figure table

# Characterization of Low Light Performance of a CMOS Sensor for Ultraviolet
Astronomical Applications

Timothee Greffe  Caltech Optical Observatories, California Institute of
Technology, Pasadena, California, USA  Roger Smith  Caltech Optical
Observatories, California Institute of Technology, Pasadena, California, USA
Myles Sherman  Cahill Center for Astronomy and Astrophysics, California
Institute of Technology, Pasadena, California, USA  Fiona Harrison  Cahill
Center for Astronomy and Astrophysics, California Institute of Technology,
Pasadena, California, USA  Hannah Earnshaw  Cahill Center for Astronomy and
Astrophysics, California Institute of Technology, Pasadena, California, USA
Brian Grefenstette  Cahill Center for Astronomy and Astrophysics, California
Institute of Technology, Pasadena, California, USA  John Hennessy  Jet
Propulsion Laboratory, California Institute of Technology, Pasadena,
California, USA  Shouleh Nikzad  Jet Propulsion Laboratory, California
Institute of Technology, Pasadena, California, USA

###### Abstract

CMOS detectors offer many advantages over CCDs for optical and UV astronomical
applications, especially in space where high radiation tolerance is required.
However, astronomical instruments are most often designed for low light-level
observations demanding low dark current and read noise, good linearity and
high dynamic range, characteristics that have not been widely demonstrated for
CMOS imagers. We report the performance, over temperatures from 140 - 240 K,
of a radiation hardened SRI 4K$\times$2K back-side illuminated CMOS image
sensor with surface treatments that make it highly sensitive in blue and UV
bands. After suppressing emission from glow sites resulting from defects in
the engineering grade device examined in this work, a 0.077
$\mathrm{m\mathrm{e^{-}}/s}$ dark current floor is reached at 160 K, rising to
1 $\mathrm{m}\mathrm{e^{-}}/\mathrm{s}$ at 184 K, rivaling that of the best
CCDs. We examine the trade-off between readout speed and read noise, finding
that 1.43 $\mathrm{e^{-}}$ median read noise is achieved using line-wise
digital correlated double sampling at 700 $\mathrm{kpix/s/ch}$ corresponding
to a 1.5 $\mathrm{s}$ readout time. The 15 $\mathrm{k}\mathrm{e^{-}}$ well
capacity in high gain mode extends to 120 $\mathrm{k}\mathrm{e^{-}}$ in dual
gain mode. Continued collection of photo-generated charge during readout
enables a further dynamic range extension beyond $10^{6}\,\mathrm{e^{-}}$
effective well capacity with only 1% loss of exposure efficiency by combining
short and long exposures. A quadratic fit to correct for non-linearity reduces
gain correction residuals from $1.5\%$ to $0.2\%$ in low gain mode and to
$0.4\%$ in high gain mode. Cross-talk to adjacent pixels is only $0.4\%$
vertically, $0.6\%$ horizontally and $0.1\%$ diagonally. These characteristics
plus the relatively large ($10\mathrm{\mu}\mathrm{m}$) pixel size, quasi
4-side buttability, electronic shutter and sub-array readout make this sensor
an excellent choice for wide field astronomical imaging in space, even at FUV
wavelengths where sky background is very low.

###### keywords:

CMOS,SRI mK$\times$nK, ultraviolet, dark current, glow suppression, dual-gain

*Timothee Greffe<EMAIL_ADDRESS>
##  1 Introduction

For decades the detector of choice for ultraviolet (UV) space applications has
been the microchannel plate (MCP) coupled to various kinds of 2D charge
sensors. Space missions such as GALEX, Neil Gehrels Swift, and Hubble Space
Telescope Cosmic Origins Spectrograph adopted MCP imagers because their
sensitivity extends into the far-UV (FUV), while the wide bandgap of their
photocathode depresses sensitivity to optical photons and allows them to be
operated at room temperature. However, MCPs have relatively low quantum
efficiency (QE)[1], require high voltages in space where electrical breakdown
is a concern, and are damaged by over-illumination. The latter issue has
restricted many astronomical UV telescopes from viewing fields containing
bright stars, particularly in the FUV where over-illumination causes severe
depletion of the photocathode.

The drawbacks of MCPs have motivated the development of Silicon-based UV
imagers (CCD and CMOS) for astronomy, where higher QE provides more
sensitivity for a given telescope size, enabling powerful observatories on
moderate-sized platforms. The ability to view fields containing bright stars
and regions where high dynamic range is required, such as the Galactic plane
and Magellanic Clouds, is another significant scientific advantage, especially
for wide-field of view (FoV) systems. On the technical side, avoiding high
voltages and being able to match pixel sizes to the specific application are
additional positive factors. For wide FoV applications, CCDs and CMOS
detectors can be assembled in close butted mosaics with $\sim$85% fill factor,
supporting imaging applications on a much larger scale than MCPs[1].

The Ultraviolet Explorer (UVEX) mission, which motivates the investigation
documented here, requires two 12K$\times$12K focal planes, imaging in
FUV($1390-1900\,\mathrm{Å}$) and NUV ($2030-2700\,\mathrm{Å}$) passbands at a
plate scale of $1.02^{\prime\prime}$ per 10$\,\mathrm{\mu}\mathrm{m}$ pixel,
and a high efficiency Long Slit Spectrometer covering the
$1150-2650\,\mathrm{Å}$ wavelength range, at $0.4\,\mathrm{Å/pixel}$ sampling,
with a single detector. The sky in the FUV is so dark that even a small amount
of readout noise dominates photon shot noise from sky in a typical 900s
exposure, so the ideal sensor will have very low read noise ($\sim
2\,\mathrm{e^{-}}$) and low dark current
($<10^{-3}\,\mathrm{e^{-}}/\mathrm{s}$) at temperatures readily accessible
with radiative cooling (170K).

While CCDs can meet some of these requirements at beginning-of-life, CMOS
image sensors have very significant advantages. Since charge is converted to
voltage within the pixels, there are negligible charge transfer losses, a
problem which is particularly severe in CCDs when background is low, and gets
worse with radiation damage, requiring complex post processing based on
frequent recalibration as demonstrated on HST[2][3]. Also, CMOS imagers do not
require a shutter. While CCDs can also be operated without a shutter, the
required subtraction of averaged parallel overscan lines adds shot noise and
delivers poor cancellation of image smear in the presence of pointing jitter.

