# Digital Pixel Test Structures implemented in a 65 nm CMOS process

Gianluca Aglieri Rinella  Anton Andronic  Matias Antonelli  Mauro Aresti
Roberto Baccomi  Pascal Becht  Stefania Beole  Justus Braach  Matthew Daniel
Buckland  Eric Buschmann  Paolo Camerini  Francesca Carnesecchi  Leonardo
Cecconi  Edoardo Charbon  Giacomo Contin  Dominik Dannheim  Joao de Melo
Wenjing Deng  Antonello di Mauro  Jan Hasenbichler  Hartmut Hillemanns  Geun
Hee Hong  Artem Isakov  Antoine Junique  Alex Kluge  Artem Kotliarov  Filip
Křížek  Lukas Lautner  Magnus Mager  Davide Marras  Paolo Martinengo  Silvia
Masciocchi  Marius Wilm Menzel  Magdalena Munker  Francesco Piro  Alexandre
Rachevski  Karoliina Rebane  Felix Reidt  Roberto Russo  Isabella Sanna
Valerio Sarritzu  Serhiy Senyukov  Walter Snoeys  Jory Sonneveld  Miljenko
Šuljić  Peter Svihra  Nicolas Tiltmann  Gianluca Usai  Jacob Bastiaan Van
Beelen  Mirella Dimitrova Vassilev  Caterina Vernieri  Anna Villani

###### Abstract

The ALICE ITS3 (Inner Tracking System 3) upgrade project and the CERN EP R&D
on monolithic pixel sensors are investigating the feasibility of the Tower
Partners Semiconductor Co. $65\text{\,}\mathrm{nm}$ process for use in the
next generation of vertex detectors. The ITS3 aims to employ wafer-scale
Monolithic Active Pixel Sensors thinned down to
$2040\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and bent to form truly
cylindrical half barrels. Among the first critical steps towards the
realisation of this detector is to validate the sensor technology through
extensive characterisation both in the laboratory and with in-beam
measurements. The Digital Pixel Test Structure (DPTS) is one of the prototypes
produced in the first sensor submission in this technology and has undergone a
systematic measurement campaign whose details are presented in this article.

The results confirm the goals of detection efficiency and non-ionising and
ionising radiation hardness up to the expected levels for ALICE ITS3 and also
demonstrate operation at +$20\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and a
detection efficiency of $99\text{\,}\mathrm{\%}$ for a DPTS irradiated with a
dose of ${10}^{15}\text{\,}\mathrm{\mbox{$1\text{\,}\mathrm{MeV}$\
n${}_{\mathrm{eq}}$\ ${\mathrm{cm}}^{-2}$}}$. Furthermore, spatial, timing and
energy resolutions were measured at various settings and irradiation levels.

###### keywords:

Monolithic Active Pixel Sensors , Solid state detectors

††journal: Nucl. Instrum. Methods Phys. Res. A

scaletikzpicturetowidth[1]

[1]organization=European Organisation for Nuclear Research (CERN),
city=Geneva, country=Switzerland [13]organization=Westfälische Wilhelms-
Universität Münster, city=Münster, country=Germany [2]organization=Ruprecht
Karls Universität Heidelberg, city=Heidelberg, country=Germany
[3]organization=Università degli studi di Torino, city=Torino, country=Italy
[4]organization=Istituto Nazionale di Fisica Nucleare (INFN), Sezione di
Torino, city=Torino, country=Italy [18]organization=Universität Hamburg,
city=Hamburg, country=Germany [5]organization=Università degli studi di
Trieste, city=Trieste, country=Italy [6]organization=Istituto Nazionale di
Fisica Nucleare (INFN), Sezione di Trieste, city=Trieste, country=Italy
[17]organization=EPFL, city=Lausanne, country=Switzerland
[15]organization=Central China Normal University (CCNU), city=Wuhan,
country=China [16]organization=Yonsei University, city=Seoul, country=Republic
of Korea [7]organization=Czech Academy of Sciences, city=Prague,
country=Czechia [8]organization=Technische Universität München, city=München,
country=Germany [9]organization=Università degli studi di Cagliari,
city=Cagliari, country=Italy [10]organization=Istituto Nazionale di Fisica
Nucleare (INFN), Sezione di Cagliari, city=Cagliari, country=Italy
[11]organization=Nikhef National institute for subatomic physics,
city=Amsterdam, country=Netherlands [12]organization=Centre National de la
Recherche Scientifique, city=Strasbourg, country=France [14]organization=SLAC,
city=Menlo Park, country=California, USA [19]organization=Stanford University,
city=Stanford, country=California, USA

##  1 Introduction

Over the past decade, Monolithic Active Pixel Sensors (MAPS) have well
established their position in high energy physics experiment vertex detectors
[1, 2, 3]. By combining the readout circuitry and the sensitive volume in the
same sensor produced in commercial processes, they pave the way for ultra-thin
and large-scale tracking detectors. The state-of-art ALPIDE chip, in use in
the ALICE Inner Tracking System 2 (ITS2), was produced in the TowerJazz 180
technology and demonstrated an excellent detection efficiency (≫99) and
spatial resolution (5) performance at very low power dissipation (<40^2) and
material budget of 0.05X/X_0 up to irradiation levels of about 3 and e13 [4,
5, 6]. Other developments produced in the same technology demonstrated
comparable detection efficiency at -20 even after a non-ionising radiation
dose of e15 [7]. The next upgrade of ALICE tracker, the ALICE ITS3, planned
for the Long Shutdowns 3 (2026-2028), is extending the requirements on the
sensor characteristics. The ITS3 detector integration imposes a wafer-scale
sensor size $O(10\times\qty{27}{{}^{2}})$ and operation at temperatures
achievable by air cooling $O(\qty{+20}{})$ [8].

In order to address the arising challenges in the design of the next
generation MAPS detector, the Tower Partners Semiconductor Co. (TPSCo)
$65\text{\,}\mathrm{nm}$ CMOS imaging process [9] was chosen as the starting
point in the framework of the ALICE ITS3 upgrade [8, 10] and the CERN EP R&D
on monolithic pixel sensors [11]. The critical aspect of the new technology
node for the ALICE ITS3 is the larger wafer size (30 as opposed to 20 in
TowerJazz 180 process). The goal of the first submission designated MLR1 and
produced in summer 2021, was to verify the radiation hardness (the expected
levels for the ITS3 are below e13 and 10 [8]) and the detection efficiency
($>$99) of the MAPS produced in this technology. Therefore, a sensor prototype
featuring in-pixel amplification and discrimination was characterised using
soft X-rays and ionising particle beams and the results are described in this
paper. In particular, the sensors were irradiated111Sensors irradiated with
non-ionising, ionising, and combined doses were exposed to neutrons at JSI
Ljubljana, 10 X-rays from a tungsten target at CERN, and 30 protons at NPI
Prague, respectively. up to 100 and e15 and their detection efficiency and
spatial, timing and energy resolutions were measured. In total, $48$ sensors
have been tested, with at least two for each radiation level (three in case of
e15). For visualisation purposes and to eliminate any selection bias, each
measurement point is represented by a single device, chosen as the first one
that was tested.

##  2 The DPTS chip

The Digital Pixel Test Structure (DPTS) is the most complex prototype MAPS
produced in the first submission in TPSCo $65\text{\,}\mathrm{nm}$ technology
process [9]. In order to optimise the technology for ionising particle
detection, the submission was produced in four process splits, gradually
modifying the doping levels of various implants (cf. Fig. 1(a)). The present
work focuses only on the split expected to yield the best performance [12].

((a)) Pixel cross section. Not to scale.

((b)) Chip under microscope.

Figure 1: A cross section of a DPTS pixel and a photo of the chip under a
microscope.

To better collect the signal charge and accelerate it to the collection diode,
similar measures to those in the 180 technology have been applied [7, 13]. As
illustrated in Fig. 1(a), a deep, low-dose, n-type implant has been introduced
to displace the junction from the collection diode into the epitaxial layer
and thus deplete the epitaxial layer over the full pixel width [13]. This
additional implant does not extend to the pixel border, but there is a gap in
the implant near the pixel edges with the aim to increase the lateral field,
pushing the signal charge to the collection diode [14]. This is expected not
only to accelerate the charge collection but also to reduce charge sharing to
give more operating margin due to the larger seed pixel signal.

The DPTS chip (cf. Fig. 1(b)) measures 1.5x1.5 and features a 32x32 pixel
matrix of 15x15 pitch, controlled by a set of external reference currents and
voltages, and read out via a current mode logic (CML) output. The in-pixel
front end amplifies, shapes, and discriminates the signal from the collection
diode. The positions of the hit pixels are time-encoded (c.f. Sec. 2.2) and
all 1024 pixels are read out simultaneously via a differential digital output
line (cf. Fig. 2). The pixels can be masked from readout and selected for
pulsing via a 480 triplicated shift register. Given its space-constrained
size, the possible masking and pulsing combinations are limited. Those used in
this paper are the following: pulsing a single pixel, masking a single pixel,
and masking the whole matrix with the exception of one row (unmasking a single
pixel is not possible).

Figure 1(b) shows a photograph of the DPTS taken under a microscope. Starting
from the centre and going outwards, the pixel matrix, shift register block,
guard rings, and bonding pads can be distinguished. Most of the pads are
dedicated to supplying power and reverse bias to the chip. The power supply is
split into three domains (all operated at +1.2): analogue in-pixel front end,
CML output driver, and all other digital circuitry. The reverse bias can be
supplied separately to the substrate ($V_{sub}$) and the deep p-wells
($V_{pwell}$) hosting the circuitry (cf. Fig. 1(a)), however, in this work
they were kept at the same potential.

Figure 2: DPTS functional diagram. $1024$ pixels can be masked from readout
and selected for pulsing via a shift register. The addresses of hit pixels are
read out via a differential digital output line. The in-pixel amplifier output
of a single pixel is connected to an interface pad.

There are three variants of the chip, implementing different time-encoding
(cf. Sec. 2.2) and ground connection schemes222In one of the DPTS variants,
the ground of the digital and analogue power domains is connected on the chip.
In all the measurements presented in this paper, the ground was connected for
all three power domains off-chip.. As the laboratory testing revealed no
difference in their performance, no distinction will be made in the results
discussed here.

