# Time performance of Analog Pixel Test Structures with in-chip operational
amplifier implemented in 65 nm CMOS imaging process

Gianluca Aglieri Rinella  Luca Aglietta  Matias Antonelli  Francesco Barile
Franco Benotto  Stefania Maria Beolè  Elena Botta  Giuseppe Eugenio Bruno
Francesca Carnesecchi  Domenico Colella  Angelo Colelli  Giacomo Contin
Giuseppe De Robertis  Florina Dumitrache  Domenico Elia  Chiara Ferrero
Martin Fransen  Alex Kluge  Shyam Kumar  Corentin Lemoine  Francesco Licciulli
Bong-Hwi Lim  Flavio Loddo  Magnus Mager  Davide Marras  Paolo Martinengo
Cosimo Pastore  Rajendra Nath Patra  Stefania Perciballi  Francesco Piro
Francesco Prino  Luciano Ramello  Arianna Grisel Torres Ramos  Felix Reidt
Roberto Russo  Valerio Sarritzu  Umberto Savino  David Schledewitz  Mariia
Selina  Serhiy Senyukov  Mario Sitta  Walter Snoeys  Jory Sonneveld  Miljenko
Suljic  Triloki Triloki  Andrea Turcato

###### Abstract

In the context of the CERN EP R&D on monolithic sensors and the ALICE ITS3
upgrade, the Tower Partners Semiconductor Co (TPSCo)
$65\text{\,}\mathrm{n}\mathrm{m}$ process has been qualified for use in high
energy physics, and adopted for the ALICE ITS3 upgrade. An Analog Pixel Test
Structure (APTS) featuring fast per pixel operational-amplifier-based
buffering for a small matrix of four by four pixels, with a sensor with a
small collection electrode and a very non-uniform electric field, was designed
to allow detailed characterization of the pixel performance in this
technology. Several variants of this chip with different pixel designs have
been characterized with a $120\text{ GeV/\it{c}}$ positive hadron beam. This
result indicates that the APTS-OA prototype variants with the best performance
achieve a time resolution of $63\text{\,}\mathrm{p}\mathrm{s}$ with a
detection efficiency exceeding 99% and a spatial resolution of
$2\text{\,}\mathrm{\SIUnitSymbolMicro m}$, highlighting the potential of TPSCo
65nm CMOS imaging technology for high-energy physics and other fields
requiring precise time measurement, high detection efficiency, and excellent
spatial resolution.

###### keywords:

Monolithic Active Pixel Sensors , Solid state detectors , Silicon , CMOS ,
Particle detection , Test beam

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

scaletikzpicturetowidth[1] [columns=3, title=Alphabetical Index, intoc]

[unito]organization=University of Torino - Department of Physics, city=Torino,
country=Italy [infnTO]organization=INFN, Sezione di Torino, city=Torino,
country=Italy [polito]organization=Polytechnic of Torino - DET Department,
city=Torino, country=Italy [unica]organization=University of Cagliari,
city=Cagliari, country=Italy [infnCA]organization=INFN, Sezione di Cagliari,
city=Cagliari, country=Italy [units]organization=University of Trieste,
city=Trieste, country=Italy [infnTS]organization=INFN, Sezione di Trieste,
city=Trieste, country=Italy

[CERN]organization=European Organisation for Nuclear Research (CERN),
city=Geneva, country=Switzerland [uniba]organization=University of Bari -
Department of Physics, city=Bari, country=Italy [infnBA]organization=INFN,
Sezione di Bari, city=Bari, country=Italy [poliBA]organization=Polytechnic of
Bari - Department of Physics DIF, city=Bari, country=Italy
[IPHC]organization=Université de Strasbourg, CNRS, IPHC UMR 7178,
city=Strasbourg, country=France [nikhef]organization=National Institute for
Subatomic Physics (Nikhef), city=Amsterdam, country=Netherlands
[UPO]organization=Università del Piemonte Orientale, city=Vercelli,
country=Italy [uniJAM]organization=Department of Physics, University of Jammu,
city=Jammu, country=India [heidel]organization=Ruprecht Karls Universität
Heidelberg, city=Heidelberg, country=Germany