In the CMOS architecture studied here, the 5-transistor pixel design (Figure
2) eliminates dead time between exposures. Charge transfer to the sense node
defines the end of one exposure and the start of the next, allowing charge
collection to continue during readout without charge smearing. We use Rolling
Shutter mode which requires one frame time to clear charge at the start of a
sequence of exposures. At only $3\,\mathrm{s}$ for a 4K$\times$4K sensor this
overhead is much shorter than a typical CCD readout. Subsequent readouts
between exposures of the same scene do not represent any overhead. An
important application of this is to extend the dynamic range by combining
consecutive short and long exposures, e.g. pairing 3 s and 300 s exposures
extends dynamic range by 100 without dead time between exposures due to
readout.

Another advantage of CMOS imagers is the flexibility they afford for subarray
readout. Since pixels are addressed directly, subarrays can be read at high
cadence without disturbing signal integration on the remainder of the sensor.
This feature further extends the dynamic range to bright targets which would
saturate in the normal frame time, and enables high time resolution studies of
rapidly varying sources. For space applications where guide stars are
required, subarray readout can provide rapid centroiding of bright stars
without interfering with the use of the rest of the device for deep science
exposures.

Figure 1:  The mK$\times$nK Imager reticle consists of four modular building
blocks which are photocomposed (“stitched”) to create custom dimensions in 1k
increments. The sizes shown have been successfully produced, for ground and
space missions.

In this paper we report on the characterization of an SRI Nk$\times$Mk CMOS
sensor[4] made by Sarnoff International for scientific imaging from space.
This radiation tolerant design (Table 1) has significant flight heritage
(Parker Solar Probe, Solar Orbiter, SOLO HI EIS) [5] [6]. It can be fabricated
in 1k increments up to 4k$\times$4k from the same reticles (Figure 1) and the
compact address logic allows 4k$\times$4k tiles to be mosaiced with high fill
factor, enabling large focal plane areas. The device used in this work has a
4K$\times$2K format, as used on the Europa Clipper mission. Ultimately for
large FOV astronomical applications such as UVEX a 4K$\times$4K size is
attractive. Such devices have been made successfully with the same reticles
for Lawrence Livermore National Laboratory’s National Ignition Facility [4].
All sizes have very similar electrical characteristics since they are
fabricated using the same reticles, at the same foundry, using the same
processes.

Total Ionizing Dose |  $>100$ Krad
---|---
Non-Ionizing Energy Loss |  $>3\times 10^{11}$ protons/$\mathrm{cm^{2}}$ @ $63$ MeV protons
Single Event Latchup |  $>100$ MeV $\mathrm{cm^{2}/mg}$
Single Event Upset |  $>25$ MeV $\mathrm{cm^{2}/mg}$
Table 1: Radiation tolerance of SRI Nk$\times$Mk, reproduced from data sheet.

##  2 Provenance of Sensor Under Test

The 4K$\times$2K device used for this study was produced together with
identical wafers for the Europa Clipper mission [4]. The Jet Propulsion
Laboratory’s Advanced Detectors, Systems, and Nanoscience Group at JPL’s
Microdevices Laboratory (MDL) applied their end-to-end post fabrication
processing including bonding, thinning (to $7\pm 0.3\mathrm{\mu}\mathrm{m}$),
and delta-doping process using Molecular Beam Epitaxy [7] [8] [9] [10] at
wafer level. This process has been demonstrated over the years on a number of
CCD and CMOS formats to provide high and stable quantum efficiency across the
UV and visible spectrum [9]. Every photon not reflected or absorbed in the
anti-refection (AR) coating is both detected and collected into pixels [4].

JPL applied various AR coatings and metal dielectric filters (MDFs), returning
several die to SRI for packaging and screening tests. The in-band UV QE and
out-of-band rejection obtained with the delta doping and direct deposition of
MDFs will be described in a companion paper. An earlier broadband AR-coated
version was measured for Europa-Clipper band [11]

Unfortunately, pinhole defects in the photo-resist that protects the device
during the etching of back surface to reveal the bond pads caused damage at
random locations on the delta doped wafer. An engineering grade device without
any coatings, but with tens of these ”etch-through” defects was provided to
Caltech for evaluation at lower temperatures than previously explored. At
these temperatures several strong glow sources became apparent.

We will show that the relatively simple on-board circuitry for row/column
decoding (no timing generator or ADCs) allows for sufficient glow suppression
to meet the demanding dark current requirement with ample margin (§5.5), while
read noise rivals the best CCDs (§5.7). Linearity is good (§5.2), inter-pixel
correlation is low(§5.8), and dynamic range is exceptional when CMOS
capabilities for dual gain (§4.3.1) and dual exposure duration are harnessed.
Readout overheads are insignificant.

##  3 SRI mK$\times$nK CMOS detector

###  3.1 Pixel Topology

Each pixel is made up of a light-sensitive pinned photodiode, a transfer gate,
and 4 transistors to reset the sense node and select it during readout (Figure
2). A pixel read cycle begins by resetting the sense node to the reference
potential, $\mathrm{PIX\ VREF}$ by closing transistors $\mathrm{RESET}$ and
$\mathrm{MIMSELECT}$. If $\mathrm{MIMSELECT}$ is high during the time charge
is sensed, the $\mathrm{MIM}$ capacitance is in parallel with the sense node
increasing the conversion gain ($\mathrm{e^{-}}/\mathrm{\mu}\mathrm{V}$) and
well capacity at the expense of increased read noise (in $\mathrm{e^{-}}$). By
reading out the voltage before and after connecting the MIM capacitor, one can
read the same signal in high then low gain, to provide low noise then high
signal capacity. Transfer Gate and reset operations are performed for an
entire row and cannot be executed on single pixels. This prevents CCD-style
Correlated Double Sample (CDS) timing if using off-chip digital subtraction,
though in-pixel circuitry is provided for analog subtraction of an entire row
concurrently with a conventional short delay between baseline and signal
samples.

