# Multi-Amplifier Sensing Charge-coupled Devices for Next Generation
Spectroscopy

Kenneth Lin Department of Astronomy, University of California, Berkeley, CA
94720, USA  Lawrence Berkeley National Laboratory, One Cyclotron Rd, Berkeley,
CA 94720, USA  Armin Karcher Lawrence Berkeley National Laboratory, One
Cyclotron Rd, Berkeley, CA 94720, USA  Julien Guy Lawrence Berkeley National
Laboratory, One Cyclotron Rd, Berkeley, CA 94720, USA  Stephen E. Holland
Lawrence Berkeley National Laboratory, One Cyclotron Rd, Berkeley, CA 94720,
USA  William F. Kolbe  Lawrence Berkeley National Laboratory, One Cyclotron
Rd, Berkeley, CA 94720, USA  Peter Nugent Lawrence Berkeley National
Laboratory, One Cyclotron Rd, Berkeley, CA 94720, USA  Department of
Astronomy, University of California, Berkeley, CA 94720, USA  Alex Drlica-
Wagner Fermi National Accelerator Laboratory, Batavia, IL 60510, USA
Department of Astronomy & Astrophysics, University of Chicago, Chicago, IL
60637, USA

###### Abstract

We present characterization results and performance of a prototype Multiple-
Amplifier Sensing (MAS) silicon charge-coupled device (CCD) sensor with 16
channels potentially suitable for faint object astronomical spectroscopy and
low-signal, photon-limited imaging. The MAS CCD is designed to reach sub-
electron readout noise by repeatedly measuring charge through a line of
amplifiers during the serial transfer shifts. Using synchronized readout
electronics based on the DESI CCD controller, we report a read noise of 1.03
e- rms/pix at a speed of 26 $\mu$s/pix with a single-sample readout scheme
where charge in a pixel is measured only once for each output stage. At these
operating parameters, we find the amplifier-to-amplifier charge transfer
efficiency (ACTE) to be $>0.9995$ at low counts for all amplifiers but one for
which the ACTE is 0.997. This charge transfer efficiency falls above 50,000
electrons for the read-noise optimized voltage configuration we chose for the
serial clocks and gates. The amplifier linearity across a broad dynamic range
from $\sim$300–35,000 e- was also measured to be $\pm 2.5\%$. We describe key
operating parameters to optimize on these characteristics and describe the
specific applications for which the MAS CCD may be a suitable detector
candidate.

Astronomical detectors(84) — Astronomical instrumentation(799)

††software: Astropy (Astropy Collaboration et al., 2013, 2018), SciPy
(Virtanen et al., 2020), Source Extractor (Bertin & Arnouts, 1996; Barbary,
2016)

##  1 Introduction

Charge-coupled devices (CCDs) have played a pivotal role in scientific imaging
applications including in dark matter direct detection experiments, radiation
detection, and as astronomical photodetectors. A CCD detects incident photons
impinging on its photosensitive region by measuring the number of electron-
hole pairs created via the photoelectric effect in a semiconductor substrate,
typically silicon. Charge is then transferred along pixels in a column by
varying clock voltages until they are shifted to the last row, the serial
register, where charges are shifted horizontally to a sense node MOSFET for
charge measurement. Since their first application in astronomical imaging in
1976, CCDs have been the most widely used sensor in astronomy for both ground
and space based telescopes because of their high quantum efficiencies
($>90\%$) in the optical to near-IR wavelengths, excellent linear response,
and outstanding low-light performance (Janesick, 2001).

When performing precision astronomical measurements, multiple sources of noise
including shot noise from the source or sky background, dark current, and on-
chip amplifier read noise hamper the effective sensitivity of the detector.
While imaging observations on the ground can be designed to be shot noise-
limited and dark current can be mitigated to negligible levels ($\sim$ 1
e-/pix-hr) by cooling the detector, reducing the read noise is an important
aspect that drives improved observational reach in high-resolution
spectroscopy (Newberry, 1991). In particular, optical spectroscopic surveys
have exposure time restrictions and for shorter wavelengths where the sky is
fainter, the readout noise can dominate the overall noise budget (Drlica-
Wagner et al., 2020). Current state-of-the-art scientific CCDs used by
astronomical facilities are constrained to approximately 2.5 e- of read noise.
As observations in the low-background regime push toward fainter, more distant
objects, there is a need to overcome this barrier to achieve nearly quantum-
limited detecting capability for next generation spectroscopic measurements
from the ground (Schlegel et al., 2022a) as well as space-based spectroscopy
and imaging (NAP2023).

One of the central challenges for high-fidelity spectroscopic surveys is
balancing the mapping speed with target depth. The mapping speed is driven by
many factors including exposure times to reach required signal-to-noise ratios
(S/N), and overheads such as slewing and readout time which must be optimized
as part of the survey strategy (Schlafly et al., 2023). The Dark Energy
Spectroscopic Instrument (DESI) is collecting 40 million galaxy and quasar
redshifts to constrain the dark energy equation of state and the growth
history of the Universe by probing the baryon acoustic oscillation (BAO) scale
and clustering anisotropies (DESI Collaboration et al., 2016). A typical dark
time DESI exposure time ranges from 1000 to 1800 s to successfully obtain
redshifts in faint target samples (Guy et al., 2023; Chaussidon et al., 2023;
Zhou et al., 2023). If detector noise is minimized to the single-electron
level, the S/N can be increased up to 40-70% at the nominal DESI exposure
times at 400 nm, a significant improvement for resolving the redshifted
Lyman-$\alpha$ (Ly$\alpha$) forest of distant quasar spectra, which is
critical for understanding the intergalactic medium fluctuations carrying BAO
signatures. For the same S/N, defined to be a minimum of 1 per angstrom in the
Ly$\alpha$ forest for DESI, this would equate to about a 50% reduction in the
required exposure time. Decreasing exposure time opens the flexibility for
higher cadence observations and a viable path forward for increasing mapping
speeds of future surveys, and thus greater volumes, higher densities, and
wider redshift ranges. Improved detector technology is one crucial component
for increasing the mapping speed of spectroscopic surveys by an order of
magnitude to achieve a Stage-V spectroscopic survey (Spec-S5), which would
extend the accessible redshift range to $2<z<5$ with a projected $\sim 10^{8}$
measured redshifts in a new, unexplored discovery space (Schlegel et al.,
2022b; Murayama et al., 2023).

As a bridge toward the next generation spectroscopic instrument, a potential
upgrade of DESI in consideration will double the redshift yield currently
planned for the main DESI survey by probing intermediate high-redshift targets
around $z>2$, deep within the matter-dominated era. Such an instrument would
pilot CCDs capable of sub-electron read noise in preparation for Spec-S5. This
would also maximize scientific returns from Rubin Observatory Legacy Survey of
Space and Time (LSST) imaging surveys through cross-correlation with wide-
field (thousands of square degrees) spectroscopic samples selected from order
$10^{8}$ planned Spec-S5 targets for photometric redshift calibration
(Mandelbaum et al., 2019; Schlegel et al., 2022a).

Many other science cases also stand to benefit from ultra-low noise CCDs,
notably in space-based facilities where sky background is absent. Identifying
biosignatures in light reflected or absorbed by the atmospheres of extrasolar
planets is the scientific driver for the next flagship NASA space observatory,
the Habitable Worlds Observatory (HWO), and requires developing extremely
high-contrast coronagraphy or occulter techniques (NAP2023). Key spectral
features potentially indicative of an “Earth-like” planet include water vapor
and molecular oxygen lines at 940 nm and 760 nm, respectively, and sensitivity
in this wavelength range would be considered a minimum observational
requirement (e.g., Seager, 2014). However, even with a perfect coronagraph,
photon count rates are expected to be around only $<0.5$ photons/s/m2 for
broadband imaging (Traub & Oppenheimer, 2010; Rauscher et al., 2016). For
integral field spectrographs where an already low flux is further dispersed
over a large pixel area by additional optics, the count rate drops to a few
photons per hour per pixel, translating to a read noise requirement $\lesssim
0.1$ e- rms/pixel (Stark et al., 2015; Rauscher et al., 2016). A fast readout
from a 2k $\times$ 2k four-corner amplifier sensor of $<1$ min in addition to
exposure time limits are also necessary to prevent high-energy protons in
cosmic rays from corrupting a significant ($\gtrsim 10\%$) fraction of pixels
(Rauscher et al., 2019). This would also greatly benefit high-cadence
transient searches which aim to find and quickly provide follow-up
spectroscopic observations throughout the light curve evolution of these
objects. Consequently, photon-counting capabilities with high readout rate,
excellent response across the optical to near-infrared wavelengths, and robust
radiation tolerance are essential for candidate detectors identified for such
an application.