##  1 Introduction

In the field of high-energy physics, Monolithic Active Pixel Sensors (MAPS)
have emerged as a promising technology for vertex detectors, demonstrating
potential to revolutionize tracking capabilities in future experiments [1, 2].
Their innovative design, integrating readout circuitry with the detection
volume in single, commercially fabricated chips, facilitates ultra-thin,
large-scale tracking detectors – a breakthrough for precision and scalability
in research.

As high-energy physics experiments evolve, they are expected to cope with
higher interaction rates and to resolve several primary interaction vertices
as well as vertices from secondary decays [3]. This trend demands pixel
detectors with enhanced spatial resolution and superior timing capabilities,
essential for precise tracking in dense particle environments [4]. Recent
developments in the 180 nm TowerJazz CMOS technology have led to significant
improvements. Sensor modifications have enabled improved depletion [5] and
significantly accelerated charge collection especially for hits near the pixel
edge [6], allowing for time resolutions between 100 and 120 ps [7, 8].

A new generation of MAPS detectors is being developed for the third generation
ALICE Inner Tracking System (ITS3) [9, 10, 11], using the Tower Partners
Semiconductor Co. (TPSCo) $65\text{\,}\mathrm{n}\mathrm{m}$ CMOS Image Sensor
Process [12] introducing similar sensor modifications as in the
$180\text{\,}\mathrm{n}\mathrm{m}$ technology [6, 8]. This
$65\text{\,}\mathrm{n}\mathrm{m}$ technology enables higher circuit densities
and hence more advanced readout circuitry can be fitted in the same pixel
pitch, allowing for more precise timing measurements. An Analog Pixel Test
Structure (APTS), equipped with fast individual Operational Amplifier
(OA)-based buffering was produced to evaluate the intrinsic timing performance
of the sensors in this new technology. Several variants of the chip with
different pixel designs were implemented and characterized in Ref. [13, 14]
and are summarized in the next section. The results of a study carried out
during a test beam campaign with positive hadrons are presented in this paper,
with a focus on the sensor timing performance.

##  2 The APTS-OA

Figure 1: Photograph of the APTS-OA taken with a microscope.

APTS-OA Die size $1.5$ mm $\times$ $1.5$ mm Matrix $6\times 6$ Readout Direct
analogue of central $4\times 4$ pixels Pitch $10$ µm Process Standard Modified
Modified with gap

Table 1: Main characteristics of the APTS-OA.

The APTS-OA measures $1.5\times 1.5\text{ mm}^{2}$ and features a $4\times 4$
squared $10\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pitch pixel matrix directly
buffered to output pads for readout and controlled by a set of external
reference currents and voltages. This matrix is surrounded by dummy pixels
that help to reduce the electric field distortion effects at the edges of the
matrix. In Figure 1, the APTS-OA chip is shown where, going from the center to
the periphery, the pixel matrix, and the bonding pads can be observed. Table 1
presents the primary characteristics of the chip detailed below.

The sensor can be reverse biased by applying a negative voltage referred to as
$V_{sub}$ to the substrate and p-wells down to a minimum of
$-4.8\text{\,}\mathrm{V}$.

###  2.1 Sensor variants

Figure 2: Schematic cross section of the three pixel process variants of the
APTS. From left to right: standard, modified featuring a low dose deep n-type
implant, and modified with gap employing a low dose deep n-type implant with a
gap at the pixel’s edges. Not to scale.

The APTS was produced with three process variants of its sensor, starting from
a standard imaging CMOS design and introducing modifications resulting in
faster charge collection and reduced charge sharing [15, 13, 5].