###  2.1 In-pixel front end

The analogue in-pixel front-end circuit (cf. Fig. 3) is controlled via four
currents ($I_{bias}$, $I_{biasn}$, $I_{reset}$ and $I_{db}$) and two voltages
($V_{casb}$ and $V_{casn}$), all externally generated and supplied to the chip
via the interface pads. The front end [15] is based on a high gain cascoded
inverting amplifier, requiring direct feedback to the input to correctly
define its operating point. This is achieved by the $V_{casb}$ transistor (M6)
in combination with the $I_{reset}$ current source (M5): the feedback will
make the current through the $V_{casb}$ transistor equal to $I_{reset}$ minus
the leakage current on the collection electrode and correctly set the voltage
of the collection electrode. When charge is collected on the collection diode,
the output of the inverting amplifier at the source of the $V_{casb}$
transistor will make a positive voltage excursion and switch off the
$V_{casb}$ transistor, causing the collection diode to be reset by a constant
current and, therefore, resulting in a close to linear time-over-threshold
behaviour. The high gain amplifier output is the input to a subsequent common-
source stage (M9-M10). As soon as the amplifier output is sufficiently high
for the input transistor of this second stage to overcome $I_{db}$, the output
node of the second branch will fall and convert the signal into a digital
rail-to-rail signal.

Figure 3: In-pixel amplifying, discriminating and reset circuit. All front-end
biases are provided externally, in common to all pixels.

The front end has been designed to operate at current levels in the main
branch ($I_{bias}$, M0-M3) between 10 and 5, in a power-to-speed trade-off.
The $I_{biasn}$ current source (M8) balances the amplifier output current and
is to be operated at one-tenth of the $I_{bias}$ current. $V_{casn}$ (M7) is
used to further control the operating margin of the amplifier. In the lower
current ranges, all transistors are in weak inversion. In addition, the NMOS
transistors are subject to the reverse bias applied to the sensor
($V_{pwell}$), requiring biases like $V_{casb}$ and $V_{casn}$ to be adjusted
to $V_{pwell}$ voltage and current levels in the circuit. The power
consumption in the steady state is given by the current in the main branch
($I_{bias}$) as the reset current is orders of magnitude lower and the
$I_{db}$ current in the discriminator branch is flowing only while M10 is
active. With the typical settings used in this paper (c.f. Sec. 3.1), it
amounts to about 120.

A test circuitry, which can inject charge in the collection electrode through
a capacitance of $C_{p}=\qty{160}{\atto}$, is also integrated in the pixel
(cf. Fig. 2 and Fig. 3). The amount of injected charge can be regulated by an
external voltage reference, $V_{h}$, and the injection is triggered by
asserting the TRG signal via an interface pad.

Besides the 1024 digital output pixels, the DPTS features a monitoring pixel
with an analogue output connected to an interface pad. The analogue pixel
front end is identical to the one described above with the exception of the
last common-source stage being replaced by a source follower, which buffers
its analogue output signal to the interface pad.

###  2.2 Hit position encoding and time-over-threshold

The transition of the discriminator output triggers the address generator (cf.
Fig. 2) to send two consecutive pulses on the CML output with a duration based
on the pixel position [16]. As indicated in Fig. 4, the first pulse is of a
fixed duration, the time distance between the two pulses encodes the pixel
position in a group of columns (PID) and the duration of the second pulse the
column group position in the matrix (GID).

The assertion and the deassertion of the discriminator result in two sets of
pulses, delimiting the time interval in which the front-end pulse was over the
threshold (ToT). Because the front end is designed such that the pulse length
is monotonically increasing with the input signal, the ToT provides
information on the collected or injected charge.

Figure 4: DPTS hit position encoding scheme. The two pulses encoding the pixel
position with the matrix are sent to CML output, both at the assertion and at
the deassertion of the discriminated pixel output signal.

As the time-encoded output of the 1024 pixels is merged to a single output
line, two or more pixels firing simultaneously result in a signal collision,
i.e. non-decodable output (the firing pixels’ coordinates cannot be
determined). In order to minimise the probability of signal collisions in case
of charge sharing among neighbouring pixels, two optimisations were
implemented in the encoding scheme: (1) the output signals of pixels in every
other column are delayed by a fixed offset, and (2) in every other row of a
column pair, the GID is swapped between the two pixels.

##  3 Laboratory measurements

###  3.1 Data acquisition setup

The laboratory and testbeam measurements used a custom-designed setup for the
DPTS sensor that supplies biases and control signals to the chip. The CML and
analogue outputs of the chip were recorded on an oscilloscope, with a sampling
rate of 5 GS/s and a bandwidth of 500. For all the temperature sensitive
measurements, in particular those involving irradiated chips, the chip
temperature was controlled using a water-cooled
(+$20\text{\,}\mathrm{\SIUnitSymbolCelsius}$) aluminium jig in thermal contact
with the chip carrier card and thus the chip.

The bias settings of the chip are set to “nominal” values (defined by the
design operating point) for all measurements unless otherwise stated or varied
in the measurement. These settings are $V_{casb}=\qty{300}{}$,
$V_{casn}=\qty{300}{}$, $I_{reset}=\qty{10}{}$, $I_{db}=\qty{100}{}$,
$I_{bias}=\qty{100}{}$, $I_{biasn}=\qty{10}{}$, $V_{h}=\qty{600}{}$ (the pixel
pulsing amplitude) and $V_{sub}=V_{pwell}=\qty{-1.2}{}$. For irradiated
sensors, the $I_{reset}$ is increased to $35\text{\,}\mathrm{pA}$ to overcome
the sensor leakage current. Furthermore, when adjusting $V_{pwell}$, the
values of $V_{casb}$ and $V_{casn}$ are adjusted as well (cf. Sec. 2.1). The
maximum $V_{pwell}$ foreseen by the design is $\qty{-6}{}$, however, in this
work, the $V_{pwell}$ is capped at $\qty{-3}{}$ as further increasing it did
not improve performance, at least not in the measurements presented here.

###  3.2 Analogue response

The inclusion of an additional monitor pixel to the chip allows the analogue
pulse of the front end to be directly measured (cf. Sec. 2.1). The monitor
pixel was pulsed, and the output responses at different chip bias settings are
shown in Fig. 5, demonstrating the influence of varying $V_{h}$, $V_{casb}$,
$V_{casn}$, $I_{reset}$, $I_{bias}$ and $I_{biasn}$. For the case of
$I_{bias}$, $I_{biasn}$ was also varied, keeping $I_{biasn}=I_{bias}/10$,
which is the recommended regime

Figure 5: The analogue responses produced when the monitor pixel is pulsed and
$V_{h}$, $V_{casb}$, $V_{casn}$, $I_{reset}$ and $I_{bias}$ are varied. For
$I_{bias}$, $I_{biasn}=I_{bias}/10$. Other chip bias settings not mentioned in
the legend are at nominal values (cf. Sec. 3.1).

Increasing $V_{h}$, which controls the injected charge, increases the
amplitude and length of the pulse. It can easily be observed that, in
accordance with the amplifier design (c.f. Sec. 2.1) the pulse length, rather
than amplitude, is proportional to the amount of injected charge. $V_{casb}$
has a direct influence on the baseline, at low $V_{casn}$ the pulse changes
shape, $I_{reset}$ changes the duration of the pulse and increasing $I_{bias}$
increases the amplitude. The impact of changing $I_{db}$ on the analogue pulse
is not presented as this last stage of the front end is not included in the
monitor pixel.

###  3.3 Threshold and noise

Investigation into the front-end response of the chip used the in-pixel
pulsing circuitry to conduct threshold measurements. This involved counting
the number of hits while varying $V_{h}$, that is, the amount of injected
charge. For every $V_{h}$ value, each pixel was pulsed 25 times. As the
injected charge approaches the threshold, the number of hits increases until a
plateau is reached, producing a so-called “s-curve”. Figure 6 shows examples
of the measured s-curves. The threshold and the noise are given by the mean
and standard deviation of the derivative of the s-curve, respectively. A hit
was determined to occur if at least two sets of pulses were captured by the
oscilloscope, ensuring both the assertion and deassertion of the discriminator
were recorded (cf. Sec. 2.2). The final threshold value is calibrated to
electrons via a measurement of the $\text{Mn-K}_{\alpha}$ peak position,
details of which are given in Sec. 3.7, and this method is used throughout the
paper. This calibration is done separately for each sensor, as deviations of
up to 20 of the measured injection capacitance with respect to its design
value have been observed.

Figure 6: S-curves of a chip tuned to a threshold of
$180\text{\,}\mathrm{\mbox{$e^{\text{-}}$}}$ with $V_{casb}=\qty{180}{}$ at
$V_{sub}=\qty{-1.2}{}$. Four pixels have been highlighted along with their
s-curve fits (non-solid lines). These four pixels represent the response of
pixels with the lowest, average and highest threshold and the pixel with the
highest noise. Other chip bias settings are at nominal values (cf. Sec. 3.1).

Examples of the pixel threshold and noise distributions at
$V_{sub}=\qty{0}{}$, $-1.2\text{\,}\mathrm{V}$ and $-3\text{\,}\mathrm{V}$ are
shown in Fig. 7, with the $V_{casb}$ value chosen such that the mean threshold
of all pixels is $180\text{\,}\mathrm{\mbox{$e^{\text{-}}$}}$. The threshold
distributions show comparable performance for $V_{sub}=\qtylist{-1.2;-3}{}$,
with both having a similar width and centred around
$180\text{\,}\mathrm{\mbox{$e^{\text{-}}$}}$. However, at $V_{sub}=\qty{0}{}$,
the distribution is wider and asymmetric – indicating a substantial pixel-to-
pixel threshold spread resulting in a non-uniform response across the matrix.
For the noise distributions, $V_{sub}=\qty{0}{}$ continues to show the widest
distribution, while $V_{sub}=\qty{-1.2}{}$ has a better performance in terms
of a smaller mean and spread than $V_{sub}=\qty{-3}{}$, suggesting non-optimal
chip biasing settings for $V_{sub}=\qty{-3}{}$. In general, even with chip
biasing settings optimised for threshold and noise, a worse performance in
terms of threshold spread and noise was observed when decreasing $V_{sub}$
towards $0\text{\,}\mathrm{V}$ or increasing it towards
$-3\text{\,}\mathrm{V}$ and above.