The multiple-amplifer sensing (MAS) CCD offers a desirable array of
characteristics that appeal to the criterion for future ground spectroscopy
and space imaging (Holland, 2023). Using a modified architecture of the
Skipper CCD, described in detail in §2, the MAS CCD couples fast readout with
the sub-electron noise floors enabled by the Skipper CCD. As the latest
iteration of legacy thick, $p$-channel devices, the MAS CCD builds on the
precedence of fully depleted sensors developed at Lawrence Berkeley National
Laboratory (Holland et al., 2003; Holland, 2023) for astronomical applications
from SNAP and the Dark Energy Camera (DECam) to the Keck Telescope and DESI.
These devices feature high quantum efficiency into the near-IR and radiation
resilience due to their $p$-channel design (Roe et al., 2007; Dawson et al.,
2008; Rockosi et al., 2010; Bebek et al., 2017). In this work, we instrument,
test, and optimize a prototype MAS CCD using DESI electronics to realistically
determine its feasibility as an astronomical detector for next generation
spectroscopy, especially focusing on a DESI upgrade as a pathfinding
instrument. Complementary tests of a 16 channel MAS CCD are presented in (Lapi
et al., 2024), but in our study, we focus on the performance of the MAS CCD in
the context of astronomical spectroscopy, particularly for DESI and Spec-S5.

This paper is outlined as follows: in section §2, we place the MAS CCD in the
context of Skipper CCD developments and describe its basic properties; in
section §3, we give an overview of our experimental setup for CCD testing and
the controller electronics; in section §4, we demonstrate the noise
performance of the MAS CCD under various readout settings; in section §5, we
show key characterization measurements for the device; in section §6, we
present ongoing and future plans with the MAS CCD in light of our results; and
finally, we conclude with our main findings in §7.

##  2 From Skipper to MAS CCDs

Figure 1: Cross-sectional schematic of the MAS CCD readout structures. For the
16 channel MAS CCD, these structures are repeated 16 times. Each output stage
is identical, consisting of two transistors in the floating gate (FG) area:
reset with the reset gate (RG) and output. Each output stage is separated by
15 inter-amplifier pixels ($k_{\rm inter}$) with horizontal clocks: H1, H2,
and H3 for three-phase clocking. The other gates in the readout structure are
the summing well (SW), output gate (OG), and the pixel separation (PS). In
this work, we study the device with the output gate biased instead of clocked.

The Skipper CCD circumvents the $1/f$ readout noise limitation by employing a
floating-gate amplifier where a charge packet can be independently and non-
destructively sampled multiple times (Janesick, 1993). First proposed by
Janesick for low-signal-level imaging and spectroscopy, the repeated
measurements of each charge packet allows the readout noise to be reduced to
the sub-electron level in the first tests (Janesick et al., 1990). Modern
implementations of the Skipper CCD designed at Lawrence Berkeley National
Laboratory (LBNL) have been demonstrated to reach a readout noise as low as
0.039 e- rms/pixel (Tiffenberg et al., 2017; Cancelo et al., 2021). This
extreme sensitivity has allowed Skipper CCDs to be successfully exploited for
an array of broad applications in particle physics, including direct dark
matter detection, low-energy neutrino experiments, and fundamental physics
studies of silicon (e.g., Crisler et al., 2018; Abramoff et al., 2019;
Nasteva, 2021; Aguilar-Arevalo et al., 2022; Norcini et al., 2022; Aguilar-
Arevalo et al., 2021). Their demonstrated success in this arena and heritage
as an outgrowth of conventional silicon CCDs has attracted interest in their
adoption for cosmological surveys and direct imaging of exo-Earths from space
(e.g., Crill & Siegler, 2017; Stark et al., 2019; Drlica-Wagner et al., 2020;
Rauscher et al., 2022; Marrufo Villalpando et al., 2022; Stark et al., 2024).

While the Skipper CCD provides unprecedented sub-electron resolution, it
suffers from a readout time penalty directly proportional to the number of
reads per pixel. Unlike a conventional CCD where charge is passed to a
floating diffusion amplifier once and then drained, the averaging of many
statistically independent measurements in Skipper CCDs allows the noise to be
reduced as the inverse square root of the number of individual reads. As the
number of samples increase, the resulting readout noise is lowered but at the
cost of readout time because only a single pixel at a time can be transferred
between the sense node and floating gate in the output stage. For a survey
such as DESI, this is projected to require over a prohibitive 15 minutes of
readout time to reach a resolution of 1 e- rms/pixel for a DESI-like format
(4k $\times$ 4k pixel) four-corner readout CCD (Tiffenberg et al., 2017;
Villalpando et al., 2024). The problem of readout time is further exacerbated
for time-domain surveys, particularly with fast-evolving transients where
early-time observations conducted with high-cadence searches are crucial for
characterizing the progenitors of these objects.

First developed as part of a U.S. Department of Energy Quantum Information
Science initiative, the MAS CCD was designed to address the trade-off between
reaching sub-electron levels of read noise and extended readout time that is a
key drawback for single-amplifier Skipper CCDs (Holland, 2023). This is
accomplished by implementing a chain of floating-gate output amplifiers,
interspersed along an extended serial register. A schematic of this readout
structure is illustrated in Fig. 1. Charge packets pass through and are
sampled non-destructively by each output stage. Each charge packet is thus
repeatedly measured to reduce noise in a similar approach to the Skipper CCD,
but allows the charge to be continuously transferred to the next amplifier for
the subsequent charge packet to be measured. This architecture permits
sampling $M$ charge packets simultaneously for $M$ floating-gate amplifiers to
effectively parallelize readout, thereby decreasing the readout time. Thus,
the effective noise per pixel after averaging $N$ charge measurements for $M$
amplifiers is

$\sigma=\frac{\sigma_{1}}{\sqrt{N\cdot M}}$ (1)

where $\sigma_{1}$ is the noise per pixel for one charge measurement for an
amplifier. The theoretical read time for a MAS device with $m$ number of rows
and $n$ columns as described by Holland (2023) is

$t_{\rm read}=m(t_{n}+t_{V})$ (2)

where $t_{V}$ is the vertical clocking row shifting time and $t_{n}$ is the
time required to read a $n$ pixels in a row, equivalent to the total number of
columns of the active area. The time to read a row $t_{n}$ is given by

$t_{n}=k_{\rm ext}t_{\rm shift}+M(k_{\rm inter}t_{\rm shift}+Nt_{\rm read})\\\
+(n-1)(t_{\rm shift}+Nt_{\rm read})$ (3)

where $k_{\rm ext}$ are the number of extended serial pixels, $k_{\rm inter}$
are the number of pixels between amplifiers, $t_{\rm shift}$ is the time to
shift charge one serial pixel, and $t_{\rm read}$ is the time to perform one
charge measurement in the sense node (Holland, 2023). The first two terms are
equal to the time to read the first pixel completely through all MAS
amplifiers in the serial register and the third term is the time it takes for
all subsequent pixels to pass from the penultimate to the final amplifier,
since after the first pixel has read out, the second pixel has been read out
by all but the last amplifier. Incorporating multiple output stages also
introduces the benefit of amplifier redundancy against amplifier failures that
would otherwise put an entire conventional CCD at risk, since charge can
simply flow through non-functioning output stages.

Although the MAS output stages are also capable of measuring charge by
“skipping,” or transferring charge between the sense node and summing well
repeatedly to increase the number of charge measurements per amplifier $N$ by
virtue of the floating-gate amplifier structure (e.g., Botti et al., 2024), we
focus on the fastest readout mode for the sensor where $N=1$, measuring each
charge packet exactly once per MAS amplifier. A single-sample per amplifier
readout is desirable in light of readout time requirements for large-format,
scaled-up variants of the MAS CCD that satisfies mapping speed and noise
requirements ($\sim$ 1 e- rms/pixel) of surveys. A fast readout also minimizes
pixel dwell time inherent in “skipping” when charge must sit in the active
area as $M$ pixels are being measured by the $M$ output stages, downtime that
not only cannot be used for an additional exposure, but also increases the
fraction of pixels contaminated by cosmic rays.