Figure 2:  Five Transistors with Pinned Photo-Diode Pixel (5TPPD) Diagram.
Reproduced from [12].

The detector has the ability to reset and transfer charges from the
photodiodes to their sense nodes over the whole array in a single pulse using
a signal labelled $\mathrm{SNAP}$. This is used to run the detector in “Global
Shutter” mode, resulting in concurrent exposure start and end for all of the
pixels of the array. However we exclusively use Rolling Reset mode in which
lines are reset and read sequentially as this has yielded better noise
performance.

###  3.2 Output Buffer

The RAW video outputs are buffered by p-type transistors in a Source-Follower
topology. We use $3.3\,\mathrm{k\Omega}$ pull-up resistors to
$3.3\,\mathrm{V}$ as the load. No other processing occurs: we do not invoke
the optional RC filtering.

Alternatively, the CDS video output pins of the detector can be buffered by
n-type transistors, also in a Source-Follower topology. In this case an analog
CDS circuit embedded in each pixel, stores the reset levels of a row before
subtracting the signal obtained after charge transfer. This subtraction is
done using switched capacitors and does not deliver the optimum noise
performance, so we do not use this analog CDS mode.

##  4 Experimental Setup

###  4.1 Cryostat

A cryostat with Liquid Nitrogen (LN2) cooling is configured for operation of
the detector at temperatures down to 130 K. A large printed circuit board,
dubbed the Vacuum Interface Board (VIB), is located between the front and back
sections, sealed with O-rings on each side. The VIB transports all required
signals into the vacuum on internal layers as well as supporting electrical
components in vacuum (such as the zero-insertion-force socket housing the
detector) and in atmosphere (FPGA, connectors to detector controller, test
points, and switches that support trouble-shooting). The detector socket is
thermally strapped to the nitrogen tank at 77 K, while the VIB has cut-outs to
minimizing conduction to the outside world at room temperature. We tuned the
thermal link to the liquid nitrogen tank for 120 K equilibrium temperature
without active heating. Detector socket temperature is servo controlled to 140
K with millikelvin stability. Detector electronics are mounted directly on the
cryostat in close proximity to the VIB to limit the length of the video path.

Figure 3:  CMOST Camera. The open cryostat is shown with detector inserted
into its zero-insertion-force socket. The controller sits on top of the
cryostat, and the Vacuum Interface Board provides row and column address
generation and routing of video signals.

###  4.2 Camera Controller

The detector controller is an “Archon” made by Semiconductor Technology
Associates Inc111http://www.sta-inc.net/archon/. It offers versatile
configuration including clock and bias drivers, LVDS outputs, and 4 slots,
each with 4 video processing channels. An intuitive waveform definition
language has been added by Caltech Optical Observatories (COO).

Direct addressing of rows and columns is supported by the detector to allow
efficient subarray readout or user selectable raster scanning direction. This
requires a mix of direct selection of the 1K pixel blocks and binary coding
for row selection within those blocks. As this complexity is not supported by
the Archon controller, we have added an external FPGA to generate the
addresses, a Xilinx Zynq SoC on Picozed board which plugs into the atmospheric
side of the Vacuum Interface Board.

###  4.3 Readout Mode

The detector offers a large range of possible readout schemes thanks to its
versatile addressing topology [12]. In Global Shutter mode, one must invoke
the in-pixel (analog) CDS processor to avoid having a full frame time between
measuring baseline (post reset) level and signal. This uses switched
capacitors that introduce additional noise (when reset). To avoid this
additional noise source, all performance measurements reported here we have
used Rolling Shutter (line by line reset) and digital CDS.

Rolling Reset is widely used in CMOS detectors. Light is accumulating at all
times, so the transfer of charge from photodiodes to their sense nodes,
defines both the end of one exposure and start of the next. Each line is
addressed sequentially. The sense nodes for all pixels in one line are reset
concurrently. In our ”line-wise digital CDS scheme”, baseline samples are
digitized sequentially for the entire line, then charge is transferred from
photodiodes to all sense nodes concurrently for the same line. The resulting
signal levels for each pixel are digitized sequentially. The process then
repeats for the next line. The difference between the baseline and signal
samples is calculated in the host computer post-facto. 1.5 s is required to
scan a frame with 2048 lines at 700 kpix/s, with 16 channels being read in
parallel each servicing a block of 256 columns.

The 1.5 s frame time results in a small skew in exposure start times across
the image area but this has negligible effect in the long exposures
anticipated in our application. When acquiring a sequence of frames there is a
1.5 s overhead to reset the pixels at start of sequence (e.g. after telescope
slew) but no dead time between frames within a sequence. Table 2 and Figure 4
describe a multi-frame sequence for a hypothetical $4\,\times
4\,\mathrm{pixel}$ array.

With exposure duration being defined by the time between charge transfers, it
follows that minimum exposure time is one frame time and longer exposures are
executed by inserting a delay between frame scans. Faster cadence exposures
can be executed when reading a subset of rows usually scanning between two
preset pointers.

The Archon version used for these experiments was originally developed for CCD
readout and thus has an AC-coupled differential video input. The negative
input is grounded while positive input is connected to either the RAW or the
CDS output of the detector selected by a mechanical switch. (We prefer RAW, as
noted.) The DC level of the JFET input stage (in the Archon, post AC coupler)
is set through an analog switch typically once per row. This level is chosen
so that the differential input voltage is near the beginning of the ADC input
range.

Each channel is digitized by a separate 16 bit ADC running at 100 MHz. An
analog filter limits bandwidth into the ADC only to the extent required to
prevent aliasing. The high sample rate allows each channel to be operated in
digital oscilloscope mode for diagnostic purposes. When executing digital CDS,
noise bandwidth is set by the number of consecutive 100 MHz samples which are
averaged per pixel. This averaging occurs concurrently in FPGAs on each video
card.

The line-wise digital CDS arrangement avoids the $kTC$ noise incurred when
resetting the analog CDS capacitors. The fact that baseline and signal have
identical signal path assures good gain matching for optimal rejection of low
frequencies. Surprisingly, the 366 $\mathrm{\mu}$s interval between baseline
and signal sample proves to be short enough that low frequency noise sources
(bias voltage drift; 1/f noise) do not negate these benefits.

