 16 18
Time (min)
No
rm
alis
ed
re
sp
on
se
Drift is independent of wavelength
0.75
0.8
0.85
0.9
0.95
1
0 4 8 12 16
Time (min)
No
rm
alis
ed
re
sp
on
se
10.3 μm
4.7 μm
HgCdTe-sphere detector
HgCdTe-sphere detector with temperature controlled FOV
Back view
As the temperature of the sphere increases, the
responsivity of the HgCdTe detector decreases.
20
22
24
26
28
30
32
34
0 2 4 6
Time (h)
Te
mp
era
ture
(oC
)
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
1.01
No
rm
alis
ed
re
sp
on
se
Temperature
Normalised response
As the temperature of the sphere increases, the
responsivity of the HgCdTe detector decreases.
y = -0.0066x + 1.139
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
1.01
20 25 30 35
Temperature (oC)
No
rm
alis
ed
re
sp
on
se
Repeat with a different HgCdTe detector
18
19
20
21
22
23
24
25
26
27
28
0 1 2 3 4 5 6
Time (h)
Te
mp
era
ture
(oC
)
0.99
1
1.01
1.02
1.03
1.04
1.05
1.06
1.07
1.08
No
rm
alis
ed
re
sp
on
se
Temperature
Normalised response
Slope is very similar
y = -0.007x + 1.1475
0.95
0.96
0.97
0.98
0.99
1
1.01
1.02
1.03
18 20 22 24 26 28
Temperature (oC)
No
rm
alis
ed
re
sp
on
se
The detector cannot recognise whether the photocharges are
due to the modulated radiation or the background radiation
E. Theocharous and O. J. Theocharous
“On a practical limit of the accuracy of
radiometric measurements using HgCdTe
detectors”
Applied Optics, 45, 7753-7759, 2006
Explanation of the “Theo2 effect”
• Infrared radiation, whether modulated or unmodulated, incident on
a HgCdTe detector generates free charge carriers.
• Auger recombination is the dominant loss mechanism and this loss
mechanism is known to rise with the increasing density of charge
carriers.
• This leads to the observed high non-linearity in the response of
HgCdTe detectors (see Theo’s linearity paper in Applied Optics).
• Note that both the modulated radiation being detected as well as
the thermal background radiation produce free charge carriers
which contribute to the non-linearity.
• The contribution due to the thermal background is not modulated
and is therefore rejected by the phase sensitive detection utilised.
• However, its contribution to the non-linearity of response of the
detector cannot be avoided.
Explanation of the “Theo2 effect”
• Examination of the irradiance values involved indicates that a PC
HgCdTe with a 60o FOV (full angle) is subjected to a background
irradiance of 40 W m-2 in the 8 μm to 14 μm wavelength range. This
assumes a background temperature of 20 oC.
• Compare this with the irradiance values of a few W m-2 normally
supplied by the modulated radiation being detected.
• It is clear that the dominant source of free charge carriers is the
irradiance due to the thermal background. It is also the dominant
source the HgCdTe detector non-linearity.
• This is because the density of the free charge carriers generated by the
thermal background is over an order of magnitude greater than that
from the modulated radiation being measured.
• This confirms the importance of the irradiance due to the thermal
background in the linearity of HgCdTe detectors and to the drifts
associated with changes in the temperature of objects in their FOV.
• Fluctuations in the temperature of objects in
the FOV of HgCdTe detectors provides a
practical limit to the accuracy with which
radiometric measurements can be
performed using HgCdTe detectors.
• Other infrared photodetectors will also suffer
from a similar limit.
• See publication on the “Theo2 effect” for full
description.
Where can we expect to “suffer” from the
effects of the “Theo2 effect”?
In ALL applications of HgCdTe detectors!
• Earth Observation !!!!!!!!!!
• Radiometry
• Laser radiant power stabilisation
PV HgCdTe soldering iron test. Identical percent
change at 10.3 m and 4.7 m
0.85
0.9
0.95
1
0 4 8 12 16
Time (min)
No
rmali
sed
ou
tpu
t
10.3 μm
4.7 μm
2 mm PV HgCdTe detector
20
22
24
26
28
30
32
0 1 2 3 4
Time/hours
Te
mp
era
ture
/oC
0.96
0.97
0.98
0.99
1
1.01
No
rma
lis
ed
ou
tpu
t
Temperature
Normalised response
2 mm PV HgCdTe detector at 10.3 m, slope
less than half of that of PC HgCdTe
y = -0.003x + 1.0648
0.97
0.975
0.98
0.985
0.99
0.995
1
1.005
20 22 24 26 28 30 32
Temperature/oC
No
rma
lis
ed
re
sp
on
se
How can we extent the linear range of
operation of HgCdTe detectors?