###  2.1 Device properties

The test device was fabricated by Teledyne DALSA Semiconductor from high
resistivity (10 k$\Omega$/cm) $n$-type silicon substrate with buried $p$-type
channels and no backside processing or anti-reflective (AR) coating. There are
16 MAS readout channels along the 256-pixel extended serial register. On the
opposite end of the serial register is a DESI-like output amplifier which, if
connected, can enable the sensor to act as a conventional CCD when charge is
clocked in the direction away from the MAS amplifiers. Standard three-phase
clocking is employed to read out charge vertically and horizontally, and the
serial clocks are similar to that of Skipper CCDs with the exception of one
additional pixel separation (PS) gate. The PS gate acts as a potential barrier
between floating-gate sense node and subsequent inter-amplifier pixels. This
output structure is illustrated in the charge transfer diagram in Fig. 1. In
the final output stage, a dump gate (DG) takes the place of the PS gate, and
is structurally similar to the Skipper CCD output stage. Since the serial
register is only one edge of this prototype detector, there is only one set of
vertical clock lines, and the pads on the CCDs on both sides of the device
that correspond to these vertical clocks are connected to the same set of
clock drivers. The sets of serial clock voltages in the MAS register are also
tied together, so all MAS output stages have the same set of clock voltages.
The device has a format of 1024 x 512 pixels with 15 $\mu$m pixels and since
the sensor was not thinned, the thickness was 650 $\mu$m and was illuminated
on the frontside. These properties are summarized in Table 1.

Table 1: Summary of characteristics and operating conditions of the MAS CCD tested in this work. | Value | Units
---|---|---
Active area | 1024 $\times$ 512 | pixels
Pixel size | 15 $\times$ 15 |  $\mu$m
Pixel pitch | 15 |  $\mu$m
Device thickness | 650 |  $\mu$m
Output stages | 16 MAS + 1 DESI |
Temperature | 143 | K
Substrate voltage | 40 | V

###  2.2 Detector packaging

A “picture frame” format carrier was designed for the CCD with an opening
slightly larger than the size of the sensor centered on a printed circuit
board (PCB). The carrier board includes a 1 $\mu$F and 4 M$\Omega$ filter in
parallel visible in Fig. 2, which helps stabilize the output voltage of the
video transistor. A square silicon substrate was bonded to the back of the
PCB, covering this opening. The backside of the CCD was then carefully bonded
onto the substrate with epoxy through the opening on the front side of the
PCB, then baked to cure. The CCD pads were then wirebonded with the PCB. A
ribbon cable was used to connect this package to the dewar vacuum feedthrough.
The wirebonded detector is pictured in Fig. 2.

Figure 2: A prototype 16-channel MAS CCD packaged and wirebonded onto the
carrier board and installed in the cryostat. The active photosensitive pixels
are outlined in the dashed line and the serial register is along the left
edge. The area to the left of the active region is unused silicon. The MAS in-
line amplifiers extends from the bottom left corner of the active area, where
the 16 bonding pads corresponding to the 16 amplifiers are visible.

##  3 Experimental apparatus and readout electronics

The CCD was mounted in a dewar cooled by liquid nitrogen under vacuum at about
$10^{-4}$ torr using a diaphragm roughing pump and turbomolecular pump to
maintain high vacuum. Using a Lakeshore 336 PID temperature controller, the
CCD was operated at 143 K as measured by a temperature sensor positioned at
the cold finger on the rear of the CCD package. Since liquid nitrogen
dispenses at 77 K, the CCD operating temperature was reached by mounting the
CCD package on a cold plate that is partially thermally isolated from the cold
finger with copper foil bridging the thermal contact between the two
components. Power resistor heaters were placed on the cold plate to regulate
the the temperature. The dewar enclosure has a retractable source holder arm
on the inside next to a fused silica window on the latched dewar chamber
opening on the front where the CCD is installed. This window provides an
optical path for illumination. Optical elements, including an iris diaphragm,
focus tuning, and LED source with a built-in lens holder in front of the
diode, are attached onto a baffle connected to the dewar window. Different
lenses can be placed in front of the LED to project mask patterns onto the
CCD. The LED source is connected to a custom external controller that can
change the light intensity, synchronize the LED with a specified exposure time
to act as a shutter while operating the CCD, or provide manual control. The
dewar including the LED projection system was covered with an opaque cloth to
minimize stray light entering the dewar especially on the front side of the
dewar opening and connection points between components outside the dewar.

The dewar vacuum feedthrough links the ribbon cable from the CCD package to a
dewar side board connected to the readout electronics. The CCD control is
performed with an expanded version of the DESI front-end electronics (FEE)
system to enable the simultaneous digital correlated double sampling (CDS)
readout of the 16 output channels on the sensor. The new electronics
developed, called the Hydra, runs as a set of four synchronized DESI FEE
systems in a leader-follower configuration, consisting of a video processing
board and power conversion board for each of the four FEE sub-units and a
single clock driver board for the master FEE. The video board serves to
process and digitize four channels of CCD video signal using a 100 MHz 16-bit
analog-to-digital converter (ADC). The clock board provides the clock signals
with a range $\pm$ 12 V for the CCD with a 40 channel 16-bit digital-to-analog
converter (DAC). Each component of the FEEs within the Hydra sits on a
motherboard with an FPGA which is the timing engine and reads ADC data output
from the video board, and CDS data is sent to a MicroBlaze processor
accessible by a TCP/IP communication interface. Data products are written out
in standard FITS image format. Four main operating modes are defined for the
CCD in our setup: exposing, readout, idle, and cleaning. Cleaning is performed
prior to exposures and is intended to clear remnant charge from the active
area by completing a readout sequence without reset or signal sampling. Idle
mode continuously clocks the CCD between exposures and is stopped during a set
exposure time and readout.

An aluminum enclosure with four cooling fan exhaust ports was assembled to
shield all the electronics from the environment. To reduce interference within
the casing, thin aluminum plates were installed between each FEE subunit. Each
FEE could be power cycled by individual switches which were installed on the
exterior of the entire enclosure.

##  4 Noise performance

For a CCD image with zero exposure time, pixel values are the sum of the dark
current accumulated during the readout time, the bias level DC offset,
occasional cosmic ray signal, and amplifier read noise. As a functional
definition, we refer to dark current in this work as the signal detected when
the CCD is not exposed to light, and note that the thermal leakage current is
only one component among other dominating components including stray light and
thermal photons from the dewar walls; we do not attempt to separate these
components in this study. Extended strips of virtual pixels along the image
borders created by overclocking the CCD array comprise the overscan region,
where the distribution of pixel values reflect the read noise and bias level.
We note that these virtual pixels also contain other components such as the
dark current and cosmic ray contributions accumulated during the readout of a
rows and columns. Overscan subtraction for the entire image including the
virtual pixels corrects for the bias shift of all pixels by taking the sigma-
clipped mean of the overscan region and subtracting this from each pixel.
During testing, we found this yields similar results to a line-by-line
overscan correction where the sigma-clipped mean pixel value for each row of
the serial overscan is subtracted from each physical and virtual pixel in the
same row. We apply iterative sigma clipping which rejects outlier pixel charge
contaminated by cosmic rays from the analysis. The standard deviation derived
from fitting the resulting overscan pixel distribution after overscan
subtraction and sigma clipping corresponds to the read noise.

Because the MAS CCD produces the same number of images as the number of output
amplifiers for a single sample per amplifier in an exposure, in our case 16,
these image frames can be used to measure the noise of its corresponding
amplifier. The 16 images are then averaged to measure the combined noise for
the multiple charge measurements made per pixel. The effect of averaging on
noise as a function of the number of MAS amplifiers is shown in Fig. 3 in
comparison to the theoretical expectation from Eq. 1. However, before the
signal is averaged, the frames must be regridded to account for the 16 inter-
amplifier pixel shifts, where each image starting from the second amplifier in
the MAS chain is shifted 16 pixels serially forwards compared to the image
output from the preceding amplifier. This correction was implemented by
shifting images from the second amplifier onwards to share the pixel grid of
the image from the first amplifier. These steps of shifting, signal averaging,
and overscan subtraction were applied to each image as part of our standard
preprocessing.

Figure 3: Read noise for a single sample read per amplifier is measured for
the data points in comparison with the expected reduction curve given the
starting read noise at the first amplifier. Shown in the gray curves are
possible future optimizations in amplifier noise with a 32 channel design
which could enable deeply sub-electron noise with only a single-sample read
per amplifier. Figure 4: Frames from each of the 16 output amplifiers of the
MAS CCD under X-ray exposure (point-like clusters) after alignment correction.
The straight track is a signature of a cosmic ray muon.