Step | Action | Output
---|---|---
1 | Reset Sense Node |
2 | Read Sense Node | Baseline Image Low Gain
3 | Transfer charge from Photodiode to Sense Node |
4 | Read Sense Node | Signal Image High Gain
Table 2:  Row readout sequence in Rolling Reset mode. Figure 4:  Readout
Diagram of the Rolling Reset Mode.

####  4.3.1 Dual Gain mode

For best noise performance the smallest possible sense-node capacitance is
desired as this increases the voltage change in response to a given charge.
However the signal range is then limited by available voltage swing. To allow
greater signal range, a MIM capacitor in each pixel can be added in parallel
to the sense node capacitance by closing the appropriate analog switch (Figure
2). Since the readout of the voltage does not affect charge on the sense node,
it is possible to read the same charge packet first with MIM capacitor
isolated then again after it is connected. The sequence of steps for this Dual
Gain readout mode is detailed in Table 3.

The key here is to establish separate CDS baselines for both gain states.
There is no $kTC$ noise problem since any charge trapped when opening the
gain-select switch is measured at Step 4 and vanishes when the switch is
closed again at Step 7.

Frame time is almost doubled since each line is digitized twice as many times.
Due to the added time delay, the difference between the frames produced at
Steps 9 and 2 provides a CDS sample which is inferior to the difference
between frames produced at Steps 6 and 4. However, this slightly elevated read
noise is irrelevant since the low-gain sample is only used for large signals
that are shot-noise limited.

Step | Action | Output
---|---|---
1 | Reset Sense Node in Low Gain |
2 | Read Sense Node in Low Gain | Baseline Image Low Gain
3 | switch to High Gain |
4 | Read Sense Node in High Gain | Baseline Image High Gain
5 | Transfer charge from Photodiode to Sense Node |
6 | Read Sense Node in High Gain | Signal Image High Gain
7 | Switch to Low Gain |
8 |  Transfer charge left behind. KEY STEP |
9 | Read Sense Node in Low Gain | Signal Image Low Gain
Table 3:  Row readout sequence to generate a dual-gain image.

##  5 Performance

###  5.1 Photon Transfer Curves and Well capacity

To infer well capacity and conversion gain $(\mathrm{e^{-}}/\mathrm{ADU})$,
pairs of identical exposures with increasing integration time are acquired
with temporally stable flux and moderate spatial uniformity. We then subtract
the two frames of each pair to remove common mode patterns due to illumination
or fixed electrical patterns, leaving only the random noise component of the
signal. Spatial variance is then calculated for a region chosen to be free of
bad pixels or other artifacts such as ROIC glow. This procedure is repeated
for both low and high gains.

Figure 5:  Photon transfer curves of low and high gain modes. Readout noise,
system gain and Full Well Capacity can be directly read from this plot.

Conversion Gain ($\mathrm{e^{-}}/\mathrm{ADU}$), the inverse of the slope of
the the linear fit, is calculated separately for each gain mode. These values
are then used to convert signal and variance to values displayed in electrons,
for both gain states on the same Photon Transfer Curve (Figure 5). This plot
format is convenient to immediately highlight the signal level at which shot
noise dominates. This measurement yields readout noise of 2.1 $\mathrm{e^{-}}$
and 12.3 $\mathrm{e^{-}}$ and a Full Well Capacity of 15
$\mathrm{k}\mathrm{e^{-}}$ and 120 $\mathrm{k}\mathrm{e^{-}}$ in the high gain
and low gain modes, respectively.

However, when only spatial variance is used in photon transfer curves, total
noise is underestimated due to interpixel correlations, so system conversion
gain $(\mathrm{e^{-}}/\mathrm{ADU})$ is over estimated. The correct conversion
gain is obtained when the covariance with adjacent pixels is included in the
photon transfer curve (§5.8). Conversion gain has been corrected for Inter-
Pixel Correlation (IPC) throughout this paper resulting in a 6% reduction in
dark current and read noise compared to that inferred from simple photon
transfer method using variance alone. Corrected conversion gains are 1.13
$\mathrm{e^{-}}/\mathrm{ADU}$ in the high gain and 8.0
$\mathrm{e^{-}}/\mathrm{ADU}$ in low gain mode.

###  5.2 Linearity

Linearity has been measured in both high and low gain modes by varying the
exposure time while the detector is illuminated with a constant flux. To do
this, a red LED is attached to the LN2 tank on a separate thermally regulated
platform, operating slightly above 77 K. A bench current source injects a
current ranging from a few tens to hundreds of nanoamperes leading to a total
power dissipation well below a microwatt, resulting in very little efficiency
variation due to junction self-heating.

We infer that detector self-heating is responsible for some gain drift as
readout cadence influences the level of the video signal. Sensor current
consumption peaks at $\sim 70\,\mathrm{mA}$ during readout, dissipating
hundreds of milliwatts. This highlights the need for a more thermally
conductive package to minimize the change in detector temperature due to self
heating. The package in use is far from optimal in this regard so significant
performance improvement is probably possible. It is also clearly beneficial to
adopt clocking schemes which maintain the readout cadence even when idle to
minimize temperature drift.

An initial transient in the signal is seen in Figure 6 after turning on the
detector and continuously reading it at a constant cadence. This transient
appears only where there is illumination: not in dark areas under a mask. This
demonstrates that the CDS processing indeed corrects for offset drift of the
RAW video levels but cannot prevent the gain change. We explore this
temperature dependence in more detail in §5.3, finding that the video level
settles to 1$\mathrm{e^{-}}$ after approximately 30 min.

Figure 6: Initial transient after starting the readout of the detector at a
constant frame rate. A transient is only visible on the illuminated area,
revealing a gain change.

In order to mitigate gain changes due to self-heating during the linearity
experiment, the detector was read out at a very low duty cycle (at least 5 min
per frame), so that the effect of self-heating was negligible.