  * •

The standard process (cf. Fig. 2 left) is formed by an n-well collection
electrode of about $1\text{\,}\mathrm{\SIUnitSymbolMicro m}$ diameter on a
high-resistivity p-type epitaxial layer, grown on top of a low-resistivity
p-type substrate. In this structure, the depletion extends from the small
n-well electrode resulting in a balloon-shaped depleted zone covering only
part of the epitaxial layer. Charge collection outside this region happens
mostly by diffusion, leading to long and non-uniform collection times but also
to significant charge sharing [16]. A deep p-well, located at about
$2\text{\,}\mathrm{\SIUnitSymbolMicro m}$ from the collection electrode,
separates circuitry n-wells from the epitaxial layer, allowing to use PMOSs as
well as NMOSs in the pixel matrix without competing with the electrode for
charge collection.

  * •

The modified process (cf. Fig. 2 center) differs from the standard structure
for the addition of a low-dose n-type implant in the epitaxial layer,
resulting in a planar junction over the full pixel that helps in achieving
full depletion of the epitaxial layer.

  * •

The modified with gap process (cf. Fig. 2 right) is similar to the modified
process but the deep n-type implant no longer covers the full pixel: a gap is
introduced near the pixel edge to create a lateral field pushing the signal
charge towards the collection electrode, thus decreasing collection time (as
demonstrated in the simulation [6] for the 180 nm CMOS TowerJazz technology)
and charge sharing.

Characterization of a version of the APTS with source follower output buffers
(APTS-SF) has demonstrated the improvements described above for the
$65\text{\,}\mathrm{n}\mathrm{m}$ technology [17, 13].

###  2.2 Analog circuit

The analog circuit of APTS-OA is depicted in Fig. 3. An analog front-end
powered at 1.2 V ($AVDD$) is connected to the collection electrode of each
pixel ($IN$) and buffers its signal to an output pad ($BOARD$). To do so, the
circuit is composed of several buffering stages: a low input capacitance stage
with two source followers buffering the $IN$ signal to $OUT1$ and $OUT2$,
respectively, and a fast operational amplifier driving the output stage
$BOARD$. The circuit also provides reset current to the sensor and allows to
inject charge at the input of the front-end via a pulsing circuitry. Most of
the analog circuit is implemented in the pixel matrix, but due to lack of area
the operational amplifiers and output stages are located at the periphery
immediately surrounding the pixel matrix.

Figure 3:  Left: APTS-OA front-end circuit with the circuitry inside the
pixel. Right: circuitry located in the periphery of the matrix. The off chip
line to the measurement system is also represented.

In case there is no hit, the transistor $M0$ only compensates for the leakage
current of the sensor and maintains its collection electrode at a voltage
close to $V_{\textrm{reset}}$. The current generated after a particle hit
entails a voltage drop on the input node ($IN$), turning on the transistor
$M0$ to deliver constant current $I_{\textrm{reset}}$. $I_{\textrm{reset}}$ is
chosen larger than the sensor leakage current to ensure that $IN$ returns to
its baseline within a few microseconds.

The collection electrode ($IN$) is directly connected to the input of a PMOS
source follower stage $M2$ that makes its output $OUT1$ follow the input
voltage. To take full advantage of the low sensor capacitance in this process,
the input capacitance of the front-end is further reduced by making the drain
of $M2$ also follow the same voltage. This is achieved by the NMOS source
follower $M3$ driving $OUT2$. These source followers are biased by two current
sources: $I_{\textrm{biasp}}$ and $I_{\textrm{biasn}}$.

An in-pixel pulsing circuit can inject charge in the collection electrode
through a capacitance of $\text{C${}_{\textrm{inj}}$}=$
$242\text{\,}\mathrm{aF}$ (nominal value). The amount of injected charge is
controlled by an external voltage reference ($V_{\textrm{h}}$) and the
injection is triggered via an external signal.