Figure 7: Pixel threshold (left) and noise (right) distributions of a chip
tuned to a threshold of $180\text{\,}\mathrm{\mbox{$e^{\text{-}}$}}$ with
$V_{casb}=\qtylist[list-units=single]{110;180;500}{}$ at
$V_{sub}=\qtylist[list-units=single]{0.0;-1.2;-3}{}$, respectively. Other chip
bias settings are at nominal values (cf. Sec. 3.1).

Figure 8 demonstrates the effect of the chip bias settings on the threshold at
$V_{sub}=\qtylist{0;-1.2;-3}{}$ by plotting the mean and the RMS (given by the
error bars) of all pixels. For $V_{casb}$, it can be observed that this chip
bias has the largest impact on the threshold. Also, there is a linear
relationship between the mean threshold and $V_{casb}$ in a certain range,
which is larger for larger $V_{sub}$. This linear relationship is the
motivation for using $V_{casb}$ as the main handle to control the threshold of
the chip during operation and for all subsequent results. Figure 8 also
illustrates that at different $V_{sub}$ values, the same value of $V_{casb}$
does not produce the same mean threshold.

While the other chip biases affect the threshold as well, for $V_{casn}$,
$I_{bias}$ and $I_{biasn}$, the influence is expected to be minimal once in a
stable operating regime. The changes due to chip biases other than $V_{casb}$
are largest at $V_{sub}=\qty{0}{}$. Whereas, at lower reverse bias values, the
changes to the mean threshold (for the plotted range) are within 100 except
for $I_{reset}$, where the increase is around 150. However, this large
dependence of the threshold on $I_{reset}$ does not mean that this parameter
is a good handle to set the threshold because changing $I_{reset}$ alters the
diode biasing (cf. Sec. 2.1) and influences the charge collection properties.
Consequently, $I_{reset}$ is only used to compensate for the increased leakage
current caused by non-ionising radiation damage and not to tune the threshold.

Figure 8: The mean threshold as a function of different chip bias settings at
$V_{sub}$ of $\qtylist[list-units=single]{0.0;-1.2;-3}{}$ with $V_{casb}$ set
to [list-units=single]95;150;450, respectively. $V_{casb}$ was tuned so that
the mean threshold was $210\text{\,}\mathrm{\mbox{$e^{\text{-}}$}}$ for
nominal settings. The error bars represent the threshold RMS. The parameters
not varied in the measurement are at nominal values (cf. Sec. 3.1).

Another operating condition that impacts the threshold is the temperature.
Measurements of a non-irradiated chip have shown the mean threshold decreases
by $0.5\text{\,}\mathrm{\mbox{$e^{\text{-}}$}}$ per degree Celsius in the
measured range of $1540\text{\,}\mathrm{\SIUnitSymbolCelsius}$. However, for
an irradiated chip, the dependence is not linear. This is compatible with the
non-linear dependence of the leakage current on the temperature for higher
non-ionising radiation fluence levels.

###  3.4 Time-over-threshold

Further investigation into the front-end response was performed by observing
the impact of the chip biasing settings on the time-over-threshold (ToT, cf.
Sec. 2.2). By varying the injected charge, $Q_{inj}$, and measuring the ToT
for all pixels, it can be seen from Fig. 9 that at lower injected charge
values, around the pixel threshold, the response is non-linear. Whereas, for
larger injected charge values, the ToT response becomes linear and the spread
in the ToT increases. There is also a sizeable pixel-to-pixel variation that
is demonstrated by highlighting the response of two pixels. To account for
this spread, a ToT calibration was performed for all pixels individually, by
fitting with the empirical function

$ToT=aQ_{inj}+b-\frac{c}{Q_{inj}-d}\text{ ,}$ (1)

where $a$, $b$, $c$ and $d$ are the fit parameters. Example fits of two pixels
are shown by the solid lines in Figure 9. The effect of the ToT calibration to
normalise the pixel response over the matrix is shown and discussed in Sec.
3.7.

Figure 9: Time-over-threshold (ToT) as a function of injected charge for all
pixels with two pixels highlighted to demonstrate the pixel-to-pixel
variation. The two pixels have been fitted with Eq. 1 shown by the solid and
dashed lines.

The impact of the other chip biases on ToT was also investigated at a fixed
charged injection of $725\text{\,}\mathrm{\mbox{$e^{\text{-}}$}}$. The results
in Fig. 10 demonstrate that $I_{reset}$ produces the most significant change
in ToT (within $40\text{\,}\mathrm{\SIUnitSymbolMicro s}$), which is
compatible with $I_{reset}$ resetting the diode (cf. Sec. 2.1). For the other
biases, the change is within $10\text{\,}\mathrm{\SIUnitSymbolMicro s}$.
Furthermore, the non-linear behaviour of the ToT as a function of $V_{casb}$
for values above $70\text{\,}\mathrm{mV}$ illustrates the limited operation
margin at $V_{sub}=\qty{0}{}$.

Figure 10: Time-over-threshold (ToT) as a function of different chip biases at
a fixed charged injection of $725\text{\,}\mathrm{\mbox{$e^{\text{-}}$}}$.
Non-varied parameters are at nominal values (cf. Sec. 3.1).

###  3.5 Fake-hit rate

The impact of the chip bias settings on the fake-hit rate (FHR) was evaluated
and is shown in Fig. 11. The FHR is defined as the number of hits per pixel
and second in the absence of external stimuli as the chip operates in a
continuous readout. Given that the oscilloscope captures a fixed-size time
window, the FHR is estimated as the aggregate of hits in a number of randomly
triggered oscilloscope acquisitions divided by the sum of their duration and
the total number of pixels ($1024$). In general, the measurements show that
the lower the threshold, the higher the FHR. As with the threshold results
shown in Sec. 3.3, operating at $V_{sub}=\qty{-1.2}{}$ gives the best
performance, with many of the results below the sensitivity limit333The
sensitivity limit is defined as the lowest measurable FHR for the number of
oscilloscope captures in the measurement. of the measurements, even at the low
threshold used for the measurements. At $V_{sub}=\qty{0}{}$, the sharp
increase in the FHR from the lowest operable $V_{casb}$ further illustrates
the limited operation margin without supplying reverse bias.

Figure 11: Fake-hit rate as a function of different chip biases. At
$V_{sub}=\qty{-1.2}{}$, the threshold was set at
$120\text{\,}\mathrm{\mbox{$e^{\text{-}}$}}$, while for the other $V_{sub}$
values it was $210\text{\,}\mathrm{\mbox{$e^{\text{-}}$}}$ (for the nominal
parameters). Other chip bias settings not varied in the measurement are at
nominal values (cf. Sec. 3.1).

###  3.6 Pixel position decoding

As described in Sec. 2.2, the positions of the hit pixels are time-encoded in
the CML output pulses in terms of PIDs and GIDs. An example of the measured
PIDs and GIDs for all pixels, each pulsed 100 times, at
$V_{sub}=V_{pwell}=\qtylist{-1.2;-3}{}$ is given in Fig. 12. It can be
observed that the data points form clusters, corresponding to 1024 pixels.
Some of the clusters for the different pixels are very close (and look to be
overlapping due to an artefact of the axis scales), demonstrating where the
decoding errors can arise.

Figure 12: The PID and GID data points corresponding to all pixels pulsed 100
times at $V_{sub}=V_{pwell}=\qtylist{-1.2;-3}{}$ demonstrating the reverse
bias dependence. Each cluster consists of 100 points and represents the
measured PID and GID value for one pixel.

Given that the time constants in the encoding are dependent on the production
process and measurement conditions [16], a decoding calibration is needed to
convert the measured PIDs and GIDs of the waveforms to pixel rows and columns.
The calibration is performed by pulsing each pixel 100 times and measuring the
PIDs and GIDs of the recorded waveforms. The centre of gravity of the PID and
GID cluster for each pixel gives the decoding calibration. By associating a
(GID, PID) pair to the nearest centre of gravity, the conversion to columns
and rows is obtained.

Except for the reverse bias dependence, PIDs and GIDs were found to also
depend on supply voltage and temperature. In particular, it was found that the
mean PID and GID increase by 8;4 per degree Celsius, respectively, in the
range $1540\text{\,}\mathrm{\SIUnitSymbolCelsius}$.

###  3.7 Measurements with X-rays emitted by an 55Fe source

X-ray emissions from an 55Fe source illuminating the top side of the chip at a
distance of approximately $12\text{\,}\mathrm{mm}$ have been measured. Two
cuts have been applied to the data: the removal of all pixels on the matrix
edge and the removal of pixels with hit rates of five standard deviations
above the mean. The measured signal spectrum of clusters involving only one
pixel for a sensor with a threshold tuned to
$120\text{\,}\mathrm{\mbox{$e^{\text{-}}$}}$ is shown in Fig. 13 (in blue).

A ToT calibration for each pixel is applied to account for the variation in
the pixel-to-pixel response, as described in Sec. 3.4. After the ToT
calibration, the $\text{Mn-K}_{\alpha}$ and $\text{Mn-K}_{\beta}$ emission
peaks are resolved, as shown in Fig. 13 (in orange), as well as the
$\text{Mn-K}_{\alpha,\beta}$ escape
($\text{Mn-K}_{\alpha,\beta}-\text{Si-K}_{edge}$) and silicon fluorescence
($\text{Si-K}_{\alpha,\beta}$) peaks. The $\text{Mn-K}_{\alpha}$ and
$\text{Mn-K}_{\beta}$ peaks are fitted with a sum of two Gaussians. The
resolution of the $\text{Mn-K}_{\alpha}$ peak is defined as the FWHM divided
by the measured peak value and was calculated to be
$\qty{7.42}{}\pm\qty{0.01}{}$. For the fluorescence and escape peaks, the
signal is fitted with a Gaussian and a background fit of either exponential or
linear form for the fluorescence and escape peaks, respectively. Since the
response of ToT as a function of injected charge was found to be linear for
ToT values above $\qty{3}{}$ (cf. Sec. 3.4), the comparison between the
measured and literature peak values is fitted with a linear function, giving
the conversion from ToT to energy in
$\text{\,}\mathrm{\mbox{$e^{\text{-}}$}}$.

Figure 13: Measured 55Fe spectrum of single pixel clusters with a threshold
set to $120\text{\,}\mathrm{\mbox{$e^{\text{-}}$}}$. The initial spectrum
(blue) is ToT calibrated (orange) which resolves the two x-ray peaks
($\text{Mn-K}_{\alpha}$ and $\text{Mn-K}_{\beta}$) plus the
$\text{Mn-K}_{\alpha,\beta}$ escape
($\text{Mn-K}_{\alpha,\beta}-\text{Si-K}_{edge}$) and silicon fluorescence
($\text{Si-K}_{\alpha,\beta}$) peaks.