We estimated the non-linearity by fitting an affine function or a quadratic
with non-zero value at origin. We acknowledge that this is not ideal, but
fixing a zero offset leads to a large mismatch with our fit. The actual
detector’s transfer function most likely requires a more complex function than
a low order polynomial to produce a better fit. In order to optimize both the
residuals during our fitting process and the non-linearity itself, we included
a weighting factor, $w_{i}$, in the estimator $E$, which is defined as

$E=\sum
w_{i}^{2}\left(p(x_{i})-y_{i}\right)^{2}=\sum\left(\frac{p(x_{i})-y_{i}}{y_{i}}\right)^{2}$
(1)

where $y_{i}$ is the measured signal at exposure time $x_{i}$, and $p(x_{i})$
is the value of the linear fit at exposure time $x_{i}$. This prevents the
gain correction from increasing steeply at the lower end of the non-linearity
curve when the denominator becomes smaller.

Figure 7 summarizes the linearity behavior in high gain
($1.13\,\mathrm{e^{-}}/\mathrm{ADU}$) mode. A linear fit results in an RMS
deviation of 1.4%, with larger disagreement for higher signal. Better
agreement is achieved with a quadratic fit, yielding an RMS 0.2%. This is
consistent with typical CMOS sensors where non-linearity originates in both
the voltage-dependency of the PN junction capacitance that contributes to
Sense Node capacitance, and in the non-linearities of the source-follower
itself [13]. The inset plot shows linearity behavior for faint signals
(obtained at reduced flux), demonstrating that the fit improves to an RMS
deviation of 0.1% and projects to 0 signal for null exposure time. (We must
extrapolate to zero-length exposure since minimum exposure time is the frame
scan time which is 1.5 s when reading at $700\,\mathrm{kPix/s/ch}$.)

Figure 8 summarizes the linearity behavior in low gain
($8.0\,\mathrm{e^{-}}/\mathrm{ADU}$) mode. This shows similar behavior: the
linear fit yields an RMS value of 1.5%, while the quadratic fit gives better
agreement with RMS deviation 0.4%. Note that the faint signal is neglected
since low gain mode will not be utilized for very faint signals.

Figure 7: Linearity in high gain mode. Faint signal ranges from 0
$\mathrm{e^{-}}$ to 1000 $\mathrm{e^{-}}$. Figure 8: Linearity in low gain
mode. Note that the faint signal is neglected since low gain mode will not be
utilized for very faint signals

###  5.3 Temperature dependence of the gain

Temperature stability requirements in flight will probably be driven by the
temperature dependence of the gain. To evaluate this, we recorded identical
flat fields at moderate intensity for temperatures varying between 140
$\mathrm{K}$ to 180 $\mathrm{K}$. Light intensity was held constant while
regulating LED temperature to millikelvin precision. We allowed a settling
time of 30 min between each 5 $\mathrm{K}$ step.

Figure 9 shows that the temperature dependence of gain is not linear but
gradually flattens as the temperature increases. Around 165$\,\mathrm{K}$, the
gain varies by 0.15 $\%/\mathrm{K}$. It is not possible to determine from this
experiment whether the gain dependence on temperature is caused by variation
in QE, sense node capacitance, Source-Follower transconductance, or load
resistance.

It would be interesting to reproduce this experiment to characterize the
temperature dependence of the offset. While the per-row CDS processing removes
any slow DC-offset variation, one could track the baseline samples, however,
the AC-coupling of our video acquisition board currently prevents such
measurement.

Figure 9: Temperature dependence of the gain between 150 $\mathrm{K}$ and 180
$\mathrm{K}$. Around 165 $\mathrm{K}$, the gain varies by 0.15
$\%/\mathrm{K}$.

###  5.4 Multiplexer (Mux) glow

Electronics surrounding the image area (primarily logic and pixel drivers on
the left edge of the chip) act as glow sources that become visible in long
exposures. Figures 10(a) and 10(b) show Dark Maps generated from the
difference of 18 hour and 1 hour exposures to suppress fixed patterns and
reveal $\mathrm{m\mathrm{e^{-}}/s}$ effects.

It can be seen that light is emitted by the row select logic to the left of
the image and the column select logic well below the bottom of the image. The
device under test also had several strong glow sources in the image area to
the right and below of the area displayed.

We suppress photo-emission from the address logic by reducing the levels of
bias voltages during exposure, where not required in the charge collection
process. The only remaining biases are VDD driving the logic and the Transfer
Gate that keeps the charges in the photo-diode. Experience shows that the
three biases V_Ref, V_Reset_High, and V_MIM_High must be kept on to ensure a
valid bias of the Sense Node before readout. Some settling time was added
after turning the other biases on again and starting a readout of the image
area. This settling time, though dozens of seconds, is negligible compared to
the long integration times required for glow to be visible. This glow-
mitigation technique greatly increased the area where dark current is less
than 1 $\mathrm{m\mathrm{e^{-}}/s}$.

(a) 18 hours exposure in the dark while keeping electronics in its default
state.

(b) “Low glow” 18 hours exposure in the dark while shutting down support
electronics.

Figure 10: Dark Maps of the top left quadrant of the detector show fine
structures and glow sources in and around the image area. Most of the glow
coming from the left edge of the chip where lies the logic and pixel drivers
is turned off by lowering the biases during the exposure.

###  5.5 Dark current

Dark current has been measured at temperature between 140 $\mathrm{K}$ and 240
$\mathrm{K}$. One hour was allowed for settling between each temperature
change. No hysteresis from heating or cooling the detector is observed. We
evaluate dark current within a sub-window in the region of the detector
minimally affected by glow. In spite of the very low signal, good signal to
noise ratio is obtained by using a large number of pixels and very long
exposure times.

McGrath et al. [14] list different mechanisms as possible sources of dark
current, each having their own temperature dependence. We do not attempt to
identify the dominant source, noting only that the dark current decrease
follows the expected Arrhenius law, until a a floor is reached at 0.08
$\mathrm{m\mathrm{e^{-}}/s}$ for temperatures below 165 $\mathrm{K}$.

Given 2 $\mathrm{e^{-}}$ read noise and 900 s exposure time, the dark current
can rise to 1 $\mathrm{m\mathrm{e^{-}}/s}$ before increasing total noise by
10%. These requirements imply that the operating temperature could be as high
as 184 $\mathrm{K}$ before shot noise on dark current becomes significant.