The NMOS source follower output ($OUT2$) is connected to a high-speed
($1.9\text{\,}\mathrm{GHz}$ unity-gain bandwidth in post layout simulation)
operational amplifier ($OPAMP$) at the periphery of the matrix that, combined
with an output stage capable of driving a
$50\text{\,}\mathrm{\SIUnitSymbolOhm}$ load, allows for signal termination on
the board or on an oscilloscope to preserve the signal timing information. A
well-controlled internal feedback loop is used for the operational amplifier
to achieve better stability over a wide range of external capacitive loads
[17] and the well-controlled output is copied by $M6$ and sent off-chip
($BOARD$) where the external load is.

All voltages and current biases for the front-end and the operational
amplifier are externally generated and supplied via pads to the chip, where an
ad hoc mirroring ratio is applied to, for example, provide a front-end reset
current as low as a few tens of $\text{\,}\mathrm{pA}$.

The operating point was optimized using charge injection for the fastest
front-end response to establish the best working condition for measuring
timing. This set of parameters is referred to as the operating point and is
listed in A. Experimental optimization was necessary because the NMOS
transistors are in a p-well at voltage $V_{\rm{sub}}$, reaching values beyond
the range where the transistor model was available. Consequently, an
extrapolation of the model was used in simulation to establish the nominal
operating point, and proved afterward to deviate significantly from
measurements [18].

###  2.3 Chip readout system

Figure 4 shows the test setup used to operate the APTS-OA. It consists of an
FPGA-based data acquisition (DAQ) board, powered at 5 V and controlled by PC
via USB interface, a proximity board that hosts the analog to digital
converters (ADCs) for the readout of peripheral pixels and sends power and
biases to the chip, and a carrier board to which the chip is glued and bonded.
More details on this system can be found in Ref. [19].

Figure 4: Scheme of the APTS-OA readout system. From left to right: picture of
the DAQ board, hosting the firmware control FPGA as well as trigger, busy, and
reverse bias connection, the proximity board, hosting ADCs for external pixel
readout, and the carrier board to which the chip is glued and wire bonded. In
the bottom part, a sketch of the 4$\times$4 pixel matrix with the four inner
pixels (highlighted in red) connected to an oscilloscope.

The carrier board has four high bandwidth SMA connectors soldered to the
output lines of the four innermost pixels (highlighted in red in Fig. 4) that
can be read out with an oscilloscope (Teledyne Lecroy, WaveMaster 813Zi-B,
having a sampling rate of
$40\text{\,}\mathrm{G}\mathrm{S}\mathrm{/}\mathrm{s}$ and a bandwidth of
$13\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$). In the present work, only 3 out
of 4 pixels will be read out with the oscilloscope. The remaining pixels (12
external plus one of the inner) are read out by analog-to-digital converters
on the proximity board with a fixed sampling rate of
$4\text{\,}\mathrm{M}\mathrm{H}\mathrm{z}$.

##  3 Test Beam Measurements

To characterize the performance of the APTS-OA with respect to its time
resolution, detection efficiency and spatial resolution, a beam test was
conducted at the CERN-SPS H6 facility using positive $120\text{ GeV/\it{c}}$
hadrons [20].

###  3.1 Test beam telescope

directionBeamALPIDEAPTS-OAAPTS-SF01234567LGAD8Reference armReference
armDUTTriggerTiming
plane$25\text{\,}\mathrm{mm}$$25\text{\,}\mathrm{mm}$$48\text{\,}\mathrm{mm}$$54\text{\,}\mathrm{mm}$$48\text{\,}\mathrm{mm}$$25\text{\,}\mathrm{mm}$$25\text{\,}\mathrm{mm}$$52\text{\,}\mathrm{mm}$$x$$y$$z$

Figure 5: Schematic of the test beam setup showing each detector plane.

The setup, which is sketched in Fig. 5, consisted of nine planes, in
particular:

  * •

Planes 0, 1, 2, 5, 6, and 7, and 7, each containing an ALPIDE [21], tuned to a
$100\text{\,}\mathrm{e}^{-}$ threshold at $-3\text{\,}\mathrm{V}$ reverse
substrate bias, for track reconstruction.