###  4.1 Gain calibration

The detector gain is a conversion factor between counts or analog-digital
units (ADU) from the ADC output and number of electrons the CCD recorded,
which we measure with the commonly used technique of stimulating the CCD with
5.9 keV X-rays from the radioactive decay of a 55Fe source. Since the quantity
of electron-hole pairs generated in a pixel per X-ray photon absorbed in the
silicon bulk is proportional to the X-ray energy and known, the gain can be
derived from the measured location of the 5.9 keV Mn K$\alpha$ peak in the
spectrum (Janesick, 2001). After obtaining five second exposures, the X-ray
hits were extracted to build a histogram of the charge distribution. The Mn
K$\alpha$ X-ray peak was then fitted with a simple Gaussian to find the
position of the peak in ADU. The conversion gain is obtained as the ratio of
this peak position with 1620 e-, the average number of electrons produced by
the K$\alpha$ X-ray (Fraser et al., 1994). The gain for each amplifier is
shown in Fig. 5 for our standard ADC gain setting and a reduced ADC gain used
to extend the dynamic range to high signal levels ($\gtrsim 3\times 10^{4}$
electrons). Throughout the course of our tests in operating the CCD for one
year, we have found the amplifier gains to be highly stable over time.

Figure 5: Conversion gains for each of the active MAS amplifiers at ADC gain 5
(black) and ADC gain 3 (blue).

###  4.2 Voltages and noise optimization

The CCD was run with a substrate-bias voltage ($V_{\rm SUB}$) of 40 V at which
lateral charge diffusion is expected to be smaller than the pixel size
(Karcher et al., 2003). Because we are interested in the performance at the
fastest readout configuration where charges are sampled once for each
amplification stage (i.e., no skipping), the output gate is biased to 0 V in
our setup. The potential diagram with our voltages in the output structure is
shown in Fig. 6, where each row of clock sequences represents a state during
the readout. The output stage involves the summing gate (SG), output gate
(OG), floating-gate (FG) sensing region, and pixel separation gate (PS) and
are interleaved by three horizontal clock phases between each output stage. In
the last stage, instead of a PS gate, a dump gate (DG) leads to $V_{\rm dd}$,
a bias voltage applied at -22 V to remove the charge from the channel. Because
the sense node relies on a floating gate for non-destructive charge
measurement, the exact potential here cannot be known and is therefore denoted
as a dashed segment in Fig. 6. Several clock states are depicted in Fig. 6,
where state (a) is where charge enters the sense node, state (b) is where the
charge is being measured, and state (c) is where the charge exits the sense
node and is shifted away to the next output stage in subsequent states.

Since the prototype sensor is not divided into quadrants, we used a single set
of three vertical clocks for the parallel register and three horizontal clocks
for the serial register. Reducing the horizontal clock amplitudes was the most
significant driver of noise reduction, allowing the noise floor to be lowered
to near single-electron noise. Starting with a 15 V horizontal clock swing,
the low voltages of the clocks were gradually increased as shown in Fig. 7.
However, there is a limit to the minimum amplitude imposed by charge transfer
efficiency between amplifier stages for the first horizontal clock phase, H1.
This amplifier-to-amplifier charge transfer inefficiency is linked to the PS
gate, where the low voltage of the PS gate must be at least 1 V greater than
the H1 low state. When the H1 low state is within 1 V of the PS low state, the
reset drain voltage ($V_{R}$) must be increased to allow potential for the PS
low state to increase without causing inter-amplifier charge transfer
streaking. Increasing the low voltage of the PS gate was crucial for raising
the potential barrier between the sense node and the next stage of horizontal
clock phases, when both the PS and H1 clocks are in low states, to prevent
charge in one pixel from diffusing into a neighboring pixel. For instance, a
PS gate voltage at -6.5 V provides a 5.5 V potential well for an H1 at -12 V
whereas a PS gate voltage at -8 V only gives 4 V of potential barrier. In this
latter case, the well depth formed by this voltage difference is smaller than
the parallel clock amplitudes, which have a 5 V amplitude, and becomes a
limiting factor for the effective well depth of the detector. At the minimum
H1 amplitude with a high of 3 V and low of -8.5 V set globally for all
horizontal clocks, the compound read noise reaches just under 1.1 e- rms/pixel
with a single-amplifier read noise ranging from 3.68–4.51 e- rms/pixel
depending on the amplifier. Although the returns diminish with this approach,
it was possible to achieve 1.03 e- rms/pixel of compound noise without
incurring charge transfer problems by tuning the second and third horizontal
phases independently of the first phase. We interpret this noise to be an
effective read noise because its tight correlation with serial clock
amplitudes suggests that the noise includes not only intrinsic amplifier noise
but also a serial clock-induced charge shot noise component. The serial clock-
induced charge was found to a significant contributor to the measured noise at
greater horizontal clock heights for a Skipper CCD with a 6000-pixel long
serial register but reduces when these clock amplitudes are lowered (cf. Fig.
12 in Villalpando et al., 2024). Reducing the horizontal clock swings also
reduces the full well capacity, which should be balanced against detector
noise requirements, discussed in section 5.2.

As part of the DESI FEE standard operating parameters, vertical clocks are
wave shaped with no serial clock shaping. We explored adding clock filtering
on the horizontal clocks with a 1 nF capacitor and extending the reset delay
to accommodate the longer rise times. With the optimized clock voltages
without shaping, adding wave shaping caused significant charge transfer
inefficiency (CTI) between amplifiers. Increasing the amplitude of the PS gate
such that the high voltage is greater than -2 V and the low voltage is at
least under -9 V addresses this CTI but since the PS gate influences the
allowed neighboring H1 phase, lowering the PS gate low voltage requires H1 to
be at least below -10 V. As we have observed, increasing the horizontal clock
amplitudes increases the effective read noise and further voltage optimization
leads to a read noise slightly above 1.1 e- rms/pixel. Because adding this
level of serial shaping increases the trade-off between inter-amplifier CTI
and read noise with no noticeable performance improvements, we opted to
complete the remainder of our tests without serial clock shaping, noting that
it may still be possible to achieve improved performance with a lower
capacitance wave shaping implementation.

To estimate the cumulative effects of other noise components such as light
leaks in the dewar and parallel register clock-induced charge, zero second
exposure bias images were acquired to compare the noise in the overscan region
and the active area. The virtual pixels of the overscan region are clocked
only in the serial direction for each row. Consequently, differences in the
pixel RMS between the two regions are expected to arise from the combination
of light leakage and clock-induced charge. The bias images indicate a glow
emanating from the top of the parallel register on the “left hand side” (on
the prescan edge) of the device near a corner. The position of this glow
directly opposite of where the serial register is located appears to rule out
an amplifier origin. To prevent the signal from the glow from being
transferred down the parallel register during idle mode, a stop idle-clear was
implemented before readout. However, because the synchronization of the FEE
subsystems requires the followers to be slightly ahead of the leader, there is
a practical minimum time delay just under 0.5 s between when the clear is
executed and the readout initiated. Thus, we restrict our noise calculations
to the bottom 50 rows of the CCD near the serial register and only half the
columns on the side towards the overscan where the glow signal has not yet
been transferred in the 0.5 s of idle clocking time delay. We find that the
difference in the standard deviation of the signal between the active area and
overscan is about 0.34 e-. Since this noise quantity includes a combination of
the glow, light leaks, and total parallel clock-induced charge, we interpret
this difference in noise to be an upper limit on the clock-induced charge
generated in the parallel register, demonstrating that this effect is not
dominating our read noise measurements, making our noise calculation more
robust.

Figure 6: A potential diagram of the serial register for a given output stage
$M$ is illustrated in our charge transfer diagram, where the floating-gate
(FG) sense node denoted by the dashed segment is at an unknown voltage level
and is where the CDS is performed to measure the amount of charge present in a
pixel. The shaded regions represent the idealized transfer of charge carriers
through the phases. The voltage levels corresponding to each phase and state
are plotted for our optimized voltages that enable us to reach under the noise
of 1.1 e- rms/pixel. In the final output stage, instead of a PS gate, a dump
gate (DG) is used which leads to the highly negative $V_{\rm dd}$. Figure 7:
Combined read noise as a function of horizontal clock swing amplitudes. For
the black data points, the amplitudes are identical for all three horizontal
phases while the blue points denote a different amplitude for the H1 clock and
are instead plotted against the amplitudes of clocks H2 and H3 which are
identical.