The striations to the right in Figure 10(b) are due to light scattering from a
bright defect at the lower edge, which we assume will not be present in
science grade devices. A dozen or so larger, approximately semicircular, white
spots are are not due to cosmic rays but appear to represent weak glow sites
of order $2\,\mathrm{m\mathrm{e^{-}}/s/pixel}$ at peak, affecting fewer than
1% of pixels.

Figure 11:  Dark current for a wide range of temperatures. A simple fit of an
Arrhenius law shows the expected temperature dependency.

###  5.6 Optimizing Speed and Noise Performance

The STA Archon controller digitizes pixels at a rate of 100 MHz and supports
sample averaging in real time for each channel to provide low-pass filtering.
This is the digital equivalent of the analog integrator found in traditional
CDS processors.

Readout noise tends to increase with higher pixel frequency, as noise
bandwidth increases when there is less sample averaging. Conversely, when
pixel rate is low the increased interval between baseline and signal samples
results in poorer rejection of low frequency noise processes which begin to
dominate. We explored multiple pixel frequencies from 700 kHz to 1.4 MHz for
numerous averaging window widths.

For any given pixel time, when the averaging window is too wide, the sampling
of the video signal begins before it settles sufficiently, with adverse
effects on gain and linearity behavior. Therefore we check Gain and linearity
using low level flat illumination to infer changes in system gain and thus the
true noise in electrons.

Figure 12: Pixel Speed Noise optimization. For each pixel frequency, an
optimum window range is found.

When the window becomes too wide, the gain decreases and the noise rises. For
each pixel frequency, there is therefore an optimal window width at the bottom
of each curve in Figure 12. In this paper, we only use the optimum sample
width for any given pixel frequency.

###  5.7 Read noise

CMOS sensors can exhibit significant spatial variation in readout noise,
predominantly due to single electron traps close to the channel of the pixel
buffer MOSFET. On some pixels, this creates a bistable video level known as
Random Telegraph Noise (RTN), whose amplitude and characteristic time constant
vary from pixel to pixel, with characteristic switching rate being dependent
on temperature.

In Figure 15 a time series of a pixel exhibiting strong RTN can be seen
jumping between three states after CDS processing, representing a negative
transition between CDS samples, a positive transition, or no transition.

The noise map in Figure 13 was created by computing the (temporal) standard
deviation of each pixel from 94 dark frames.

Figure 13: Noise Map of the detector in high gain. Excess noise is visible in
the bottom rows, next to the amplifiers. The bad column generates noise in its
surrounding as well as four distinct clusters.

The histogram in Figure 14, was created from data in subset at top left of the
temporal noise map, chosen to exclude defective areas. Instead of following
the ideal Gamma distribution, the measured distribution is skewed with many
pixels being noisier than expected.

Given this highly skewed distribution, it may not be obvious what is the best
metric for noise performance. The modal noise is 1.33 $\mathrm{e^{-}}$, the
median noise is 1.43 $\mathrm{e^{-}}$, and the mean is 1.70 $\mathrm{e^{-}}$.
We propose that a better metric is the square root of the average variance
across all pixels not excluded as “too noisy” to be used. The square of this
“RMS noise” times the number of pixels in a photometric aperture then
represents expected total variance which can be used for making SNR
projections. Figure 16 shows the RMS Noise as a function of the number of
pixels included. As more pixels are classified as “bad” the RMS Noise improves
but at the expense of lost information where interpolation across bad pixels
is employed.

Figure 14: Noise distribution of pixels in a clean sub-array of the detector.
The ideal gamma distribution describes distribution if noise were distributed
normally in the detector. Figure 15: Fluctuating level of a pixel affected by
Random Telegraph Noise. The amplitude of the step is much higher than the read
out noise. Note that the size of the step is constant while transition timing
is random. Figure 16: Square root of average noise variance for all pixels
included in window, after exclusion of noisiest pixels, plotted for three
different pixel rates.

###  5.8 Inter-Pixel Correlation (IPC) - Cross-correlation

Pixels may couple to their neighbors via two main effects [15][16]: 1)
Brighter Fatter Effect (BFE) [17] [18] is the tendency for previously
accumulated charge to repel incoming charge, allowing neighboring pixels to
collect additional electrons; 2) Inter-Pixel Capacitance leads to voltage
coupling between neighboring pixels [19]. The method described below is used
to evaluate the total contribution of inter-pixel effects (BFE and Inter-Pixel
Capacitance) to cross-correlations without distinguishing them. This total
effect will be referred to as the Inter-Pixel Correlation (IPC). A method to
distinguish underlying inter-pixel phenomena using correlations in flat feilds
is described in papers by Hirata et. al. [15] and Choi, et. al [19].

We extracted the impulse response from a difference of two flat frames using a
2D auto-correlation method. To limit errors due to illumination non-uniformity
and imperfections within the device itself, the area we used for processing
was limited to well chosen $256\times 256$ pixel subarrays. This is only
enough to provide a $\sim 0.4\%$ error bar with our results according to [15].
We performed a Monte Carlo simulation using fake shot-noise limited frames
with no IPC to confirm this error bar. Forty-eight pairs of frames were then
combined to reduce the errors. The normalized kernel of the inferred impulse
response is shown in Figure 17.

Figure 17: Left: Auto-correlation of the difference of two flat frames. The
noise is reduced by averaging 48 $256\times 256$ pixel patches. Right: Impulse
response or IPC reconstructed from the Autocorrelation in low gain mode

We reproduced this analysis for a range of illumination levels (Figure 18). We
define the horizontal (vertical) correlation as the ratio of the first
horizontal (vertical) neighbors over the central peak of the PSF. Here, the
noise associated with each sample is evaluated by computing the standard
deviation of the correlation coefficient of pixels far away from the center of
the PSF. Both horizontal and vertical directions display a similar rate of IPC
increase with signal, a characteristic associated with decreasing slope in the
variance versus mean as signal increases. Both effects are typically
associated with BFE but confirmation awaits spot projection tests in which the
dependence of lateral charge diffusion on signal contrast can be measured
directly. It is relevant to note here that the pixel clock was slowed down to
1.25 kHz to eliminate any inter-channel coupling or bandwidth limit coming
from the video acquisition chain.