Figure 14 shows the measured 55Fe spectra for sensors irradiated with
different non-ionising doses (non-irradiated, [list-
units=single]1e13;1e14;1e15). For these measurements, the seed pixel ToT is
plotted, where the seed pixel is defined as the pixel with the largest ToT in
the set of adjacent pixels firing within the same oscilloscope capture. As the
level of irradiation increases, the $\text{Mn-K}_{\alpha}$ peak becomes
broader, with a notable broadening between
$1\text{\times}{10}^{14}\text{\,}\mathrm{\mbox{$1\text{\,}\mathrm{MeV}$\
n${}_{\mathrm{eq}}$\ ${\mathrm{cm}}^{-2}$}}$ and
$1\text{\times}{10}^{15}\text{\,}\mathrm{\mbox{$1\text{\,}\mathrm{MeV}$\
n${}_{\mathrm{eq}}$\ ${\mathrm{cm}}^{-2}$}}$. These differences are shown in
the resolution of the $\text{Mn-K}_{\alpha}$ peak between the irradiated
sensors whose values are given in Table 1. The table shows that the largest
increase in the resolution is from
$1\text{\times}{10}^{14}\text{\,}\mathrm{\mbox{$1\text{\,}\mathrm{MeV}$\
n${}_{\mathrm{eq}}$\ ${\mathrm{cm}}^{-2}$}}$ to
$1\text{\times}{10}^{15}\text{\,}\mathrm{\mbox{$1\text{\,}\mathrm{MeV}$\
n${}_{\mathrm{eq}}$\ ${\mathrm{cm}}^{-2}$}}$. In addition, at the largest
irradiation dose, the four peaks are no longer resolved and the contribution
from seed pixels with energy in the range of
$4001400\text{\,}\mathrm{\mbox{$e^{\text{-}}$}}$ becomes more prominent. These
changes to the spectrum at
$1\text{\times}{10}^{15}\text{\,}\mathrm{\mbox{$1\text{\,}\mathrm{MeV}$\
n${}_{\mathrm{eq}}$\ ${\mathrm{cm}}^{-2}$}}$ indicate an alteration to the
charge collection mechanisms in the sensor due to radiation damage, such as
the increased recombination rate and the changes in the electric fields.

Figure 14: Measured 55Fe spectra of seed pixels for different levels of non-ionising irradiation: non-irradiated, [list-units=single]1e13;1e14;1e15. Table 1: Measured resolution of the $\text{Mn-K}_{\alpha}$ peak for different levels of non-ionising irradiation in seed pixel signal spectra in Fig. 14. Irradiation | Resolution ($\mathrm{\%}$)
---|---
Non-irradiated | 7.40$\pm$0.02
$1\text{\times}{10}^{13}\text{\,}\mathrm{\mbox{$1\text{\,}\mathrm{MeV}$\ n${}_{\mathrm{eq}}$\ ${\mathrm{cm}}^{-2}$}}$ | 7.42$\pm$0.03
$1\text{\times}{10}^{14}\text{\,}\mathrm{\mbox{$1\text{\,}\mathrm{MeV}$\ n${}_{\mathrm{eq}}$\ ${\mathrm{cm}}^{-2}$}}$ | 8.73$\pm$0.02
$1\text{\times}{10}^{15}\text{\,}\mathrm{\mbox{$1\text{\,}\mathrm{MeV}$\ n${}_{\mathrm{eq}}$\ ${\mathrm{cm}}^{-2}$}}$ | 12.05$\pm$0.07

##  4 Measurements with ionising particle beams

The DPTS sensors were also characterised at facilities providing charged
particle beams. The results presented in this section are based on data taken
from September 2021 to July 2022 at DESY II [17] and CERN PS testbeam
facilities. As such, the sensors were subject to normally incident
$5.4\text{\,}\mathrm{G}\mathrm{eV}\mathrm{/}\mathrm{c}$ electrons and
$10\text{\,}\mathrm{G}\mathrm{eV}\mathrm{/}\mathrm{c}$ positive hadrons,
respectively.

###  4.1 Setup

A beam telescope comprising of reference planes equipped with ALPIDE chips [4,
5, 6] has been used to reconstruct particle tracks. Two DPTS sensors were
installed in-between the reference planes. A sketch of the beam telescope is
shown in Fig. 15. The data acquisition was based on the EUDAQ2 framework [18].
The trigger signal was provided either by one of the DPTS chips or by a
discriminated output of photomultiplier tubes (operated in the plateau regime)
connected to a set of three 2x2 scintillators placed in front and behind the
telescope. One of the scintillators (S1) features a 1 hole in its centre and
is operated in anti-coincidence with the other two
($\neg\text{S1}\wedge\text{S2}\wedge\text{S3}$, cf. Fig. 15). The $x$ and $y$
position of a DPTS and the anti-coincidence scintillator were adjustable via
micro-positioning stages to achieve the overlap with the other DPTS. The DPTS
chip(s) not used for triggering are the device(s) under test or DUT(s). An
aluminum cooling jig (cf. Sec. 3.1) with a 1 opening corresponding to the chip
position was used to keep the DUT at a controlled temperature of
$+20\text{\,}\mathrm{\SIUnitSymbolCelsius}$ during the detection efficiency
and position resolution measurements.

directionBeamALPIDEDPTS01234567S1S2S3ScintillatorsScintillatorReference
armReference armDPTS 1DPTS
2$25\text{\,}\mathrm{mm}$$25\text{\,}\mathrm{mm}$$30\text{\,}\mathrm{mm}$$30\text{\,}\mathrm{mm}$$40\text{\,}\mathrm{mm}$$25\text{\,}\mathrm{mm}$$25\text{\,}\mathrm{mm}$$x$$y$$z$

Figure 15: Sketch of the beam telescope (not to scale). Two DPTS are
sandwiched between reference planes comprised of ALPIDE chips. Two
scintillators (S2 and S3), operated in coincidence, and one featuring a 1 hole
(S1), operated in anti-coincidence, are used for triggering. The trigger can
also be provided by one of the two DPTS.

###  4.2 Analysis tools and methods

Data were processed in the Corryvreckan test beam reconstruction software
framework [19] by fitting General Broken Lines [20] to clusters found in the
reference planes and interpolating the tracks to the DUT(s). Event and track
quality selection criteria were applied to ensure a clean data sample:
precisely one track per event, reduced track $\chi^{2}<3$, and track points on
each reference plane. Pixels on the reference planes with too large hit-rate
(more than $1000$ times the average; $<1$ pixel per plane were affected) were
masked. Furthermore, the tracks intersecting the DUT within two pixel pitches
from the sensor edge were rejected.

The DPTS hit pixel position was derived from the CML output corresponding to
the assertion of the in-pixel discriminator (cf. Sec. 2.2). The non-decodable
events, resulting from the collisions on the CML lines when multiple pixels
fire simultaneously, were associated to pixel $(15,15)$, i.e. to the centre of
the matrix. Given the negligible likelihood that two fake hits coincide in
time and result in a non-decodable event, these events are considered as real
hits with an undetermined position. The fraction of such events was below 3,
for all chips and settings.

In the detection efficiency calculation, the DUT clusters were associated to
tracks passing within a circular window with a radius of 480. The loose
spatial cut prevents the underestimation of the efficiency that would result
from the exclusion of non-decodable events associated to pixel $(15,15)$. In
order to minimise the probability of associating a fake (noise) hit to a
track, the DUT response was required to be within
$1.5\text{\,}\mathrm{\SIUnitSymbolMicro s}$ of the trigger signal. The
efficiency of the DUT is then estimated by the fraction of tracks with
associated clusters. The relative uncertainties are obtained by calculating
the 68.3 Clopper-Pearson confidence interval and summing in quadrature the
probability of associating a fake hit (given by the in-situ measured fake-hit
rate, cf. Sec. 3.5 and Sec. 4.3).

For the position resolution evaluation, a spatial acceptance window with a
radius of 45 around the track and a time acceptance window of
$1.5\text{\,}\mathrm{\SIUnitSymbolMicro s}$ were applied. The distance between
the intercept on the DUT plane and the associated cluster position (given by
the centre of mass of pixels in the cluster) in column and row direction is
determined for each track, yielding two spatial residual distributions. By
fitting the latter with two Gaussian functions, the standard deviation
parameters $\sigma_{col}$ and $\sigma_{row}$ are obtained. The position
resolution is then retrieved by quadratically subtracting the estimated
telescope tracking resolution of $\sigma_{track}=\qty{2.4}{}$ [21]. Given that
the obtained position resolution in the two directions is equal within the
measurement precision and compatible with square pixel geometry, their average
will be referred to as the position resolution in the rest of the paper.

The timing resolution analysis involved no time acceptance window, while the
spatial acceptance window was the same one used in the position resolution
analysis.

###  4.3 Detection efficiency and fake-hit rate

Figure 16(a) shows the detection efficiency and the fake-hit rate (measured in
situ) as a function of the average chip threshold set by changing $V_{casb}$
at different reverse biases for a sensor irradiated with protons, i.e. that
has received a combination of an ionising dose of $10\text{\,}\mathrm{kGy}$
and a non-ionising dose of
${10}^{13}\text{\,}\mathrm{\mbox{$1\text{\,}\mathrm{MeV}$\
n${}_{\mathrm{eq}}$\ ${\mathrm{cm}}^{-2}$}}$ (levels compatible with the ITS3
requirements). Instead of showing the data for a non-irradiated sensor, which
exhibits fake-hit rates below the measurement sensitivity limit, this
particular sensor was chosen to better illustrate the effect of the reverse
bias on the performance. In particular, it can be observed that by increasing
$V_{sub}=V_{pwell}$, the onset of the measured fake-hit rate is offset to
lower thresholds, thus increasing the operational margin at above 99 detection
efficiency.

((a)) Sensor irradiated to a dose of $10\text{\,}\mathrm{kGy}$ and
${10}^{13}\text{\,}\mathrm{\mbox{$1\text{\,}\mathrm{MeV}$\
n${}_{\mathrm{eq}}$\ ${\mathrm{cm}}^{-2}$}}$ at different $V_{sub}=V_{pwell}$.

((b)) Sensors irradiated to different levels.