###  4.3 Integration time

In the CDS readout scheme, the time window in which samples from the CCD video
signal are averaged for the signal or pedestal levels is defined as the pixel
integration time. This translates to the number of samples per pixel taken at
each of these levels, such that with more samples, the noise is expected to
decrease but at the expense of the readout time. This is illustrated in Fig.
8, where a larger number of samples per pixel corresponds to a much lower read
noise. We read out our device with 1000 samples per pixel, corresponding to a
readout time of slightly above 26.1 $\mu$s/pixel, giving a read noise floor of
slightly under 1.1 e- rms/pixel. However, the noise does not decrease
monotonically and we observe two bumps around 450 and 1150 samples per pixel
where the noise increases slightly. This shows that there is a non-white noise
component contributing to the overall noise budget, which we attribute to
electronics-related pattern noise, particularly since the second bump occurs
approximately three half-periods from the first peak, where multiples of half
a period constructively increases the pattern noise contribution. We also
observe that larger clock amplitudes are associated with higher noise floors
consistent with our result in Fig. 7, which we attribute to charge injection
from clock-induced charge (Janesick & Elliott, 1992), an effect which becomes
a significant component of the measured noise in the photon-counting regime
for Skipper CCDs (Barak et al., 2022).

Figure 8: Combined noise as a function of the number of samples per pixel
(i.e., integration time) taken each at the pedestal and at the signal level.
The corresponding readout time is also displayed with the same curve measured
at different voltage amplitudes for the H2 and H3 clocks. We operated at 1000
samples per pixel at a readout time of 26.1 $\mu$s/pixel (38.3 kHz) but as
shown here, running slightly faster at 900 samples per pixel would give
similar noise performance.

##  5 Characterization & Analysis

###  5.1 Charge transfer efficiency

Conventionally, charge transfer efficiency (CTE) is described by the transfer
efficiency along the parallel register as charge is shifted in columns and
along the serial register where charge is passed towards the amplifier. The
additional inter-amplifier pixels in the MAS CCD motivates a consideration of
the CTE between each amplifier stage. This differs from serial CTE because
when charge is passed to the sense node in each amplifier, other charge
packets in the inter-amplifier region must be restricted from flowing into
neighboring pixels by a sufficiently high potential barrier from the PS gate.
We describe both effects in detail by first establishing a baseline serial CTE
measured in the first MAS amplifier, then treating the inter-amplifier
efficiency between this first stage and subsequent MAS amplifiers.

####  5.1.1 Horizontal register

Horizontal CTE was measured by the standard X-ray transfer method because up
until the first amplifier, the CCD is similar in structure to that of a
conventional CCD. The CCD was exposed to X-rays from the 55Fe source for 10
seconds and the gain-corrected signal in each pixel of the output image from
the first amplifier was plotted for each column to obtain the stacking plot,
as shown in Fig. 9, following Janesick (2001). The X-ray event line is then
fit to within $3\sigma$ around the X-ray Mn K$\alpha$ line, and the tilt of
this line corresponded to a CTE of $0.999988\pm 3\times 10^{-6}$. This is
computed for a stack of X-ray images and with different exposure times as
well, with a similar result to within statistical uncertainties; thus, the
uncertainty quoted here is the standard deviation of repeating this
measurement for several frames. As noted in Janesick (2001), this is at the
sensitivity limit for X-ray transfer curve CTE measurements, and thus we
interpret this to be a lower limit of the CTE in the serial register up until
the first amplifier. This demonstrates a traditional horizontal CTE that is
consistent with unity and no charge is effectively lost in the pixel charge
shifts up to the first amplifier. This is important to establish at the outset
because of the distinct effect of inter-amplifier charge transfer inefficiency
described in the next section that should be disentangled from any clear CTI
upstream from the first amplifier in the MAS output chain.

Figure 9: Horizontal X-ray transfer does not show evidence of significant
charge transfer inefficiency in the serial register before the charge is
shifted beyond the first amplifier. A greater charge transfer inefficiency
would manifest as a greater tilt in the X-ray line. The tilt of the X-ray line
which is the red fit line corresponds to a CTE of $0.999988\pm 3\times
10^{-6}$. The fit of the red line is performed for pixels with a total energy
within $3\sigma$ of the expected Mn K$\alpha$ line shown by the blue dashed
lines.

####  5.1.2 Inter-amplifier charge transfer efficiency

For a perfect transfer efficiency between the output stages in the MAS serial
register, each amplifier should measure the same amount of charge per pixel.
Any losses in the extended serial register, which we refer to as inter-
amplifier charge transfer efficiency (ACTE), can be quantified by comparing
the image output from each amplifier stage.

Charge transfer problems arise when the potential difference between the
floating-gate sense node and subsequent horizontal clock phases is too
shallow. This new additional gate between the sense node and horizontal clocks
is the PS barrier gate. After the charge is read, the PS gate is in the low
state for the charge to be transferred to the horizontal phases. If this low
PS voltage is too high compared to the floating gate, charge in pixels may not
fully exit the sense node. This effect manifests as increasing streaking in
signal as charge is shifted down the amplifier chain. In this situation, the
output produced in the first output stage is absent of charge transfer
problems and streaking; any streaking is observed starting in the second stage
with increasing severity as the charge is passed into further stages until the
image produced at the last stage is nearly uniformly filled with streaks in
each row. This strongly suggests inter-amplifier charge transfer issues
because the first amplifier presents no evidence of charge transfer problems
even with the same sequence of clocks that leads into each output stage, and
instead points to a transfer inefficiency in charge removal from and shifting
between output stages.

To measure the low-signal ($\sim 10^{3}$ electrons) inter-amplifier CTE
(ACTE), we expose the CCD to X-rays. After overscan correction, the location
of each X-ray event is identified by a standard source extraction algorithm,
where aperture photometry is performed to obtain the conversion gain. The gain
is computed for each MAS amplifier and each image output was converted to
electrons from ADU to compensate for any gain variations between amplifiers.
The peak pixel value in electrons and its corresponding coordinate for a
cluster of pixels affected by an X-ray photon in the first MAS amplifier is
compared against the number of electrons at this same pixel location in
subsequent serial amplifiers. If charge transfer efficiency is perfect, the
pixels should have an identical number of electrons at each MAS output stage.
As Fig. 10 demonstrates, deviations from a unity slope is indicative of
imperfect charge transfer between amplifiers. After correcting for the
respective gains of the amplifiers, we find that the inter-amplifier
efficiency between the first and last amplifiers is $0.9984\pm 0.0033$ below
the 2000 electron signal level, the energy range where most of the X-ray
induced charges are concentrated. This was computed from measuring several
X-ray exposures and averaging the result; the relatively high scatter in the
measured ACTE value when repeating this method for many images drives the
elevated uncertainty, motivating us to pursue a complementary approach to more
precisely quantify the ACTE effect.

Figure 10: Peak X-ray signal (in electrons) in a pixel in amplifier 1,
$S_{1}$, is compared with the same pixel in amplifier 16, $S_{16}$ for an
example image. For perfect inter-amplifier charge transfer efficiency, the
slope should be unity (red dashed curve). Each X-ray hit is plotted and
linearly fit (gray curve) to measure any deviation from unity. The cluster of
signal charge near 1600 e- arises from the X-ray events around the Mn
K$\alpha$ line. Fitting with the high scatter in this method is primarily what
limits the precision of this measurement.

This secondary method we have developed to quantify the ACTE involves linearly
modeling charge transfer efficiency between the peak X-ray flux pixel in the
first output stage with the adjacent pixel in the direction opposite to the
serial shifts. This simple model, parameterized by the charge transfer
inefficiency (CTI), is described by

$S_{M}(x_{p}+1,y_{p})=(1-\text{CTI})\cdot S_{0}(x_{p}+1,y_{p})\\\
+\text{CTI}\cdot S_{0}(x_{p},y_{p})$ (4)

where $S_{M}(x,y)$ is the signal, in number of electrons, at pixel coordinate
$(x,y)$ of amplifier $M$, and $(x_{p},y_{p})$ denotes the pixel with the
highest flux from a given X-ray hit. In this model, the number of electrons in
the pixel next to the X-ray peak pixel opposite to the serial shift direction
(i.e., trailing pixel) is expressed as $S_{M}(x_{p}+1,y_{p})$. This quantity
is the sum of two components to first order: the number of electrons in this
pixel as measured in the first amplifier (i.e., amplifier 0) with some loss
due to non-zero CTI and the number of electrons lost from the peak X-ray pixel
in the first amplifier due to non-zero CTI. A CTI value can be calculated for
each X-ray hit on the image, and the distribution of these values can be
fitted with a Gaussian to statistically estimate the ACTE as exhibited in Fig.
11. Using our lowest noise voltage configuration, we find that our lower limit
for the inter-amplifier charge transfer efficiency between the first and last
MAS amplifiers is $0.9973\pm 0.0001$ by this statistical approach. This is in
agreement with the simpler first approach illustrated by Fig. 10 to within
uncertainties.