  * •

Plane 3: an APTS-OA, as a device under test (DUT), placed on xy moving stages.

  * •

Plane 4: an APTS-SF [13], in the modified process with
$15\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pitch is used as trigger plane.
Only the central four pixels were activated for the trigger signal generation
in order to achieve a coverage slightly larger than the DUT. The modified
process was chosen to enhance single pixel clusters and therefore the
probability to trigger on a seed signal. The APTS-SF plane is mounted on xy
moving stages and is operated with a $-1.2\text{\,}\mathrm{V}$ reverse
substrate bias and all other biases at the optimal operating point, based on
Ref. [13].

  * •

Plane 8: a Low Gain Avalanche Detector (LGAD) produced by Fondazione Bruno
Kessler [22] as a time reference, operated at $110\text{\,}\mathrm{V}$ bias
voltage. The signal is amplified with a commercial external circuit
(MiniCircuits TB-409-52+) and readout with one channel of the oscilloscope.

The reference system is defined with the positive $z$-axis along the beam
direction and with $x$\- and $y$-axis defining the sensor planes.

Two chips having different sensor processes were considered in this study: the
modified and the modified with gap variants, as these processes demonstrated
the best performance in terms of charge collection [17]. The substrate bias
($V_{\textrm{sub}}$) was varied from $-1.2\text{\,}\mathrm{V}$ to
$-4.8\text{\,}\mathrm{V}$ with steps of $1.2\text{\,}\mathrm{V}$, consequently
varying the depletion and electric field in the sensor. Table 2 shows the
acquired number of triggers recorded for the different configurations. A
larger sample of events was accumulated for the modified with gap structure to
study the in-pixel contribution of the lateral electric field.

$V_{\rm{sub}}$ | Modified with gap | Modified
---|---|---
$-1.2\text{\,}\mathrm{V}$ | $290,000$ | $15,000$
$-2.4\text{\,}\mathrm{V}$ | $334,050$ | $15,000$
$-3.6\text{\,}\mathrm{V}$ | $15,000$ | $20,000$
$-4.8\text{\,}\mathrm{V}$ | $258,600$ | $58,100$
Table 2: Total number of events recorded during test beam measurements in each
configuration.

###  3.2 Data reconstruction and analysis

#### DUT signal extraction

The data recorded in the telescope, which includes the analog waveform from
each pixel, was analyzed offline. Figure 6 shows an example of a typical
signal acquired with the oscilloscope. In the inset at the left bottom, the
full waveform is shown, while the main plot highlights the main parameters
used to extract the amplitude of the waveform:

Figure 6: Typical signal acquired by the oscilloscope with baseline,
underline, and $t_{0}$ definitions. The $x$-axis is shifted to put $t_{0}$ at
the origin to highlight the time intervals for the baseline and underline
definitions.

  * •

the time zero ($t_{0}$ showed as a pink marker in Fig. 6), estimated as the
minimum of the signal’s derivative [23];

  * •

the baseline, calculated as the average of 100 points (corresponding to a time
interval of $2.5\text{\,}\mathrm{n}\mathrm{s}$),
$15\text{\,}\mathrm{n}\mathrm{s}$ before $t_{0}$ (orange segment in Fig. 6);

  * •

the underline, computed as the average of 100 points
($2.5\text{\,}\mathrm{n}\mathrm{s}$), $15\text{\,}\mathrm{n}\mathrm{s}$ after
$t_{0}$, corresponding to the waveform minimum (green segment in Fig. 6);

  * •

the signal amplitude, determined as the difference between the underline and
the baseline;

These values are chosen to accurately extract the amplitude of the signal
while being robust to noise and the low frequency variation of the baseline.
For the external pixels and one of the 2 $\times$ 2 central ones the signal
amplitude is calculated as the difference between the baseline, defined as the
4th sample before the minimum of the signal, corresponding to its underline,
and the minimum itself, following the definition adopted in Ref. [13]. This
definition avoids short-range auto-correlation among points and is not
influenced by the signal edge.