Figure 16: Detection efficiency (filled symbols, solid lines) and fake-hit
rate (open symbols, dashed lines) as a function of average threshold, measured
with 10c positive hadrons.

The effect of different irradiation levels on the detection efficiency and the
fake-hit rate is shown in Fig. 16(b), where the reverse bias is kept at
$-2.4\text{\,}\mathrm{V}$. It can be observed that non-ionising irradiation
leads to a decrease in the detection efficiency, while ionising irradiation
leads to an increase in the fake-hit rate. These trends are consistent with
the expectation that the largest effect of the non-ionising and ionising
radiation damage is on the charge collection and the noise (front-end)
performance, respectively. For the $100\text{\,}\mathrm{kGy}$ irradiated
sensor, a significant increase in the fake-hit rate can be noticed, with onset
at a much higher threshold than in the other cases. Finally, although the
${10}^{15}\text{\,}\mathrm{\mbox{$1\text{\,}\mathrm{MeV}$\
n${}_{\mathrm{eq}}$\ ${\mathrm{cm}}^{-2}$}}$ irradiated sensor shows notable
performance deterioration, it can still be operated at 99 efficiency at the
temperature of +20.

The origin of the detection efficiency loss was investigated by studying its
dependency on the particle hit position within a pixel. Figure 17 shows the
detection efficiency of a e15 irradiated sensor as a function of reconstructed
track position relative to the nearest pixel centre. As expected, the
detection efficiency decreases when the particle track is further away from
the collection diode. A similar result was obtained for a non-irradiated
sensor, with the same magnitude of efficiency loss observed at higher
thresholds.

Figure 17: In-pixel detection efficiency of a e15 irradiated sensor with
threshold set to 160, measured with 10c positive hadrons. The tracking
resolution is represented by the white circle ($r=\sigma_{track}=\qty{2.4}{}$)
in the top left corner.

###  4.4 Spatial resolution and cluster size

Figure 18(a) shows the sensor spatial resolution and average cluster size as a
function of the average threshold for different $V_{sub}$ applied, measured
with 10c hadrons for the device irradiated with both an ionising radiation
dose of $10\text{\,}\mathrm{kGy}$ and a non-ionising radiation dose of
${10}^{13}\text{\,}\mathrm{\mbox{$1\text{\,}\mathrm{MeV}$\
n${}_{\mathrm{eq}}$\ ${\mathrm{cm}}^{-2}$}}$ (levels compatible with the ITS3
requirements). The benefit of applying higher $V_{sub}$ is not evident without
combining the information from Fig. 16(a), which shows that higher $V_{sub}$
is necessary to operate at lower thresholds. In this regime, the additional
positional information, given by a larger average cluster size, results in a
spatial resolution better than that of a purely binary sensor (pixel pitch
divided by $\sqrt{12}$).

The effect of different irradiation levels on the spatial resolution and the
average cluster size is demonstrated in Fig. 18(b), where the reverse bias is
kept constant at $-2.4\text{\,}\mathrm{V}$. Regardless of the irradiation
level, the measured spatial resolution is equal or even slightly better than
pixel pitch divided by $\sqrt{12}$, with no degradation of the spatial
resolution performance related to the received dose. The average cluster size
exhibits a slight, but systematic, decrease with the increasing non-ionising
radiation dose. This trend is compatible with the previous observations of a
deteriorated charge collection process.

((a)) Sensor irradiated to a dose of $10\text{\,}\mathrm{kGy}$ and
${10}^{13}\text{\,}\mathrm{\mbox{$1\text{\,}\mathrm{MeV}$\
n${}_{\mathrm{eq}}$\ ${\mathrm{cm}}^{-2}$}}$ at different $V_{sub}=V_{pwell}$.

((b)) Sensors irradiated to different levels.

Figure 18: Spatial resolution (solid lines) and average cluster size (dashed
lines) as a function of the average threshold, measured with 10c positive
hadrons.

###  4.5 Timing resolution

The timing resolution was estimated by measuring the output signal coincidence
of two DPTS using a $5.4\text{\,}\mathrm{G}\mathrm{eV}\mathrm{/}\mathrm{c}$
electron beam. The trigger signal and thus the time reference is given by the
scintillators signal (cf. Fig. 15).

Figure 19 (top), shows the correlation of the signal arrival time and ToT,
i.e. signal amplitude, for one of the two DPTS chips. The influence of the
chip readout scheme on the signal time response is notable at high ToT, where
the distribution splits into two tails which correspond to odd and even
columns (cf. Sec. 2.2). The correction for this effect is applied by
subtracting the asymptotic value of the two tails from even and odd columns,
respectively. The time walk observed for the lower input amplitude is
corrected by fitting the data with the empirical function

$\text{Signal time}=A+\frac{B}{ToT-C}\text{ ,}$ (2)

where $A$, $B$ and $C$ are fit parameters, and then subtracting its value from
the measured data points. The signal (arrival) time vs ToT correlation
corrected for the chip readout scheme and the time walk is shown in Fig. 19
(bottom). As intended, it can be observed that the amplitude of the time walk
is reduced by a factor of about $3$ and its asymmetric feature is removed. The
correlation between the amplitude of the time walk and the time-over-threshold
remains but was not further investigated in this study.

Figure 19: Signal time vs ToT for the upstream DPTS measured with
$5.4\text{\,}\mathrm{G}\mathrm{eV}\mathrm{/}\mathrm{c}$ electrons, with no
corrections applied (top) and after readout scheme and time walk corrections
(bottom). The conversion to charge is obtained by applying the procedure
discussed in Sec. 3.7.

The distribution of time residuals, i.e. the time differences of the output of
the two DPTSs is shown in Fig. 20 for non-corrected data (in blue) and with
corrections discussed above applied independently for the two DPTSs (in
orange). The timing resolution of a single DPTS is obtained by fitting the
distribution with a Gaussian, and the fit parameter $\sigma$ is divided by
$\sqrt{2}$, resulting in $\sigma_{t}=\qty{6.3}{ns}\pm\qty{0.1}{ns}$ (stat). It
is worth highlighting that this result is obtained by operating the chips at
the low end of the in-pixel front-end power consumption range (i.e. nominal
conditions in Sec. 3.1). An improvement in timing performances is expected by
increasing the front-end current, namely $I_{bias}$ and $I_{biasn}$.

Figure 20: Time residuals distributions of two DPTSs measured with
$5.4\text{\,}\mathrm{G}\mathrm{eV}\mathrm{/}\mathrm{c}$ electrons with no
corrections (blue) and with readout scheme and time walk corrections applied
(orange). The corrected distribution is fitted with a Gaussian function in the
time residuals range from $\qty{-15}{ns}$ to $\qty{15}{ns}$ (black solid line,
dashed line for points outside the fit range).

##  5 Conclusions

Laboratory and in-beam measurements have been used to systematically validate
the charge detection and radiation hardness of the Digital Pixel Test
Structure MAPS prototype submitted in the TPSCo $65\text{\,}\mathrm{nm}$
process. The front end has shown a robust performance that can maintain a
suitable operation regime in terms of threshold spread, noise and fake-hit
rate. In addition to measuring the ToT response from X-ray emissions of an
55Fe source, the DPTS achieved a resolution of $\qty{7.40}{}\pm\qty{0.02}{}$
for the $\text{Mn-K}_{\alpha}$ peak. The impact of irradiation on the
performance becomes evident at
$1\text{\times}{10}^{15}\text{\,}\mathrm{\mbox{$1\text{\,}\mathrm{MeV}$\
n${}_{\mathrm{eq}}$\ ${\mathrm{cm}}^{-2}$}}$; however, the sensor is still
able to effectively detect the X-ray emissions. This demonstration of the
radiation hardness is reinforced further by the excellent detection efficiency
of $99\text{\,}\mathrm{\%}$ and spatial resolution below the binary resolution
for chip irradiation doses compatible with the ITS3 requirements (e13 and 10)
as well as to doses above these levels at
$1\text{\times}{10}^{15}\text{\,}\mathrm{\mbox{$1\text{\,}\mathrm{MeV}$\
n${}_{\mathrm{eq}}$\ ${\mathrm{cm}}^{-2}$}}$ and $100\text{\,}\mathrm{kGy}$ at
+$20\text{\,}\mathrm{\SIUnitSymbolCelsius}$ while preserving a fake-hit rate
below $10$ pixel-1 s-1. The DPTS also demonstrates a timing resolution of
about $6\text{\,}\mathrm{ns}$ for the nominal chip bias settings, with
improvements expected if operated at conditions optimised for timing
performance.

The first step to validate this sensor technology has been presented and makes
up an important aspect of the R&D for the ALICE ITS3 as well as a significant
contribution to the CERN EP R&D on monolithic sensors. The excellent
performance of the DPTS opens the way for further developments in this
technology and with this sensor design. The next step towards a wafer-scale
bent sensor and a fully cylindrical detector is the validation of stitching
and yield via the full-scale sensor prototypes produced in the second
submission in the 65 process, designated ER1.

Further work to investigate the limit of the radiation hardness of this
technology and probe the performance of the DPTS with ionising particles at
non-zero incident angles is foreseen. Moreover, the front-end operating point
is being tuned to optimise the power consumption for low power applications,
such as ALICE ITS3, where high radiation hardness and fast timing response are
not crucial requirements.

## Acknowledgements

The measurements leading to these results have been performed at the Test Beam
Facility at DESY Hamburg (Germany), a member of the Helmholtz Association
(HGF). We would like to thank the coordinators at DESY for their valuable
support of this testbeam measurement and for the excellent testbeam
environment.

P. Becht acknowledges the support by the HighRR research training group [GRK
2058] and funding by the German Federal Ministry of Education and
Research/BMBF (project number 05H21VHRD1) within the High-D consortium.

W. Deng acknowledges the support by the National Key Research and Development
Program of China (2022YFA1602103).

This work has been sponsored by the Wolfgang Gentner Programme of the German
Federal Ministry of Education and Research (grant no. 13E18CHA).