The comparison between the transfer efficiency of each consecutive amplifier
with the same measurement shown in the right panel of Fig. 12 reveals that
amplifier 10 stage has about a $0.2\%$ lower than expected signal measured,
suggesting a possible device-specific issue such as a localized charge trap
from lattice defects in the register between amplifier 9 and 10. In the next
transfer from amplifier 10 to 11, we observe a recovery in the ACTE, meaning
that charge was properly transferred to amplifier stage 11 from 10. However,
despite the lack of measured CTI between each output stage from amplifier 10
onwards, the measured charge in these latter stages were all below the
expected signal level read out by amplifier 0. This is shown by the drop in
the ACTE curve relative to amplifier 0 at amplifier 10 where this efficiency
is at a plateau around $0.9973$. Since charge in each pixel must pass through
each output stage, losses due to defects along the way can become cumulative
and can be a potential drawback for the MAS design. While it may be possible
to reduce the impact of obstacles in the channel that degrade charge transfer
performance by tuning clock voltages and timing, this first prototype device
and existing CCD controllers that we are aware of do not support individual
clock lines to multiple output stages and are impractical for scaling to
larger amplifier count devices. Excluding the possible defect in our detector
between amplifier 9 and 10, we observe promising ACTE $>0.9999\pm 0.0001$ at
the level of up to $2\times 10^{3}$ e-.

Figure 11: Inter-amplifier charge transfer inefficiency is calculated by
modeling the trailing pixel to the pixel with the peak X-ray signal in an
X-ray hit following Eq. 4. Accumulating statistics for all X-ray hits in an
exposure gives a measurement of the inter-amplifier charge transfer efficiency
at the mean of the Gaussian fit, which as shown in this plot is 99.8% across
all 16 output stages, comparing the first and the last amplifier. Figure 12:
X-ray measurements of inter-amplifier charge transfer efficiency across
successive output stages based on CTI modeling. The left panel shows the CTE
at each amplifier relative to the first amplifier (amplifier 0). For example,
at amplifier 8, the output between amplifier 8 and amplifier 1 is being
measured. The right panel shows the inter-amplifier charge transfer efficiency
between each amplifier. For example, at amplifier 8, the transfer efficiency
between amplifier 7 and 8 is being measured.

However, X-rays are limited in energy range to the absorption lines of the
55Fe source, so probing for transfer problems at higher signal levels at the
$10^{4}$ level and above requires an alternate approach. To reach higher
illumination levels, the LED projector was triggered as a virtual shutter for
a specified exposure time during which the CCD is in expose mode before the
CCD is read out. The LED was connected externally to an external controller
that connected to the synchronization lines of the Hydra and included options
for adjusting the LED intensity.

Our first approach is based loosely on the extended pixel edge response (EPER)
method, which is a standard horizontal CTI measurement technique for
conventional CCDs relying on flat field images to determine the amount of
deferred charge in the overscan region. However, in addition to charge
transfer in the inter-amplifier pixels, since charge enters and is removed
from the charge sensing areas multiple times in the MAS architecture, the
traditional EPER formulation is inadequate for analyzing the potential charge
transfer loss and deferral between one output stage and the next. Thus, we
follow Eq. 4 to compute the inter-amplifier CTI given the signal measured in
the first overscan column between the first and last amplifiers. Applying this
technique with EPER-like data exploits the sharp edge between the active and
overscan regions. Because the overscan region is not expected to contain
incident signal if the CTI is ideally zero, the sharp edge provides a
sensitive probe of charge in the overscan area after shifts through multiple
sense nodes that is independent of the surface uniformity of the illumination
from imperfect optics.

Illumination at varying signal levels was obtained by increasing the exposure
time in increments of 250 ms up to 28 s in a linear ramp, with exposures taken
at each exposure time. Using a reduced ADC gain, this ramp extends up to
$7.8\times 10^{4}$ e- in incident signal level. The gain was again calibrated
at this ADC configuration for each amplifier and all images were bias-
subtracted with a master bias for each amplifier. The horizontal profiles are
shown in Fig. 13, where the signal average of each column of pixels up to the
vertical overscan are compared at various exposure times. The last active
column is 538 and like typical LBNL $p$-channel CCDs contains more charge than
other pixels in the flat field. This effect may arise because charge from the
flat field diffuses from material outside of the array at the edges (Janesick
et al., 1989) and because fringing fields result in pixel size variations at
the edges (Plazas et al., 2014). If we consider the first amplifier, as the
signal level increases with the exposure time, at a certain point of high
signal ($\gtrsim 4.6\times 10^{4}$ e-) the charge begins overflowing into the
overscan region, leading to catastrophic charge loss in the active pixels
which rapidly degrades as the active area completely saturates close to
$8\times 10^{4}$ e- where the horizontal profiles develop the characteristic
flat top. This is an expected effect present in each amplifier that reflects
the physical pixel full well given our operating parameters. However, the
horizontal profile for amplifier 16 shows that the charge overflow into the
overscan pixels occurs earlier compared to the first amplifier, pointing to an
inter-amplifier CTI effect that dominates the overall charge losses along the
extended MAS register even before the pixel full well capacity is reached.

To diagnose the amount of charge where the inter-amplifier charge transfer
efficiency breaks down, we apply Eq. 4 for the mean of the final active column
as the “peak pixel” and the first overscan column as its “trailing pixel.”
This is evaluated at the first amplifier stage in relation to each of the
subsequent stages from 5,000 to 80,000 e-. The results for this ACTE analysis
is summarized in Fig. 14, where the measured ACTE for each output stage
relative to amplifier 0 is plotted, showing the signal regime at which the
amplifier-to-amplifier transfer drops. The inter-amplifier CTI between
amplifier 0 and 1 is consistent with unity until above 53,000 e- where ACTE
degrades swiftly. However for amplifier 15, the ACTE has a slightly steeper
slope as seen in the inset of Fig. 14 and rapidly drops starting around 50,000
e-. This initial decay leads to a rapid turnover starting just under 55,000 e-
where charge transfer between amplifiers becomes unreliable with increasing
blooming of charge into the overscan columns. For scientific requirements
where conventional CTI $<10^{-5}$, this imposes a strict upper limit on the
effective dynamic range of this MAS device with our operating parameters at
$50,000$ e- for reading out through all 16 channels. This demonstrates that
the amplifier-to-amplifier transfer efficiency breaks down well before the
actual physical well depth of the pixels given our clock voltages, and thus
acts as an “effective full well.” This behavior where the ACTE rather than the
physical pixel well depth imposes an effective full well is analogous to how
the output-amplifier voltage swing limits the full well of conventional CCDs
(Bebek et al., 2017).

Figure 13: Horizontal profiles around the boundary of the active and overscan
regions at varying exposure times. The solid lines are profiles from the first
amplifier (amplifier 0) and lines with dots are profiles from the last
(amplifier 15) with the color spectrum representing the exposure time. The
blue vertical dashed line indicates the last column in the active area and the
orange dashed line the first overscan column. Blooming at the edge of the
active region into the overscan is clearly caused by both pixel saturation at
physical full well as shown in the first amplifier and the imperfect charge
transfer between amplifiers as shown by the degradation of the profiles at
lower signal levels than the apparent full well in amplifier 15.

Although $\sim$50,000 e- dynamic range is limiting for imaging which typically
requires $\gtrsim 90,000$ e- full well minimum (e.g., Radeka et al., 2009;
Flaugher et al., 2015), this is sufficient for spectroscopic surveys such as
DESI and photon-starved applications. In exploring additional voltage
configurations, we find that it is possible to change the signal level at
which the drop off of the ACTE occurs through different combinations of the H1
and PS clock swings. The critical step in the readout sequence of clock states
where PS and H1 have direct impact is state (c) in Fig. 6, immediately
following the measurement of charge in the sense node. For example, smaller
voltage swings for H1 where its lower state is raised above -12 V, maintaining
a potential difference ranging between 1 V to 5 V between the low voltages of
PS and H1, moves this ACTE drop off to even lower signal levels. With high
signal levels and a collecting potential phase that is too shallow, when the
charge is transferred into the inter-amplifier pixels after measurement at one
output stage, not all charge in the sense node is transferred and unwanted
charge diffusion back into the sense node before the PS gate is raised as a
potential barrier may occur, increasing the charge loss down the serial line
of amplifiers. These observations suggest that larger H1 clock swings or a
higher PS low state at least at the clock amplitudes of the vertical clocks
(which determine well depth in the array) would potentially enable a greater
dynamic range than what we are able to measure, given the constraints of the
$\pm 12$ V range of the Hydra electronics. Increasing clock amplitudes to
increase the ability to transfer charge at high signal levels must be tempered
with the effective read noise trade-off, since greater horizontal clock
voltage swings as presented in Fig. 7 correlate with higher read noise $>1.5$
e- rms/pix. Therefore, key elements such as the target noise and effective
full well required must be well-defined and optimized on simultaneously
because the multivariate relationships between the clock voltages and the
resulting behavior are interconnected in the MAS architecture, as single-
parameter only optimization is likely to jeopardize another aspect of device
performance.