#### DUT signal calibration

To merge the information from different pixels and compare results taken under
different working conditions, the measured signal amplitude is converted into
the charge collected by the sensor (expressed in $\text{\,}\it{e^{-}}$). The
calibration is performed analysing the X-ray spectrum from a
${}^{55}\textrm{Fe}$ source: the ${}^{55}\textrm{Mn}-K_{\textrm{$\alpha$}}$
and ${}^{55}\textrm{Mn}-K_{\textrm{$\beta$}}$ peaks are fitted simultaneously
with 2 Gaussian functions to account for the partial overlap of the peaks at
low reverse bias voltages. Then the mean of the
${}^{55}\textrm{Mn}-K_{\textrm{$\alpha$}}$ peak is used to perform the
conversion to electrons with the following formula:

$Q=V_{\rm{out}}\frac{E(K_{\textrm{$\alpha$}})}{V_{\rm{mean}}(K_{\textrm{$\alpha$}})\epsilon}\
,$ (1)

where $E(K_{\textrm{$\alpha$}})$ is the energy of the
${}^{55}\textrm{Mn}-K_{\textrm{$\alpha$}}$ photon,
$V_{\rm{mean}}(K_{\textrm{$\alpha$}})$ is the mean of the
${}^{55}\textrm{Mn}-K_{\textrm{$\alpha$}}$ peak estimated from the fit, and
$\epsilon$ is the average energy required to produce an electron hole pair in
silicon. For this method the linearity of the energy response of the APTS is
assumed, since it has been demonstrated in Ref. [13].
The signal amplitude spectrum from a single pixel of the modified with gap
sensor operated at $V_{\textrm{sub}}$ = $-4.8\text{\,}\mathrm{V}$ is shown in
Fig. 7.

Figure 7: Amplitude distribution of signals acquired with the
${}^{55}\textrm{Fe}$ source for a single pixel read out with the oscilloscope.
The ${}^{55}\textrm{Mn}$–$K_{\textrm{$\alpha$}}$ and $K_{\textrm{$\beta$}}$
peaks are fitted together with the sum of 2 Gaussian functions.

#### Clustering

Data from DUT, trigger, and tracking planes have been analyzed with the
Corryvreckan software framework [24]. Adjacent pixels recording a charge above
a certain threshold form a cluster. The clustering threshold, introduced in
the DUT data analysis to emulate the effect of a discriminator, is only
applied offline and not during data taking. Each signal amplitude is converted
into units of electrons following the calibration procedure described above.
The seed pixel is defined as the one collecting the highest amount of charge
within the cluster and the charge-weighted center-of-gravity defines the
cluster position.

#### Track reconstruction

The Corryvreckan framework uses the General Broken Line (GBL) algorithm [25]
to reconstruct the particle tracks by fitting the cluster position on the
reference planes and taking into account the multiple scattering effect
through the detector material budget. Software alignment of the telescope
planes has been performed in subsequent steps in which the different planes
are shifted and rotated iteratively with respect to a chosen reference plane
to increase the tracking quality. These tracks are then interpolated at the
plane of the DUT. The six ALPIDE planes and the trigger plane (APTS-SF) are
included in the tracking, excluding the DUT in order to obtain unbiased
results. The following quality selection criteria are applied to filter the
data for the analysis:

  * •

a cluster is required in each tracking plane;

  * •

tracks are selected based on the quality of the fit, such that
$\chi^{2}/{\textrm{dof}}<5$, where dof stands for the number of degrees of
freedom;

  * •

only events with a single reconstructed track are selected, where an event has
to be triggered by the APTS-SF (cf. Sec. 3.1, Plane 4);

  * •

DUT clusters are associated to tracks passing within a radial distance of
$15\text{\,}\mathrm{\SIUnitSymbolMicro m}$. A study was performed to select
the proper association window radius, choosing it in order to guarantee the
independence of the efficiency from this parameter (cf. B).