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poorly constrained in these clusters. Moreover, clustered UV sources within
the SSCs can have the effect of cancelling out the radiation pressure terms
from other sources (Skinner & Ostriker, 2015), reducing the net momentum to
drive a cluster-scale outflow. In the case of stellar winds, cooling is
expected to be important for these clusters. Although recent simulations find
that even in the presence of strong cooling O star stellar winds may be
sufficient to power outflows (Lancaster et al., 2020), we find that the
expected momentum is insufficient to explain the observed properties of the
outflows in SSC 14 and possibly in SSC 4a. For SSC 14, the outflows are likely
dominated by dust-reprocessed radiation pressure, whereas the outflow in SSC
5a may be dominated by stellar winds. For SSC 4a, the deep absorption renders
the outflowing mass estimate especially uncertain and likely overestimated, so
we can only say that the outflow in that cluster is likely a combination of
dust-reprocessed radiation pressure and stellar winds. Therefore, the precise
mechanism(s) powering these outflows remains uncertain.

###  4.3 SSC 5a and HST NIR Clusters

Figure 12: (Left) The HST Pa-$\alpha$ image. The blue contours show the ALMA
HCN $4-3$ peak intensity at 2, 5, and 10$\times$ the rms of the peak intensity
image. The red circles show the NIR clusters identified by Watson et al.
(1996), where the size of the circle reflects their 0.3$\arcsec$ positional
uncertainty. Only one of the primary clusters (SSC 5a) corresponds to the
previously identified NIR clusters. (Right) The HST Pa-$\alpha$ image centered
on SSC 5a (white plus sign) over the 3$\arcsec\times$3$\arcsec$ black square
from the left panel. There is an asymmetry in the Pa-$\alpha$ emission, which
Kornei & McCrady (2009) posit may be due to an outflow. The contours show the
HCN $4-3$ emission in selected the velocity channels relative to the systemic
velocity of SSC 5a (Table 2) showing a shell-like structure with a velocity
gradient across the shell. The contours are drawn at 3$\times$ the rms of the
HCN $4-3$ cube. The location of SSC 4a is also marked for context (black
cross). The asymmetry in the Pa-$\alpha$ emission does not align with the HCN
$4-3$ shell. This shell of HCN $4-3$ may be the signature of an earlier
(stronger) outflow phase from SSC 5a.

Several clusters and one SSC have been previously identified in the center of
NGC 253 based on HST near-infrared (NIR) images (Watson et al., 1996; Kornei &
McCrady, 2009), with the NIR-detected SSC corresponding to SSC 5 (Leroy et
al., 2018). To be able to see the NIR emission, the cluster must have
dispersed much of its natal gas and dust or it aligns with a serendipitous
hole in the extinction screen. If the presence of NIR emission at this cluster
location is from gas clearing, this implies that the cluster must be older
than the other, highly extincted clusters. As shown in Figure 6, we see
evidence for a weak outflow in the dense gas tracers from this cluster, which
may be the tail-end of this gas dispersal process from the timescale arguments
in Section 4.1. The measured mass outflow rate and momentum injection are also
lower than for SSCs 4a and 14. It is important to note, however, that SSC 5a
still has a high overall gas fraction (${\rm M_{H_{2},tot}/M_{*}}$) of 0.8,
though it is not as high as SSCs 4a and 14 (1.3 and 1.6, respectively).

Further support for this picture comes from the discovery of a shell near SSC
5a in HCN $4-3$ as shown in Figure 12. This feature is too faint to be seen in
CS $7-6$ or H13CN $4-3$ at this resolution. The shell is visible from $\sim
35-70$ km s-1 relative to the cluster systemic velocity (Table 1) and has a
projected radius of $\sim 6$ pc, though it is not perfectly centered on SSC
5a. Using these projected velocities, this implies an age of $\sim 8-16\times
10^{4}$ years. At its largest extent, the shell reaches the location of SSC 4a
(in projection) which also has a dense gas outflow. This shell-like structure
is not seen around any other SSCs.

Kornei & McCrady (2009) note that the Pa-$\alpha$ emission around SSC 5a is
asymmetric (Figure 12) and could be indicative of an outflow. We investigate
how this asymmetric geometry corresponds to the observed shell in HCN $4-3$.
There are systematic offsets between the location of SSC 5a in the ALMA data,
the NIR clusters identified in the HST NICMOS data by Watson et al. (1996),
and the F187N and F190N HST NICMOS data used by Kornei & McCrady (2009). Leroy
et al. (2018) corrected the positions of the Watson et al. (1996) NIR clusters
by $\Delta\alpha,\ \Delta\delta=+0.32\arcsec,\ -0.5\arcsec$, so that the NIR
cluster corresponding to SSC 5a has $\alpha,\ \delta=00^{\rm h}47^{\rm
m}32.985^{\rm s},\ -25^{\circ}17^{\rm m}19.76^{\rm s}$ (J2000). The positions
of the F187N and F190N mosaics555These calibrated and reduced HST NICMOS
(NIC2) images were downloaded from the Mikulski Archive for Space Telescopes
(MAST) database from M. Rieke’s August 1998 program with exposure times of
$\approx$384 s. The mosaic tiles were stitched together using the reproject
package in Astropy. were corrected by matching the locations of the NIR
clusters identified by Watson et al. (1996). A linear shift of $\Delta\alpha,\
\Delta\delta=+1.48\arcsec,\ -0.85\arcsec$ brings the HST images into agreement
with the NIR clusters and the ALMA datasets. Figure 12 shows the Pa-$\alpha$
(F187N-F190N) image around SSC 5a with the HCN $4-3$ contours overlaid. The
expanding HCN $4-3$ shell is not particularly aligned with the asymmetry seen
in the Pa-$\alpha$ emission, though it does seem to align with the north-
western edge.

It is therefore possible that this shell is a previous (stronger) version of
the outflow detected spectrally in this work. The shell age of $\sim 10^{5}$
years is in good agreement with the minimum ZAMS age and the end of the period
of active gas accretion (Section 4.1). It is unlikely that the outflow is due
to a supernova explosion both because synchrotron emission is a negligible
component of SSC 5’s spectral energy distribution (E. A. C. Mills et al., in
prep) and because the current momentum injection is well below what is
expected from supernovae (e.g. Kim & Ostriker, 2015; Kim et al., 2017a).

##  5 Summary

The central starburst in NGC 253 harbors over a dozen massive ($M_{*}\sim
10^{5}$ M⊙, a likely lower limit inferred from radio recombination lines and
radio continuum) and extremely young star clusters which are still very rich
in gas and likely in the process of formation (Leroy et al. 2018, E. A. C.
Mills et al. in prep.). Using high resolution ($\theta\approx 0.028\arcsec$,
equivalent to $0.48$ pc) data from ALMA we study the 350 GHz (0.85 mm) spectra
of these objects. We summarize our main results below, indicating the relevant
figures and/or tables.

  1. 1.

We observe P-Cygni line profiles — indicative of outflowing gas — in three
super star clusters in the center of NGC 253, sources 4a, 5a, and 14 (c.f.,
Table 1). These line profiles can be seen in the full-band spectra in many
lines (Figure 3), and particularly cleanly in the CS $7-6$ and H13CN $4-3$
lines which are the focus of this analysis (Figures 1 and 6). Among these
clusters, 5a is notable for being the only one of the massive clusters that is
observable in the near IR (Figure 12), suggesting it has cleared much of its
surrounding gas.

  2. 2.

By fitting the absorption line profiles (Figure 6), we measure outflow
velocities, column densities, masses, and mass outflow rates (Table 2). The
outflow crossing times — a lower limit on the outflow age — are short
($\sim\rm few\times 10^{4}$ yr), suggesting we are witnessing a short-lived
phase. The outflowing mass in these objects is a non-negligible fraction of
the total gas or stellar mass.

  3. 3.

To place limits on the opening angles and line of sight orientations of the
outflows we construct a simple radiative transfer model aiming at reproducing
the observed P-Cygni profiles in CS $7-6$ and H13CN $4-3$ (Figures 7 and 8).
By varying the input temperatures, densities, velocities, and velocity
dispersion of each component as well as the opening angle and orientation of
the outflow component, we find that very wide opening angle models best
reproduce the observed P-Cygni profiles (Figure 6). While we cannot precisely
determine the opening angle for each cluster, the outflows must be almost
spherical, although somewhat smaller opening angles are acceptable if the
outflows are pointed almost perfectly along the line of sight (Figure 9). This
modeling also provides measurements of the outflow velocity, column density,
masses, and mass outflow rates (Table 3). In general, these two sets of
measurements agree, given the large uncertainties (Figure 10).

  4. 4.

We compare measurements of the ZAMS age (Rico-Villas et al., 2020) to the gas
free-fall time (Leroy et al., 2018), outflow crossing time, gas removal time
implied by the mass outflow rate, and the gas depletion time (Table 4). These
estimates are consistent with the SSCs still being in a period of active gas
collapse, though SSC 5a could be past this phase. The gas removal timescale
(assuming a constant mass outflow rate) is about an order of magnitude smaller
than the gas depletion time due to star formation, showing that the outflows
will have a substantial effect on the star formation efficiency of these SSCs.
Reaccretion of gas that was expelled by the outflows is perhaps a likely
scenario, which complicates the interpretation of the clusters’ evolutionary
sequences.

  5. 5.

Given our measured velocities, masses, radii, surface densities, and momentum
per unit stellar mass, we investigate the mechanisms responsible for driving
the observed outflows. Possibilities are supernovae, photoionization, UV
(direct) radiation pressure, dust-reprocessed (indirect) radiation pressure,
and O star stellar winds. While none of these mechanisms completely explains
the observations, the two explanations that are potentially in play are dust-
reprocessed radiation pressure and stellar winds. It is possible that the
outflows are powered by a combination of both mechanisms, with the feedback in
SSC 14 dominated by dust-reprocessed radiation pressure and the feedback in
SSC 5a dominated by stellar winds (Figure 11, Section 4.2).

  6. 6.

We report the discovery of an expanding shell (seen in HCN $4-3$) around SSC
5a with $r\sim 6$ pc (Figure 12). As mentioned above, SSC 5a is the only
cluster visible in the near IR, which coupled with it having only a lower
limits on the ZAMS age suggests that SSC 5a is the most evolved cluster. SSC
5a also has the weakest P-Cygni profile among the three detected and the
smallest current mass outflow rate. Given its velocity and size, the shell is
$\sim 10^{5}$ yrs old, in good agreement with the minimum ZAMS age of the
cluster and estimates of the end of the period of active gas collapse (Table
4). It is thus likely that the expanding shell is a remnant from the earlier
stages of the gas clearing phase when the outflow was stronger. It is unlikely
that this shell was created by a past supernova explosion as synchrotron
emission is a negligible component of this cluster’s spectral energy
distribution on 5 pc scales (E. A. C. Mills et al. in prep.).