Figure 14: Inter-amplifier CTE at high signal levels shown for each amplifier
stage relative to amplifier 0 show a catastrophic inter-amplifier CTE decline
past 55,000 e-. The inset shows in detail this drop off at high signal.

Another method explored for this analysis involved projecting a pattern of a
grid onto the detector surface. At the front of the LED, a mask lens with a
grid pattern was inserted and manually aligned to the CCD rows and columns.
The grid was focused by minimizing the width of the illuminated column that
the LED projects onto the active area. The grid pattern mask ensures that the
illumination level is consistent in a given column or row of the grid. As with
flat fields, different signal levels in the illuminated areas of the grid
could be obtained by varying the exposure time. To measure the CTE through the
full dynamic range up to the full well capacity, we took images in a ramp of
increasing exposure times up to 30 s at a low gain ADC setting.

To account for non-uniformities in our mask, vertical profiles were measured
for the illuminated grid areas. We base our measurements on areas of the grid
that do not intersect, because pixels in the intersection of illuminated grid
areas have higher signals that have contributions from optical effects that
are challenging to disentangle from the potential imperfect charge transfer
that we are measuring. To quantify CTE with this setup, we measured the
averaged horizontal profiles of an illuminated column segment of the grid for
each amplifier. This column was carefully chosen where the vertical profile of
the segment is flat and is at the leading edge of the illuminated strip,
illustrated in Fig. 15. The leading edge between dark and illuminated pixels
is ideal since a charge transfer issue is expected to result in deferred
charge starting at the illuminated region which blooms past the trailing edge.
For perfect CTE, the profiles for each output amplifier stage should be
identical and completely overlap, whereas charge transfer issues result in
profile differentiation illustrated in Fig. 16. Significant CTI at high signal
levels can be observed on images as a broadening of the illuminated grid
column on the trailing pixel side.

The results using the grid illuminated at varying signal levels is presented
in Fig. 17, where the ratio of the signal in each amplifier at the location of
the column along the edge of the grid is interpreted as a measure of the ACTE.
Although using this technique gives noisier results than with our EPER-like
measurement, the shape and drop off of the curve is nearly identical to what
we find in Fig. 14. Inter-amplifier charge transfer becomes unsustainable and
drops rapidly at signals between 54,000–55,000 e-. More precise measurements
are limited for this approach by imperfections in the alignment of the grid to
the pixel columns, micron-scale scratches on the surface of the mask, and
possible non-uniformities in the optics and the mask itself that are not
straightforward to resolve. These are extraneous effects at the $0.8\%$ level
that dominate over $<0.1\%$ effects from ACTE that play a role prior to the
complete drop off of the ACTE.

Figure 15: Grid mask projection onto the active area of the CCD with the edge
of the illuminated strip where profiles are taken denoted by the dashed line.
Stray light from a few isolated micron-scale scratches are visible in the dark
areas. Figure 16: Horizontal profiles around the illuminated grid columns
plotted for each amplifier demonstrates significant inter-amplifier charge
transfer issues that compounds with every successive output stage. The
vertical dashed line denotes where there is a “cliff” along the border between
the illuminated and non-illuminated columns. The signal flux at this cliff is
used to evaluate the ACTE. Figure 17: The ratio of the mean signal between the
first and subsequent amplifiers as a function of the signal level. The column
number where the mean signal is evaluated is denoted by the dashed vertical
line shown in Fig. 16. The degradation of ACTE shown here is consistent with
what was found with Fig. 14.

###  5.2 Full well capacity

While low-signal spectroscopy typically does not require high full well
capacity, maximizing full well elevates the versatility of a detector by
increasing its dynamic range. This is an important consideration for
spectroscopic observations capable of capturing the full intensity of bright
lines and photometrically imaging complete transient event light curves from
the low-signal tails of the rise to peak flux without flat-topping due to
saturation. For amplifier 0, we find that the full well capacity at a low ADC
gain setting with our low-noise voltages is $\sim 80,000$ e-, as observed with
the amplifier 0 horizontal profiles in Fig. 13 at the highest signal levels.
However, this full well is only valid for amplifier 0 because this level
cannot be reached due to ACTE degradation. Full well measurements for multiple
amplifiers must appropriately account for the inter-amplifier charge transfer
efficiency, which adds excess charge that has bloomed over in the serial
direction at very high signal levels.

Our measurements with the inter-amplifier charge transfer efficiency indicate
that there is an “effective full well” in the MAS architecture bounded by non-
linearities at high signal that is distinct from the physical well depth of
the pixel given the clock voltages. These non-linearities result from the
highly inefficient charge transfers between amplifier sense nodes in the MAS
register that dominate all other effects starting at the 50,000 e- signal
level. This is specifically the limit contributed by amplifier 15, the final
output stage, and thus can be interpreted as an effective charge level
constraint for the device. Because this effective full well is not set by the
pixel well depth but by the PS-H1 clock voltages that dictate ACTE, it is
another parameter that should be optimized on, akin to how the sense-node
conversion gain impacts the full well of conventional CCDs.

###  5.3 Linearity

Detector nonlinearity was explicitly measured by acquiring flat field images
in a sequence of exposure times that provide different illumination levels.
Since our system was not set up for a mechanical shutter and because shutters
also have intrinsic limitations on precision timing, the LED illumination
source was kept on at fixed intensity even between exposure readouts to ensure
that the timing of the LED warm-up and on-off cycle was not a systematic
uncertainty in our measurement. In idle mode, the Hydra continuously clocks
the parallel register until an exposure is triggered for a time, where the
clocks are frozen for charge to collect in the active area. Without a
mechanical shutter with the LED constantly on, charge will accumulate in the
array that will compound into the subsequent exposure if there is insufficient
idle time for the charge collected during the readout time to be clocked away.
To minimize timing variation and obtain as flat a background as possible in
this setup, an idle duration of 20 s was inserted between each exposure, and a
zero-second exposure was interleaved between each image acquired with nonzero
exposure time to correct for the baseline signal on the detector at any given
time by the fixed LED light. Thus, bias correction was accomplished by
subtracting each nonzero exposure time image from its preceding zero frame.
Three exposure pairs per unique exposure time were taken with an exposure time
sequence that was in randomized order to further reduce systematic effects.

Figure 18: Nonlinearity of all amplifiers for the MAS CCD, with data points
shown in the upper panel and a linear curve fit in a single color assigned to
each amplifier. The dashed horizontal line indicates the signal at which the
ADC saturates, since we selected a high gain setting to acquire these
exposures. The bottom panel quantifies the residual as a function of the
expected flux for the optimal fit linear model.

We acquire data across a broad dynamic range of 28 illumination levels,
ranging from 330 e- to about 35,000 e-, corresponding to where the ADC
saturates and before where the inter-amplifier charge transfer efficiency
starts a gradual decline. This allows us to capture detector nonlinearity in a
regime that is not dominated by ACTE effects. The data is shown on the upper
panel of Fig. 18 for each output stage. After bias correction, the average
signal of the image was computed by taking the median value of a clean,
central subregion of the active area. First degree polynomial fitting by
minimizing squared errors was performed on this measured signal flux up until
35,000 e-. This model was used to compute the expected signal level plotted as
the independent variable in Fig. 18, resulting in the linear curves shown on
the upper panel. To quantify the linearity, the residuals to this linear
optimal fit are calculated in the bottom panel, where the residual quantity is
defined as the ratio of the measured flux level and the flux expected from the
linear model, and is proportional to the exposure time. A perfectly linear
response would yield a flat line at unity. This linear model demonstrates that
for each amplifier there is a consistent $\pm 2.5\%$ nonlinearity in the MAS
CCD across the 330 e- to 35,000 e- dynamic range. This mild nonlinearity
becomes more significant as the signal nears the effective full well with the
onset of inter-amplifier charge transfer efficiency deterioration, and thus is
excluded from the linear fitting. These results demonstrate that the MAS CCD
is on par with or slightly better than typical DECam CCD nonlinearity
characterized using a similar approach (Bernstein et al., 2017). At the very
low signal levels under a few hundred electrons, this method is limited by
systematics that may vary with time such as light leakage, and thus we do not
probe signals at this very low regime. However, we note that it is possible to
probe very low signal levels by operating MAS CCD in photon-counting mode as a
Skipper CCD using repeated skipping sampling to count the number of electrons
per pixel in relation to the number of ADUs output by the ADC. This is
essentially an absolute measure of gain stability and was studied for Skipper
CCDs by counting electron peaks up to 1800 e- where a $<2.5\%$ nonlinearity
was found at this low photon-counting regime (Rodrigues et al., 2021). Our new
readout electronics being developed will enable the capability to switch
seamlessly to the photon counting mode, where we will be able to extend our
measurements down to a few tens of electrons. An initial demonstration of
photon-counting with a MAS CCD by “skipping” has been shown in Botti et al.
(2024), using a low-threshold acquisition (LTA) controller optimized for dark
matter experiments.