  * •

a Region Of Interest (ROI) is set to include only the associated tracks
crossing one of the three central pixels read out via the oscilloscope, in
order to avoid border effects.

The applied selection cuts reduce the statistics to roughly 20% of the
recorded samples quoted in Tab. 2.

#### Detection efficiency analysis

In order to estimate the detection efficiency, a cluster is searched on the
DUT plane, within the ROI, for each track. The detection efficiency is
computed as the ratio between the number of tracks providing an associated
cluster in the DUT and the total number of tracks crossing the ROI. It is
worth noting that the choice of the above mentioned association window radius
allows one to estimate the efficiency without any bias, taking into account
that the tracking resolution is much smaller, being equal to
$\sigma_{\textrm{track}}$ = $1.8\text{\,}\mathrm{\SIUnitSymbolMicro m}$ $\pm$
$0.1\text{\,}\mathrm{\SIUnitSymbolMicro m}$, as obtained by the telescope
optimiser tool [26]. Moreover, to assess the chip noise, an analysis of the
baseline fluctuations was conducted (cf. C). The results shown in the
following figures are with thresholds above 3 times the noise RMS.

#### Spatial resolution analysis

For this analysis, the so-called $\eta$-algorithm [27, 28] has been applied to
correct for the non-linear charge-sharing mechanism among the pixels. Residual
distributions are obtained by evaluating the distance between the intercept of
each track on the DUT plane (reconstructed position) and the associated
cluster position (corrected with the $\eta$-algorithm), in both the $x$ and
$y$ directions. The spatial resolutions $\sigma_{x}$ and $\sigma_{y}$ in,
respectively, the $x$ and $y$ directions are computed by quadratically
subtracting the estimated telescope tracking resolution
$\sigma_{\textrm{track}}$ from the standard deviation of the residual
distributions in the $x$ and $y$ direction, respectively. The final position
resolution is then defined as the arithmetic average between $\sigma_{x}$ and
$\sigma_{y}$ and it will simply be referred to as spatial resolution in the
rest of the paper.

#### Time resolution analysis

The sensor time residuals are computed as the difference between the time when
the APTS-OA DUT seed pixel signal reaches 10% of its full amplitude and the
time reference provided by the LGAD in the beam telescope (cf. Fig. 5).
Selecting a constant fraction of the signal amplitude aims at mitigating time
walk effects in the time resolution; 10% proved to provide the lowest RMS of
time residual distribution (cf. D). A similar method is applied to the LGAD
signals, for which the signal leading edge time at 40% of its amplitude is
chosen as it provides the best time resolution. Consequently, the distribution
of the time residuals, namely the time difference between the signals of the
DUT and the time reference, is defined as follows:

$\Delta t=t^{\textrm{DUT}}_{10\%}-t^{\textrm{LGAD}}_{40\%}\ .$ (2)

Only the seed signals of the three pixels read out by the oscilloscope can be
used in the analysis, being the only ones providing precise time information.
This further reduces the events previously selected by cluster association via
tracking by another 15%, resulting in a number of available signals for the
time resolution analysis equal to 17% of the number of recorded triggers
reported in Tab. 2.
Finally, the LGAD time resolution $\sigma_{\textrm{LGAD}}=$
$30\text{\,}\mathrm{p}\mathrm{s}$ $\pm$ $3\text{\,}\mathrm{p}\mathrm{s}$
111The LGAD time resolution was characterized with a positive hadron beam (cf.
Ref. [29]). is quadratically subtracted from the standard deviation of the
time residuals to calculate the time resolution of the DUT $\sigma_{t}$:

$\sigma_{\textrm{t}}=\sqrt{\sigma^{2}_{\textrm{$\Delta${t}}}-\sigma^{2}_{\textrm{LGAD}}}\
.$ (3)

as the two quantities are assumed to be independent.

