Photon-Counting and Dark-Current

Radobs 42

This document intends to show that it is technically feasible to construct a
photon-counting receiver based on a low-noise avalanche photodetector (APD)
operating in the linear or Geiger mode, and produce a performance that is
consistent with assumptions made about the sensitivity of incoherent
receivers with negligible dark-current.  In short, it will be shown that
cooled high-quality APDs have dark-currents that are unlikely to limit the
performance of our receivers; that the dominant noise sources are quantum
shot-noise and Planckian starlight and/or daylight background.

In order to achieve quantum shot-noise limited detection sensitivity in the
81 cm diameter Perkins telescope for signal strengths (flux densities) of
the order of 10^-10 W/m^2 (an approximate EIRP = 250 dBW over 10 light years
- Phew!), the unity-gain dark-current must be less than 0.1 pA.  This is
equivalent of saying that if the avalanche gain M = 100, the dark-current
must be less than 10 pA.  Shot-noise limited photon-counting is assumed,
i.e, the thermal kT front-end noise component is taken to be negligible.

On the subject of very high EIRPs, the reader should note that in Dr. John
Rather's paper to be published in next month's JBIS (LASERS REVISITED: Their
Superior Utility for Interstellar Beacons, Communications, and Travel), he
assumes effective long distance EIRPs of the order of 2.3 X 10^23 W (as
produced by a 1 MW CW Free-Electron Laser beam though a 100 meter diameter
transmitting aperture).  The thing that is inspiring about John's paper is
that he also suggests that advanced technical civilizations with a Mercury-
sized laser array could put out simultaneously one beam for each of the 400
billion stars in the galaxy.  Being more conservative, I would limit the
number of beams to a much smaller number, but would assume individual beam
powers up to at least 1 GW (equivalent EIRP for 100 m aperture > 260 dBW).

The major parameter values used in the models are given below:

Wavelength = 656 nm,
Effective Isotropic Radiated Power (EIRP) = 10^25 W (250 dBW),
Range = 10 L.Y.,
Night Sky,
Intensity Outside Atmosphere = 8.9 X 10^-11 W/m^2 (6th Magnitude),
Atmospheric Transmission = 0.4,
Telescope Aperture = 0.81 m (32"),
Antenna Efficiency = 0.7,
Spectrometer Efficiency = 0.5,
Quantum Efficiency = 0.5,
Avalanche Gain = 100,
Excess Noise Factor = 0.

Generally, APDs may be used for ultra-low light detection (optical powers
< 1 pW), and can be used in either their normal linear mode (bias voltage
slightly less than the breakdown voltage) at gains (M) up to about 250 or
greater, or as photon-counters in the "Geiger" mode (bias voltage slightly
greater than the breakdown voltage).  In the case of the latter, a single
photoelectron may trigger an avalanche pulse of about 10^8 carriers.  In
this mode, no amplifiers are necessary, and single-photon detection
probabilities of up to approximately 50% are possible.

The 250 dBW ETI signal is at the threshold of dark-sky naked-eye visibility,
assuming for a moment that the 2nd Magnitude alien star is not present to
obscure the transmitter.  For a 32" (0.81 m) diameter telescope, such as the
one at the Perkins Observatory, we find that the received signal power is
-111.4 dBW (7.2 pW), equivalent to a photon detection rate of 11.9 million
per second.  In the normal linear mode of operation, since an electron has a
charge of 1.6 X 10^-19 coulombs, a photon count-rate can be converted into
an equivalent dark-current by multiplying the count-rate by the electronic
charge and avalanche gain.  Thus, 11.9 million counts per second (cps)
produces a mean photodiode current of 190 pA for an avalanche gain M = 100.

In the Perkins telescope, Planckian starlight from a solar-type star at a
range of 10 light years will produce a background power per diffraction
limited pixel of 3.9 X 10^-15 W.  This background, produced in a 100 GHz
optical bandwidth (0.143 nm), causes a photodetector current of 0.1 pA at a
gain of 100.  This is a factor of 1900 times smaller than the 190 pA
produced by the 7.2 pW signal, and is equivalent to a background count-rate
of about 6,400 cps.

RCA/GE/EG&G produce a packaged Single Photon Counting Module type
Model SPCM-100-PQ for about $2,500, and Model SPCM-200-PQ for $3,700; the
latter having a two-stage Peltier (thermoelectric) cooler.  Cooling APDs
down from 22 C to -25 C reduces dark-count typically by a factor of 50; the
dependence of dark-count rate on temperature is exponential, i.e.,
proportional to exp(-0.55eV/kT).  The modules have a peak photon detection
efficiency = 43% at 633 nm and a dark-count rate specification of 500 cps at
a case (module) temperature of about 300 K.  This count-rate is equivalent
to a dark-current of 8 X 10^-5 pA, and is less than one thousandth of the
Planckian starlight background count-rate (0.1 pA).  These photon-counting
modules have TTL output interfaces.