While the SSCs in the heart of NGC 253 constitute a very young population of
clusters, there is evidence for differing evolutionary stages among them. A
major step towards better characterizing these clusters is better measurements
of their stellar masses. Current stellar mass estimates use the 36 GHz
continuum emission — assuming that it is all due to free-free emission — to
calculate the ionizing photon rate and hence the stellar mass (Leroy et al.,
2018). Due to the enormous extinctions towards these clusters, it is not
feasible to use traditional optical and near IR recombination lines as tracers
of the ionized gas. High resolution hydrogen radio recombination lines (RRLs)
offer direct probes of the ionizing photon rate and hence the stellar mass,
and are uninhibited by dust extinction (Emig et al. 2020 in NGC 4945, E. A. C.
Mills et al. in prep. in NGC 253). In the near future, James Webb Space
Telescope observations may allow us to independently establish stellar masses,
radiation fields, and ages by accessing mid IR spectral line indicators. In
the next decade, the combination of sensitivity and exquisite resolution of
the Next Generation Very Large Array (ngVLA) may make studies at this high
resolution possible for galaxies out to the Virgo cluster and beyond.

R.C.L. thanks Eve Ostriker for very helpful discussions and feedback which
greatly improved this paper. R.C.L. also thanks Todd Thompson, Stuart Vogel,
Lachlan Lancaster, and Pavel Kroupa for useful conversations and advice. The
authors thank Nicolas Bolatto for his help in making the 3D visualizations for
Figures 8 and 13. Publication support was provided by the NRAO. R.C.L.
acknowledges support for this work provided by the NSF through Student
Observing Support Program (SOSP) award 7-011 from the NRAO. K.L.E.
acknowledges financial support from the Netherlands Organization for
Scientific Research through TOP grant 614.001.351. E.R. acknowledges the
support of the Natural Sciences and Engineering Research Council of Canada
(NSERC), funding reference number RGPIN-2017-03987. This paper makes use of
the following ALMA data: ADS/JAO.ALMA#2017.1.00433.S. ALMA is a partnership of
ESO (representing its member states), NSF (USA) and NINS (Japan), together
with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in
cooperation with the Republic of Chile. The Joint ALMA Observatory is operated
by ESO, AUI/NRAO and NAOJ. The National Radio Astronomy Observatory is a
facility of the National Science Foundation operated under cooperative
agreement by Associated Universities, Inc. Based on observations made with the
NASA/ESA Hubble Space Telescope, obtained from the data archive at the Space
Telescope Science Institute. STScI is operated by the Association of
Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555.

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##  Appendix A Measuring Outflow Properties from Fitting the Absorption
Features

For each outflow candidate SSC, we measure important outflow properties based
on the H13CN $4-3$ and CS $7-6$ spectra (Section 3.1, Table 2). Below, we
explain how each of these properties is calculated. First, we fit the
foreground-removed (Section 2.4) H13CN $4-3$ and CS $7-6$ spectra with a two-
component Gaussian of the form

$\begin{split}{\rm I(V)=}\\\ {\rm I_{\rm max-emis}e^{-(V-V_{\rm max-
emis})^{2}/2\sigma_{\rm emis}^{2}}+I_{\rm max-abs}e^{-(V-V_{\rm max-
abs})^{2}/2\sigma_{\rm abs}^{2}}+I_{\rm cont}}\end{split}$ (A1)

with terms to fit the emission, absorption, and continuum components
respectively. These fits are shown in Figure 6 as the blue dashed curves. We
define the outflow crossing time, which the time it takes a gas parcel to
travel from the center of the cluster to $r_{\rm SSC}$ (half the major axis
FWHM sizes listed in Table 1) moving at the typical outflow velocity (${\rm
V_{max-abs}}$) as

${\rm t_{cross}}=\frac{r_{\rm SSC}}{\rm V_{max-abs}}.$ (A2)

This is a lower limit to the outflow age, assuming a constant outflow
velocity, since the outflows are observed out to at least $r_{\rm SSC}$ and
could be present at larger distances from the cluster. The maximum outflow
velocity is defined as

${\rm V_{\rm out,max}\equiv V_{\rm max-abs}+2\sigma_{abs}}.$ (A3)

We determine the optical depth of the center of the absorption feature where

${\rm\tau_{\rm max-abs}=-\ln\Big{(}\frac{I_{\rm max-abs}}{{}I_{\rm
cont}}\Big{)}}.$ (A4)

From there, we calculate the column density in the lower state of each
molecule following Mangum & Shirley (2015)

${\rm N_{\ell}=16\pi\sqrt{2\ln
2}\Big{(}\frac{\nu_{u\ell}}{c}\Big{)}^{2}\sigma_{\rm abs}\frac{\tau_{\rm max-
abs}}{A_{u\ell}}\Big{[}e^{h\nu_{u\ell}/kT_{ex}}+1\Big{]}^{-1}}$ (A5)

(combining their equations 29, A1, and A7), where ${\rm\nu_{u\ell}}$ is the
frequency of the transition, ${\rm c}$ is the speed of light, ${\rm
A_{u\ell}}$ is the Einstein A coefficient for the transition, and ${\rm
T_{ex}}$ is the excitation temperature. By replacing ${\rm T_{\ell}}$ with
${\rm T_{ex}}$, we are assuming LTE, which we will assume throughout. We
assume ${\rm T_{ex}}=130\pm 56$ K, which is the excitation temperatures found
in these clusters (Krieger et al., 2020). The uncertainty is the difference
between this value and the excitation temperature measured at lower resolution
(74 K; Meier et al., 2015). Our assumption on ${\rm T_{ex}}$ is a major source
of uncertainty in these calculations. We then calculate the column density in
the upper state

${\rm N_{u}=N_{\ell}\frac{g_{u}}{g_{\ell}}e^{-h\nu_{u\ell}/kT_{ex}}}$ (A6)

(e.g. equation 6 of Mangum & Shirley, 2015, assuming the upper and lower
states have the same density distribution along the line of sight). The total
column density of each molecule (e.g. of all energy levels) is

${\rm N_{\rm mol}=\frac{N_{u}}{g_{u}}\mathscr{Z}e^{h\nu_{u\ell}/kT_{ex}}}$
(A7)

(e.g. equation 31 Mangum & Shirley, 2015), where $\mathscr{Z}$ is the
partition function calculated assuming LTE

$\mathscr{Z}=\sum_{i}g_{i}e^{-E_{i}/{\rm kT_{ex}}}$ (A8)

where $g_{i}$ and $E_{i}$ are the degeneracy and excitation energy of each
level $i$. We calculate $\mathscr{Z}$ assuming LTE up to $i=19$ for CS and
$i=16$ for H13CN666Level population data are from
https://www.astro.umd.edu/rareas/lma/lgm/properties/cs.pdf for CS and
https://www.astro.umd.edu/rareas/lma/lgm/properties/h13cn.pdf for H13CN. . To
convert from the column density of each molecule to the column density of H2
in the outflow (${\rm N_{H_{2},out}}$), we need to know the abundance ratio of
each molecule with respect to H2:

${\rm N_{{\rm H}_{2},out}=2\frac{[{\rm H}_{2}]}{[{\rm mol}]}N_{\rm mol}}$ (A9)

where the factor of 2 accounts for the redshifted outflowing material,
assuming it is the same as the blueshifted component. The abundance ratios
vary with environment, so we use those calculated in the center of NGC 253 by
Martín et al. (2006), where [CS]/[H2] $=5.0\times 10^{-9}$ and [H13CN]/[H2]
$=1.2\times 10^{-10}$. The assumed abundance ratio is another large source of
uncertainty in our measurements and can vary substantially by environment
(e.g. van Dishoeck & Blake, 1998, and references therein). We take an order-
of-magnitude uncertainty on the abundance fractions, which limits subsequent
calculations to order-of-magnitude precision as well (see the discussion in
Section 3.1.1).

To calculate the H2 mass along the line of sight,

${\rm M_{{\rm H}_{2},out}=4\Sigma_{{\rm H}_{2},out}A=4m_{\rm H_{2}}N_{{\rm
H}_{2},out}A}$ (A10)

where ${\rm m_{H_{2}}}$ is the mass of a hydrogen molecule, $A$ is the area of
the source measured from the continuum (Table 2), and the factor of 4 converts
the projected area to a sphere.

From the mass in the outflow and the crossing time, we calculate the mass
outflow rate (${\rm\dot{M}_{H_{2},out}}$) where

${\rm\dot{M}_{H_{2},out}=\frac{M_{H_{2},out}}{t_{cross}}}.$ (A11)

From the total gas mass of the cluster (Leroy et al., 2018) and the mass
outflow rate, we calculate the gas-removal time, or the time it would take to
expel all of the gas in the cluster at the current mass outflow rate:

${\rm t_{remove-gas}=\frac{M_{H_{2},tot}}{\dot{M}_{H_{2},out}}}.$ (A12)

The timescale assumes that the mass outflow rate is constant with time, which
is likely not the case (e.g. Kim et al., 2018). The momentum injected into the
environment normalized by the stellar mass (${\rm M_{*}}$) by the outflow is

${\rm\frac{p_{r}}{M_{*}}=\frac{\sqrt{3}V_{\rm max-abs}M_{{\rm
H}_{2},out}}{M_{*}}}$ (A13)

assuming spherical symmetry (Leroy et al., 2018). We assume the SSC stellar
masses reported by Leroy et al. (2018), and the uncertainties in these ${\rm
M_{*}}$ measurements are discussed in Section 2.6. The kinetic energy in the
outflow is

${\rm E_{k}=\frac{1}{2}M_{H_{2},out}V_{max-abs}^{2}}.$ (A14)

Values calculated using CS $7-6$ and H13CN $4-3$ for each outflow candidate
are listed in Table 2 along with the propagated uncertainties.

##  Appendix B Outflow Modeling Details

We perform simple radiative transfer modeling of the source with varying
outflow geometries and input physical parameters to constrain the outflow
opening angles and orientations as described in Section 3.2.