Figure 18: Horizontal and Vertical Correlation of first neighbors in low gain
mode.

The classical Variance vs. Mean method [20] assumes pixels are uncorrelated
and therefore underestimates the shot noise of the incident photons due to the
smoothing effect of the spatial correlation. Figure 19 shows such a Photon
Transfer Curve. A similar Variance vs. Mean curve that integrates the power
distributed in the wings of the impulse response reveals the true conversion
gain. Before correction for correlations, the conversion gain is overestimated
by $\sim 6\%$. The corrected Conversion Gains have been used throughout this
paper wherever units are in $\mathrm{e^{-}}$.

Figure 19: Photon Transfer curve obtained in Low-Gain mode by taking into
account the pixel correlation. The total conversion gain drops by 6% from
$8.5\,\mathrm{e^{-}}/\mathrm{ADU}$ to $8.0\,\mathrm{e^{-}}/\mathrm{ADU}$.

###  5.9 Cosmic Ray Statistics

We have examined the distribution of cosmic rays incident on the detector from
three 18 hour dark exposures of the CMOS detector in order to confirm that
event rates and number of pixels affected are as expected. This information is
useful for understanding how particle event sizes (track lengths) are likely
to scale if thickness is changed, and to check that the detector package and
AR coatings do not produce additional events. Bad pixels were masked to avoid
spurious detections, but this masking did not include the noisiest pixels.

Cosmic rays were identified as any contiguous region above a threshold set to
50 e-, well above the median read noise. This resulted in 31,877 events, or
1.45 $\mathrm{CR/min/cm^{2}}$, which is in agreement with the expected 1
$\mathrm{CR/min/cm^{2}}$ [21], with the excess being typical for background
radiation from our concrete building based on prior in-house measurements with
CCDs. Figure 20 shows four examples of cosmic ray events identified with this
method.

Figure 20: Example of various length cosmic ray events identified by finding
contiguous regions above 50 $\mathrm{e^{-}}$ in dark frames.

For this experiment, the detector was facing the horizon. The incident angle
of incoming cosmic rays, $\theta$, was then calculated to follow the
distribution shown in Figure 21(b). Equation 2 accounts for the typical
angular distribution of muons at the ground according to [21].

$P(\theta)=cos^{2}(\theta-\pi/2)*cos(\theta)$ (2)

A diagram of the incident angle in reference to the cosmic ray and detector
facing the horizon is shown in Figure 21(a). The length $l$ of each Cosmic Ray
track can then be related to the incident angle $\theta$ and the thickness $T$
of the detector by $l=T*tan(\theta)$.

(a) Reference diagram for incident angle $\theta$ and azimuthal angle $\phi$.

(b) Expected angular distribution of cosmic rays hitting the detector.

Figure 21: Muons and cosmic rays are preferentially coming from the zenith
while our camera system is pointing towards the horizon. Note muons coming
with a high incidence onto the detector leave a longer trace than those coming
with a normal incidence.

Using this geometric model, we are able to use the cosmic ray length
distribution to infer the thickness of the detector, previously measured
optically to be $7.0\pm 0.3\mathrm{\mu}\mathrm{m}$. This was done by running a
Monte Carlo simulation for the incident angle of cosmic rays, $\theta$, drawn
from the distribution in Figure 21(b). We calculated the distribution in
length of the simulated cosmic ray using the angle and thickness of the
detector for 4 different thicknesses: 5 microns, 10 microns, 15 microns, and
20 microns. Histograms of these simulated events were then compared to the
measured distribution of track length to see which thickness agrees with the
data. We estimate the measured length distribution by taking the diagonal
length of the bounding box of each cosmic ray. The length distribution agrees
with the expectation that shorter events are more likely, as longer cosmic ray
tracks correlate with steeper incident angle. The mean track length is 3.6
pixels. The results of the Monte Carlo simulation are compared to the measured
length distribution in Figure 22. The implied detector thickness is closer to
5 microns than to 10 microns, thus only slightly less than the direct optical
measurement.

Figure 22: Comparison of cosmic ray track length distribution to Monte Carlo
simulation.

We determine from this length distribution that the total rate of pixels
affected by cosmic rays is 4.1 $\mathrm{pixel/min/cm^{2}}$ and that the
fractional area is $4.1\times 10^{-4}\,\%/\mathrm{min}$.

Figure 23 shows the charge distribution for all events and just multi pixel
events for comparison. We observe that single pixel events produce excess
counts near the minimum charge deposition, suggesting that this is due to some
pixels having sufficient Random Telegraph Noise (RTN) to exceed the CR
detection threshold. We assume the multi-pixel event distribution is the true
distribution, and will return to masking pixels with excess RTN later. The
modal value of the multi-pixel charge distribution is 175
$\mathrm{e^{-}}$/pixel with estimated width 309 $\mathrm{e^{-}}$/pixel.

Figure 23: Cosmic Ray Charge Distribution for (left) all events and (right)
multi-pixel events. The excess counts at lowest charge levels (at left) may be
due to RTN and must be investigated further.

98% of cosmic rays are expected to be muons which create linear tracks with
known deposition rate[22]. To measure this deposition rate, we plotted the
total charge deposited versus track length. This was measured in pixels, and
thus is projected onto two dimensions rather than being the true three
dimensional track length for each event. The contribution of device thickness
is significant only for track lengths less than $\sim
100\,\mathrm{\mu}\mathrm{m}$. Figure 24 shows an average
$70\,\mathrm{e^{-}}/\mathrm{\mu}\mathrm{m}$ charge deposition rate in the
longest tracks region ($>100\mathrm{\mu}\mathrm{m}$), which is higher than the
$27\,\mathrm{e^{-}}/\mathrm{\mu}\mathrm{m}$ reported in [22] for comparably
thin silicon, but very similar to deposition rate measured with thick CCDs.

Figure 24: Charge vs. track length for cosmic ray events. The estimated slope
is printed in $\mathrm{k\mathrm{e^{-}}/\mathrm{\mu}m}$, with uncertainty
estimated from the covariance matrix.