• Reduce the thermal background reaching
the detector:
– Enclose detector in a “cold chamber”
– Reduce temperature of objects in the FoV
of the detector (reduce size of cold shield
aperture)
– Use cold filter
Normalised response of HgCdTe Filter Radiometer
1.0E-07
1.0E-06
1.0E-05
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
2 4 6 8 10 12 14
Wavelength/um
No
rmalised
resp
on
se
Linearity characteristics of the 10.1 m PV CMT filter radiometer
0.99
0.995
1
1.005
1.01
0.01 0.1 1 10 100 1000
lock-in RMS output/mV
Lin
ea
rity
fa
cto
r
0.1 mm0.16 mm0.4 mm0.6 mm0.8 mm1.0 mm2.0 mm
The introduction of the cold filter
has two benefits:
1. Reduces noise due to the reduction of the
thermal background being detected.
2. Improves linearity because it reduces
the photo-generated charges produced by
the thermal background, thus reducing the
effect of the “Theo2 effect”.
Penalty: Limited spectral response range
Conclusions
The linearity characteristics of PV HgCdTe detectors
were experimentally investigated in the infrared.
Measurements were completed with the test detector
operating under conditions identical to those in which it
would operate when used in typical infrared radiometric
applications.
The non-linearity of the PV HgCdTe detectors was
shown to be a function of photon irradiance rather than
the total radiant power incident on the test detector.
The “Theo2 effect” dominates the detector non-linearity.
Methods of increasing linear range of operation
of HgCdTe detectors:
Operate PV HgCdTe detectors with their active areas
overfilled.
Adjust cold shield to give small FoVs (remove “hot”
objects from the detector FoV)
Use “cold filters” whenever possible.
Nine publications from NPL on detector linearity 1. E. Theocharous, J. Ishii and N. P. Fox, “Absolute linearity measurements
on HgCdTe detectors in the infrared”, Applied Optics, 43, 4182-4188, 2004.
2. E Theocharous, “Absolute linearity measurements on PbS detectors in the infrared”, Applied Optics, 45, 2381-2386, 2006
3. E. Theocharous and O. J. Theocharous, “Practical limit of the accuracy of radiometric measurements using HgCdTe detectors” Applied Optics, 45, 7753-7759, 2006.
4. E. Theocharous, “How linear is the response of your detector?”, Europhotonics Magazine, February edition, Pages 33-35, 2007.
5. E. Theocharous, “Absolute linearity measurements on a PbSe detector in the infrared”, Infrared Physics and Technology, 50, 63-69, 2007.
6. E. Theocharous, “Reply to comments on “Absolute linearity measurements on a PbS detector in the infrared””, Applied Optics, 46, 6495-6497, 2007
7. E. Theocharous, “Absolute linearity characterisation of lock-in amplifiers” Applied Optics, 47, 1090-1096, 2008.
8. E. Theocharous, “Absolute linearity measurements on a gold-black-coated deuterated L-alanine-doped triglycine sulphate pyroelectric detector”, Applied Optics, 47, 3731-3736, 2008.
9. E. Theocharous, “Absolute linearity measurements on LiTaO3 pyroelectric detectors”, Applied Optics, 47, 3397-3405, 2008
Drift in a HgCdTe detector due to “topping up” of the
Dewar (Infrared Physics & Tech. 48, 175-180, 2006)
0.99
0.995
1
1.005
1.01
0 1 2 3 4 5
Time/hours
No
rm
alis
ed
re
sp
on
se
Top-up
Dewar
Larry Gordley Principal Associate,
GATS, Inc. [email protected] • I'm the PI for a differential absorption occultation
experiment called SOFIE (Solar Occultation For Ice Experiment)
designed to sound the atmosphere at polar mesospheric cloud
levels (83 Km). The instrument developer selected MCT PC
detectors for most of the channels, but failed to realize (as
did the detector manufacturer Judson) that the predicted flux
levels would drive the detectors into a severely non-linear
region, given our under-fill design. When the first full up
tests (in late July) showed extreme, intolerable, non-
linearity, the budget and schedule constraints threatened the
whole mission, which included two other instruments on the AIM
(Aeronomy of Ice Mission). In a panic literature search on
linearity of MCTs, at the airport on the way back from the
depressing tests, Google pointed me to your paper. Now, armed
with the realization of the dependence linearity on irradiance
(as opposed to flux), I simply had the detectors moved to an
overfill position (3mm shim) which brought the response into
an easily manageable range of non-linearity. Tests yesterday
validated the improvement, which has spawned both relief and
celebration.
• Thanks a million and all the best.