As an economy measure, photon-counting receivers can be built around
discrete components and APDs like the RCA C30902E/C30902S or the RCA
C30921E/C30921S.  The quantum efficiencies peak up at a wavelength of 800 nm
to about 80%, and are greater than 50% between 550 nm and 900 nm.  Quantum
efficiencies fall below 10% at 1000 nm.  The noisier "E" suffix devices
(I presently have one C30902E and one C30921E) can be obtained for $74.8 and
$85.8, respectively.  The C30921 devices have a short light-pipe interface. 
The real differences between the "E" and "S" suffix devices, is that the
former have typical noise currents at 22 C of about 0.8 pA/rHz at a gain of
400, while the latter noise currents are about 0.2 pA/rHz.  Not
surprisingly, the "S" suffix devices are considerable more expensive.  I
have been told that the APDs used in the SPCM modules are not these
particular devices.

In order to maintain high photoelectron detection probability, we need to
set the Geiger mode threshold level at a low value.  This can only be done
if the dark-current is very low, i.e., if the device is cooled.  On the
other hand, if the threshold is set too low, thermal kT noise in the front-
end amplifier and load may increase the apparent background and noise floor.

A dark-current of 8 X 10^-5 pA is much smaller than 10 pA, which is the
multiplied dark current level that just begins to significantly degrade the
SNR at Ir = 10^-10 W/m^2.  Thus, a linear-mode dark-current of 8 X 10^-5 pA
would not impact the detection sensitivity for an intensity
Ir = 10^-10 W/m^2.  In fact, the received signal flux would have to fall to
about Ir = 10^-15 W/m^2 (EIRP = 200 dBW over 10 light years), before the
dark-current reduces detection sensitivity.  At that signal flux level, the
Planckian starlight background is already degrading the SNR.  In short, we
may conclude that under the assumptions made here about very strong visible
and near-infrared ETI EIRPs, the dark-current count in high-quality cooled
photon-counters and medium size telescopes will not be a limiting factor in
signal detectability and SNR.  Dark-current is not the only sensitivity
limiting factor.  There is a small degradation in detectability caused by
the Excess Noise Factor of an avalanche photodiode.  A typical Excess Noise
Factor x = 0.2 produces an SNR reduction of about 4 dB.

Although to date I have suggested the use of an APD as a photon-counter, in
some situations it might be preferable to use a photomultiplier.  The
spreadsheet analyses of photon-counting receivers that I have modelled
usually assume ideal photon-counters, i.e., that the probability of
detecting a photon is 50%, there are no excess noise sources, no dark
current, and that the count rate is Gaussian.  In practice, the photon-count
rate of an APD when used in the Geiger mode (thresholded) is non-Gaussian.

Other problems and design techniques associated with Geiger mode photon-
counters such as photo-detection efficiency, dead time, after-pulsing,
saturation, dynamic range, electrical bandwidth and different circuit
configurations, will be dealt with in a later document.

One last remark concerning Amateur Optical SETI in the infrared and far-
infrared.  As readers will be aware, the Carbon Dioxide wavelength of
10,600 nm is thought by some to be "magic", and this author tends to agree
with that opinion.  However, my spreadsheets appear to indicate that it is
unlikely that incoherent detection techniques can be used at 10,600 nm
because of the high background produced by the 300 K sky temperature (night
or day).  Almost by definition, amateurs are presently constrained to
observations within our atmosphere.  Notwithstanding the problems of
infrared photodetector sensitivity, cooling the infrared photodetector to
limit the dark-current, and producing a cold-shield to limit the field-of-
view (FOV) so that thermal radiation from the telescope itself does not
generate a high background, the level of sky background puts severe
constraints on optical bandwidth.  Of course, CO2 optical bandpass filters
can be considerably more narrow-band than visible bandpass filters.  Even
so, because flux densities at 10,600 nm are likely be substantially less
than predicted for 656 nm (due to lower gain transmitters), even a 1 GHz
optical bandwidth (as compared to 100 GHz for the visible) accepts too much
thermal background radiation.

It would appear that only heterodyne systems would be suitable for the CO2
wavelength, with their substantial immunity to background radiation and high
detector gain.  This immunity to background radiation behavior is
demonstrated and described for visible heterodyning systems in RADOBS.43A,
RADOBS.43B & RADOBS.43C.  These files will be uploaded shortly.  Thus, an
Amateur Infrared SETI receiver would likely be very complex and expensive,
and essentially no different to that proposed for a Professional Infrared
SETI receiver, save for the use of a smaller infrared telescope.  This is
probably a good argument for limiting Amateur Optical SETI activities just
to the visible and near-infrared.  Somewhat tongue in cheek I would say that
if ETIs wanted amateurs and not professionals to discover their signals
first, they might therefore find good reason for avoiding the magic
wavelength of 10,600 nm!  Full details of the CO2 analysis will be given in
later documentation.

July 15, 1991
RADOBS.42
BBOARD No. 609

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
* Dr. Stuart A. Kingsley                       Copyright (c), 1991        *
* AMIEE, SMIEEE                                                           *
* Consultant                            "Where No Photon Has Gone Before" *
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