##  6 Summary

The SRI 4K$\times$2K described here is an “engineering grade” device produced
from a wafer that was part of a production run for the Europa Clipper mission.
In spite of a post-processing error (in the etching step to expose bond pads
after backside processing), which produced several severe glow sites, dark
current and read noise in the unaffected areas are excellent, rivalling the
best CCDs. In addition to being much more radiation tolerant than any CCD,
this sensor offers higher exposure duty cycle, electronic shuttering, extended
Dynamic Range (dual gain, dual exposure), and the ability to read subarrays
(for guiding and/or photometry of very bright stars) while continuing long
exposures on the remaining pixels. The device exhibits excellent linearity,
low correlation between adjacent pixels and the weak dependence of this
correlation on signal bodes well for future measurements of brighter-fatter
effect. The low thickness in relation to pixel size minimizes cosmic ray track
length, while the narrowness of the tracks suggests low lateral charge
diffusion, though this has not yet been carefully measured.

Future tests will include projection and scanning of thousands of sub-pixel
spots to characterize charge diffusion, to investigate the brighter-fatter
effect, and to verify that photometry does not vary appreciably with sub pixel
spot motion. More sensitive image persistence tests are also planned.

Meanwhile work is proceeding (at JPL) to validate coating performance,
optimizing both in-band QE and out-of-band rejection. An essential part of
this work is the validation of Quantum Yield (the production of more than one
electron per photon) and the study of how QY statistics affect SNR as a
function of fluence, a property shared by all silicon detectors.

We thank the SRI team for packaging multiple detectors and performing
screening tests, and for their advice during our detector characterization
effort. We acknowledge the support of JPL and Caltech’s President and
Director’s Research and Development Fund (PDRDF Program). We also gratefully
acknowledge the collaborative agreement between APL-SRI-JPL that made wafers
available for this work.

## References

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###### List of Figures

  1. 1  The mK$\times$nK Imager reticle consists of four modular building blocks which are photocomposed (“stitched”) to create custom dimensions in 1k increments. The sizes shown have been successfully produced, for ground and space missions.
  2. 2  Five Transistors with Pinned Photo-Diode Pixel (5TPPD) Diagram. Reproduced from [12].
  3. 3  CMOST Camera. The open cryostat is shown with detector inserted into its zero-insertion-force socket. The controller sits on top of the cryostat, and the Vacuum Interface Board provides row and column address generation and routing of video signals.
  4. 4  Readout Diagram of the Rolling Reset Mode.
  5. 5  Photon transfer curves of low and high gain modes. Readout noise, system gain and Full Well Capacity can be directly read from this plot.
  6. 6 Initial transient after starting the readout of the detector at a constant frame rate. A transient is only visible on the illuminated area, revealing a gain change.
  7. 7 Linearity in high gain mode. Faint signal ranges from 0 $\mathrm{e^{-}}$ to 1000 $\mathrm{e^{-}}$.
  8. 8 Linearity in low gain mode. Note that the faint signal is neglected since low gain mode will not be utilized for very faint signals
  9. 9 Temperature dependence of the gain between 150 $\mathrm{K}$ and 180 $\mathrm{K}$. Around 165 $\mathrm{K}$, the gain varies by 0.15 $\%/\mathrm{K}$.
  10. 10 Dark Maps of the top left quadrant of the detector show fine structures and glow sources in and around the image area. Most of the glow coming from the left edge of the chip where lies the logic and pixel drivers is turned off by lowering the biases during the exposure.
  11. (a) 18 hours exposure in the dark while keeping electronics in its default state.
  12. (b) “Low glow” 18 hours exposure in the dark while shutting down support electronics.
  13. 11  Dark current for a wide range of temperatures. A simple fit of an Arrhenius law shows the expected temperature dependency.
  14. 12 Pixel Speed Noise optimization. For each pixel frequency, an optimum window range is found.
  15. 13 Noise Map of the detector in high gain. Excess noise is visible in the bottom rows, next to the amplifiers. The bad column generates noise in its surrounding as well as four distinct clusters.
  16. 14 Noise distribution of pixels in a clean sub-array of the detector. The ideal gamma distribution describes distribution if noise were distributed normally in the detector.
  17. 15 Fluctuating level of a pixel affected by Random Telegraph Noise. The amplitude of the step is much higher than the read out noise. Note that the size of the step is constant while transition timing is random.
  18. 16 Square root of average noise variance for all pixels included in window, after exclusion of noisiest pixels, plotted for three different pixel rates.
  19. 17 Left: Auto-correlation of the difference of two flat frames. The noise is reduced by averaging 48 $256\times 256$ pixel patches. Right: Impulse response or IPC reconstructed from the Autocorrelation in low gain mode
  20. 18 Horizontal and Vertical Correlation of first neighbors in low gain mode.
  21. 19 Photon Transfer curve obtained in Low-Gain mode by taking into account the pixel correlation. The total conversion gain drops by 6% from $8.5\,\mathrm{e^{-}}/\mathrm{ADU}$ to $8.0\,\mathrm{e^{-}}/\mathrm{ADU}$.
  22. 20 Example of various length cosmic ray events identified by finding contiguous regions above 50 $\mathrm{e^{-}}$ in dark frames.
  23. 21 Muons and cosmic rays are preferentially coming from the zenith while our camera system is pointing towards the horizon. Note muons coming with a high incidence onto the detector leave a longer trace than those coming with a normal incidence.
  24. (a) Reference diagram for incident angle $\theta$ and azimuthal angle $\phi$.
  25. (b) Expected angular distribution of cosmic rays hitting the detector.
  26. 22 Comparison of cosmic ray track length distribution to Monte Carlo simulation.
  27. 23 Cosmic Ray Charge Distribution for (left) all events and (right) multi-pixel events. The excess counts at lowest charge levels (at left) may be due to RTN and must be investigated further.
  28. 24 Charge vs. track length for cosmic ray events. The estimated slope is printed in $\mathrm{k\mathrm{e^{-}}/\mathrm{\mu}m}$, with uncertainty estimated from the covariance matrix.

###### List of Tables

  1. 1 Radiation tolerance of SRI Nk$\times$Mk, reproduced from data sheet.
  2. 2 Row readout sequence in Rolling Reset mode.
  3. 3 Row readout sequence to generate a dual-gain image.