###  5.4 Crosstalk

Multiple channels measure charge simultaneously in the MAS CCD, introducing a
risk of electronic crosstalk between channels that generates ghost images that
can contaminate neighboring channels. One indication of crosstalk we observed
especially in flat fields was the slightly different baseline levels within
the overscan and prescan regions of the image. In column-averaged horizontal
profiles of the prescan and overscan regions, after the sharp drop-off in
signal from the active region, the first 16 pixels into the overscan form a
“step” before dropping to a stable baseline. This 16-pixel wide step
corresponds to the number of inter-amplifier pixels separating the output
stages, and is characteristic of crosstalk generated by amplifiers that are
reading pixels at the same time for pixels physically ahead and behind
horizontally. The signal difference between this 16-pixel step and the
overscan baseline scales linearly with the signal in the final active column
until inter-amplifier CTI losses cause blooming into the overscan itself.
Using this feature to estimate the level of this ghosting signature present in
each channel, we found the upper limit of this crosstalk to be $0.08\%$ of the
signal in the final active column in the amplifiers 4-8, in the middle of the
chain. The amplifiers with lower levels of ghosting were 0-3 and 9-15, where
the crosstalk amplitude was measured to be $<0.04\%$, comparable to common
requirements for multi-output conventional CCDs (e.g., O’Connor, 2015).

##  6 Upcoming plans

For photon-limited observations required for the more aggressive space imaging
application, single-photon resolution is essential and necessitates a
combination of further reductions in noise per amplifier, additional MAS
output stages, and taking advantage of the ability to “skip” with the
floating-gate amplifier. In the photon-counting regime, systematic noise
backgrounds normally hidden underneath read noise in silicon detectors become
dominant, imposing a potential detection limit that must be characterized.
When the magnitudes of the carriers created from thermal leakage (dark)
current and clock-induced charge are comparable to incident optical signals,
the photons are to be detected become indistinguishable from the background
generated from the detector itself. While amplifier thermal leakage is
typically managed by cooling the detector, clock-induced charge spuriously
generated during readout is a well-documented but not yet fully-understood
single-electron event mechanism that single-photon resolving Skipper and
electron-multiplying CCDs are sensitive to detecting (e.g., Janesick, 2001;
Barak et al., 2022; Wilkins et al., 2014). Because the MAS CCD has additional
clocks owing from inter-amplifier pixels in its extended output register,
investigating the nature of spurious charge in the photon-counting regime is
especially important, and our next phase of testing enables output gate
clocking for “skipping” capability to extensively quantify its dependence on
clock amplitude, edge shape, and pixel rate. Re-sampling charge to reach
photon-counting resolution also provides the additional benefit of direct gain
self-calibration and very low-signal linearity measurements during potential
daytime detector calibrations in survey operations. New readout schemes that
benefit from multiple amplifiers will also be studied. To accommodate these
functionalities with a large format MAS CCD, a 64-channel readout electronics
system has been designed where these tests will be carried out.

Thinned MAS CCDs with 8 and 16 channels have been fabricated with the same
high-efficiency ITO/ZrO2 AR coating applied as DESI detectors (Groom et al.,
2017). Tests are underway to analyze the optical properties of these devices.
Potential future designs being considered such as four-corner MAS amplifier
layout with 32 channels each to accommodate simultaneous readout from
quadrants is anticipated to reach sub-electron read noise and may be suitable
for space-based imaging and spectroscopy applications.

##  7 Conclusions

We have packaged and instrumented a thick MAS CCD prototype designed at LBNL
using a synchronized adaptation of the DESI readout electronics with all 16
channels fully functional. The development of the MAS CCD was driven by the
motivation to reduce the readout time required by Skipper CCDs to achieve
single to sub-electron read noise by placing multiple video output stages
along a longer serial register where pixel charge can be measured multiple
times. Reducing the readout time while maintaining the capability to sample
charge multiple times to lower read noise is critical for enabling next
generation ground-based astronomical spectroscopy and especially for all-sky
surveys where exposure time is limited by cosmic ray contamination and
practical observational strategy constraints. Future spectroscopic surveys
including a DESI upgrade or a Spec-S5 will require a single-electron read
noise floor to reach fainter objects at higher redshift, particularly in blue
optical wavelengths were detector read noise currently dominates the noise
budget. Multiple on-chip amplifiers also provide additional layers of
redundancy against amplifier failures with the ability for charge to non-
destructively pass through dead or high-noise amplifiers which regularly
plague CCDs. Since the information carried by the charge is preserved, only
functioning amplifiers with acceptable noise can be selected for readout or
for optimizing the compound read noise. All of these features would benefit
any survey especially when detectors cannot be replaced during operations.

After voltage optimization on noise, we have demonstrated a near single-
electron compound read noise of 1.03 e- rms/pix with a single read per
amplifier at a pixel time of 26 $\mu$s/pix. This is nearly a factor of 8.5
less in readout time per pixel compared to that of a Skipper CCD performing at
an equivalent noise level (e.g., Villalpando et al., 2024). With this
performance demonstrated as a prototype device, a MAS CCD with twice as many
amplifiers would be a promising contender for a detector upgrade in the second
phase of DESI and as a candidate detector for a Spec-S5 spectrograph. These
optimization tests have shown the interplay amongst the noise, full well, and
pixel charge transfer efficiency between the extended multiple stage outputs
of this architecture. To investigate the inter-amplifier charge transfer
efficiency, we proposed and tested several methods to quantify the ability for
charge to shift from one amplifier to the next across a dynamic range from
$10^{3}$ to $10^{4}$ e-. The inter-amplifier charge transfer efficiency was
consistent with unity until close to a high signal level of $\sim 50,000$ e-,
limited by a gradual deferral of charge through the stages that is cumulative
and presents most prominently in the last output stage. We find that the sense
node, PS gate, and first horizontal clock phase are most important for
ensuring that charge is removed and shifted away from an output stage once it
is measured, and these voltages can be optimized further to obtain a greater
dynamic range. We find that this inter-amplifier charge transfer efficiency
establishes an effective detector full well capacity that is distinct from the
full wells defined by typical serial clock phases or pixels in conventional
CCDs. Since charge deferral between amplifiers compounds through the stages
and is not observed in the first amplifier, the maximum amount of charge that
can be efficiently read out through the multiple amplifiers is the effective
full well for the MAS CCD. Finally, we measure the nonlinearity of the MAS CCD
from 400 e- to nearly 40,000 e- to be $\pm 2.5\%$ in this dynamic range, which
is consistent for each amplifier stage and comparable to previous generations
of LBNL CCDs.

The progress presented here is the beginning of an extensive effort to fully
optimize a MAS CCD as a candidate detector for future spectroscopic
experiments and space-based imaging such as HWO. Similar results with respect
to noise and inter-amplifier charge transfer efficiency have also been found
with a 16 channel MAS CCD operating with LTA readout electronics (Botti et
al., 2024; Lapi et al., 2024). With a fundamental proof-of-concept presented
here, upcoming large format, high channel count designs have been pushed
forward for prototyping, and new readout electronics solutions that
accommodate high channel counts including ASICs are being explored.

Acknowledgments: This research was supported by the Laboratory Director’s
Research and Development (LDRD) Program at Lawrence Berkeley National
Laboratory under Contract DE-AC02-05CH11231. KL was partially supported by the
U.S. Department of Energy, Office of Science, Office of Workforce Development
for Teachers and Scientists, Office of Science Graduate Student Research
(SCGSR) program. The SCGSR program is administered by the Oak Ridge Institute
for Science and Education for the DOE under contract number DE‐SC0014664. ADW
was partially supported by Fermilab LDRD (2019.011 and 2022.053), NASA APRA
(80NSSC22K1411), and a grant from the Heising-Simons Foundation (#2023-4611).
We thank the CCD group at Fermilab for sending the die back to LBNL that was
the subject of this study.

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