To set up the model, we define a three-dimensional grid that is 65
($=2^{6}$+1) pixels in each dimension; we refer to this grid as the simulated
box. The physical scale of the box is such that the length of each size is
$4\times r_{\rm SSC}$, or twice the diameter of the SSC to be modeled. Every
pixel in the box is given a fourth dimension, corresponding to the spectral
axis (in terms of frequency or velocity, which we use interchangeably here).
The spectral axis has 129 ($=2^{7}+1$) channels. The velocity range of the
spectral axis and hence the spectral resolution of the model is defined
adaptively for each model to maximize the number of channels over the emission
and absorption features. The spectral axis is centered on zero velocity (the
rest frequency of the line to be modeled) and spans ${\rm\pm 4\sqrt{V_{max-
abs}^{2}+\Delta V_{out,FWHM}^{2}}}$, where ${\rm V_{max-abs}}$ and ${\rm\Delta
V_{out,FWHM}}$ are the outflow velocity and FWHM outflow velocity dispersion
input into the model. This is done to optimize the velocity resolution over
the velocities relevant for the cluster and outflow as opposed to picking a
fixed velocity range. This is shown most clearly in Figure 7, where the
portions of the spectra within the vertical line segments show the velocities
actually modeled and the thin lines are extrapolations.

Figure 13: An example outflow, in the style of Figure 8; for clarity, the
ambient gas is not shown. The simulated box is shown in gray. The orientation
angle definitions are marked, where $\theta$ is the outflow opening angle and
$\Psi$ is the orientation angle to the line of sight measured from the center
of the outflow cone with components $i$ and $\phi$ to the $x$\- and $y$-axis
respectively. Figure 14: Radial profiles of the input parameters to the
modeling for the dust continuum (green dashed), hot gas (gold dash-dotted),
outflowing cold gas (blue solid), and the ambient cold gas (light blue dotted)
as described in Section 3.2. For the dust continuum, the optical depth per
pixel is specified, whereas for the other components, the H2 density per pixel
is specified. For the ambient cold gas, input parameters are identical to the
outflowing cold gas except for the velocity. Cold gas inside the outflow cones
has the properties of the outflowing cold gas, whereas cold gas outside the
outflow cones has the properties of the ambient cold gas. The vertical gray
line marks $r_{\rm SSC}$ which is the boundary between the cluster (e.g.
continuum and hot gas components) and the cold gas components (outflowing or
ambient). These input parameters are scaled to the best-fit spherical model
for the CS $7-6$ line in SSC 14 (Table 3).

Once the four-dimensional box is defined, the three physical components
representing the cluster and outflow are constructed. It is helpful to define
coordinates related to the simulated box in cartesian coordinates, whereas
coordinates pertaining to the cluster and outflow are in spherical
coordinates, as shown in Figure 13. As described in Section 3.2, the three
components of the system are:

  1. 1.

Dust continuum component: Shown in green in Figures 7, 8, 13, and 14 this
component is a sphere with $r=r_{\rm SSC}$ and a constant (in space and
velocity) temperature (Tcont). The optical depth is a maximum ($\tau_{\rm
cont,max}$) at the center, then decreases like a Gaussian with FWHM $=2\times
r_{\rm SSC}$, so that the continuum source is semi-transparent. The
temperature and optical depth are set to zero for $r>r_{\rm SSC}$.

  2. 2.

Hot gas: Shown in yellow in Figures 7 and 14 (and encompassed within the green
sphere in Figures 8 and 13), this spherical component is required to reproduce
the strong emission component of the P-Cygni profiles. This component has a
hot gas temperature (Thot), a central H2 volume density (nhot), and a velocity
dispersion ($\rm\Delta V_{hot,FWHM}$). Thot is constant (spatially) for $r\leq
r_{\rm SSC}$, and is set to zero outside. The density falls off $\propto
r^{-2}$ from the center, and is set to zero for $r>r_{\rm SSC}$. The line is
centered on zero velocity along the spectral axis, and the Gaussian linewidth
is given by ${\rm\Delta V_{hot,FWHM}}/2.355$.

  3. 3.

Cold, outflowing gas: Shown in dark blue in Figures 7, 8, 13, and 14 this is
the outflow component which produces the absorption features. This component
is defined by a gas temperature (Tout), a maximum H2 volume density (nout), a
constant outflow velocity (Vout), a velocity dispersion ($\rm\Delta
V_{out,FWHM}$), and opening angle ($\theta$), and an orientation to the line
of sight ($\Psi$). The gas temperature is constant (spatially) within this
component and is set to zero for $r<r_{\rm SSC}$. The density is a maximum at
$r=r_{\rm SSC}$ and deceases $\propto r^{-2}$ until the edges of the box; the
density is set to zero for $r<r_{\rm SSC}$. The line is centered on along the
frequency axis at Voutflow, and the Gaussian linewidth is given by $\Delta
V_{\rm out,FWHM}$. Since the outflow velocity is constant and the density
$\propto r^{-2}$, the outflow conserves energy and momentum. The outflow cones
are masked to the given opening angle ($\theta$) and rotated to the given
orientation from the line of sight ($\Psi$) (Figure 13). For outflows with
$\theta<180^{\circ}$, the outflowing gas component outside the outflow cones
is replaced by an ambient gas component (shown in light blue in Figures 8 and
14), which has the same properties as the outflowing gas but with V${}_{\rm
out}=0$. We refer to these together simply as the "cold" component.

The optical depths of the hot and cold (outflowing and ambient) gas are needed
at every pixel and as a function of frequency ($\tau_{\rm\nu,hot}$ and
$\tau_{\rm\nu,outflow}$ respectively) for the radiative transfer. For
simplicity in the following equations, we will drop the "hot" and "cold"
subscripts since the calculations are the same for both components. First, we
calculate the intrinsic line shape assuming Doppler broadening is dominant

$\phi_{\nu}=\frac{1}{\sqrt{\pi}\nu_{u\ell}}\frac{c}{b}e^{-V^{2}/b^{2}}$ (B1)

where $b\equiv\sqrt{2}\sigma_{V}=\frac{\Delta V_{\rm FWHM}}{2\sqrt{\ln{2}}}$,
$\nu_{u\ell}$ is the rest frequency of the transition being modeled, and $V$
is the velocity along the spectral axis (with $V=0$ corresponding to
$\nu=\nu_{u\ell}$) and where $\int\phi_{\nu}d\nu=1$ (Draine, 2011). The
absorption cross section is

$\sigma_{\ell
u}(\nu)=\frac{g_{u}}{g_{\ell}}\frac{c^{2}}{8\pi\nu_{u\ell}^{2}}A_{u\ell}\phi_{\nu}$
(B2)

where $g_{u}$ and $g_{\ell}$ are the upper and lower level degeneracies and
$A_{u\ell}$ is the Einstein A value of the transition6 (Draine, 2011). Given
the H2 number density at every pixel (${\rm n_{H_{2}}}(x,y,z)$), the number
density in the lower state of the modeled transition is

$n_{\ell}(x,y,z)=\frac{\rm[mol]}{\rm[H_{2}]}\frac{g_{\ell}}{\mathscr{Z}}e^{-T_{\ell}/T}{\rm
n_{H_{2}}}(x,y,z)$ (B3)

where $\frac{\rm[mol]}{\rm[H_{2}]}$ is the fractional abundance of the
molecule being modeled with respect to H2, $\mathscr{Z}$ is the partition
function (Equation A8), $T_{\ell}\equiv E_{\ell}/k$ is the excitation energy
of the lower energy state, and $T$ is the input temperature of the gas. The
absorption coefficient is then

$\kappa_{\nu}(x,y,z)=n_{\ell}(x,y,z)\sigma_{\ell
u}(\nu)\left(1-e^{-k\nu/kT}\right)$ (B4)

(Draine, 2011). Finally, the optical depth of each pixel and as a function of
frequency is

$\Delta\tau_{\nu}(x,y,z)=\kappa_{\nu}(x,y,z)\Delta z$ (B5)

where $\Delta z$ is the size of each pixel in the $z$ direction (though in
this simulation the pixels are equal size in all spatial dimensions).

For each component—now also including the continuum component— the intensity
(expressed in Rayleigh-Jeans brightness temperature units) at every pixel and
as a function of frequency is

$\Delta T_{\nu}(x,y,z)=T\left[1-e^{-\Delta\tau_{\nu}(x,y,z)}\right].$ (B6)

We perform the radiative transfer along the line of sight from the back of the
box to the front (e.g. along the $+z$-axis):

$T_{\nu}(x,y,z_{i})=T_{\nu}(x,y,z_{i+1})e^{-\sum_{\rm
comp}\Delta\tau_{\nu}(x,y,z_{i})}+\sum_{\rm comp}\Delta T_{\nu}(x,y,z_{i})$
(B7)

where $z_{i}$ denotes an individual step along the $z$-axis and $\sum_{\rm
comp}$ means a sum over the dust continuum, hot gas, and cold (outflowing and
ambient) gas components.

The observed spectra are averaged over the FWHM continuum source size. To best
compare with the observed spectra, we mask the simulated box of
$T_{\nu}(x,y,z)$ to a cylinder along the $z$-axis with $r=r_{\rm SSC}$ as
shown in Figure 8, setting pixels outside this region equal to zero. The final
modeled spectrum is

$T_{\nu}=\frac{1}{N_{\rm pix}}\sum_{x,y}T_{\nu}(x,y,z=z_{\rm max})$ (B8)

where $z=z_{\rm max}$ denotes the slice (in the $xy$ plane) at the front of
the box and $N_{\rm pix}$ is the number of non-masked pixels in that slice.
The best-fitting modeled spectra are shown in red in Figure 6.

There are degeneracies between input parameters. The observed continuum level
is a combination of the intrinsic continuum temperature (Tcont) and the
continuum optical depth ($\tau_{\rm cont}$); a higher $\tau_{\rm cont}$ with a
lower Tcont can produce the same fit as a lower $\tau_{\rm cont}$ with a
higher Tcont. The temperature and density of the hot gas component (Thot and
nhot) are linked in a similar way. More, a lower $\tau_{\rm cont}$ means less
of the hot gas and redshifted outflow are attenuated, and so lower Thot and
nhot values are required. These degeneracies, especially with regards to the
density, lead to a very uncertain total mass for the modeled cluster. The
outflow parameters, however, are more robust. The gas temperature in the
outflow (Tout) is linked to the density in the outflow (nout), but are not as
degenerate as for the hot gas component for the following reason. For
absorption, the minimum modeled brightness temperature cannot be less than the
given Tout, even for an arbitrarily high density. That is, in order to match
the models with the observations, the observed temperature at maximum
absorption sets the maximum possible Tout in the model. For these reasons,
though we report all input parameters for the best-fitting models, we only
report derived parameters for the outflow in Table 3.