###  3.3 Results and discussion

In the following section, the results of the analysis are presented. They are
grouped in three main paragraphs and results are presented in the following
order: detection efficiency, spatial resolution and cluster size, and,
finally, the time resolution.

#### Detection efficiency

Figure 8: Detection efficiency for the modified (left) and modified with gap
(right) pixel processes as a function of the applied threshold and for
different Vsub. The dashed line in both plots indicates the 99$\%$ detection
efficiency. Figure 9: Spatial resolution and cluster size as a function of the
applied threshold for the modified (left) and modified with gap (right)
structures, comparing different reverse substrate voltages in different
colors. The grey dashed line represents the pixel pitch divided by
$\sqrt{12}$.

Figure 8 shows the detection efficiency for the modified (left) and modified
with gap (right) process as a function of the threshold at different reverse
bias voltages. The results are plotted for thresholds exceeding 3 times the
RMS of the noise distribution to ensure unbiased efficiency values. As
expected, a clear decreasing trend of the detection efficiency with the
increasing threshold can be observed for both the modified and modified with
gap process.

Both pixel variants achieve a detection efficiency higher than 99$\%$ up to a
threshold of $150\text{\,}\rm{e^{-}}$, in agreement with the results obtained
in Ref. [13], offering a comfortable operational range for the sensor.
Furthermore, achieving a high detection efficiency is essential to prevent any
bias in time resolution. No significant differences are observed between the
two variants for this $10\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel pitch
at the threshold of $100\text{\,}\rm{e^{-}}$ (cf. E).

#### Spatial resolution and cluster size

Figure 9 shows the spatial resolution, computed as described in Sec. 3.2, and
the average cluster size as a function of the applied threshold. The cluster
size decreases with increasing threshold, degrading the spatial resolution,
which, nevertheless, for both processes at all biases, is always better than
the pixel pitch divided by $\sqrt{12}$. For both processes, the cluster size
also reduces with increasing the reverse bias, because of the enhanced lateral
electric field, resulting in a reduced charge sharing. This
V${}_{\textrm{sub}}$ dependence, clearly visible at lower thresholds,
gradually becomes undetectable with increasing threshold as the information
from low amplitude signals is removed. All the observations are in agreement
with the results from APTS-SF (cf. Ref. [13]).

#### Time resolution

Figure 10: Time residuals measured for the modified with gap process DUT
operated at $V_{\textrm{sub}}$=$-4.8\text{\,}\mathrm{V}$, before (blue
distribution, bottom horizontal axis) and after (orange distribution, top
horizontal axis) time walk-like correction. The latter distribution is fitted
with a Gaussian function on a range of $\pm~{}3\sigma$ (black solid line,
dashed line for points outside the fit range).

Figure 10 shows, as an example, the time residual distribution for the DUT
based on the modified with gap process operated at
V${}_{\textrm{sub}}$=$-4.8\text{\,}\mathrm{V}$ (blue histogram). The measured
time reference signals are delayed with respect to the DUT ones, resulting in
negative time residuals (cf. Eq. 2).

Figure 11: Time residuals versus seed signal charge with no correction applied
(top) and after the correction (bottom) for the DUT featuring modified with
gap process operated at V${}_{\textrm{sub}}$=$-4.8\text{\,}\mathrm{V}$.

Despite the efforts in the analysis to reduce the dependence of the measured
signal time on the signal amplitude, the longer tail towards higher time
residual values suggests a remaining presence of time walk, confirmed by Fig.
11 (top) showing the correlation of time residuals and DUT seed signal charge.
This can be explained by considering that a time measurement based on constant
amplitude fraction only suppresses time walk in case of a constant signal
shape [30]. Since the acquired analog waveforms differ in shape depending on
the collected charge (cf. F), a correction is needed to compensate for these
effects.
Figure 12 shows the dependence of the deviation from the mean value of the
non-corrected time residual distribution reported in Fig. 10 and of the
cluster size on the in-pixel reconstructed track incidence position. It can be
seen that, on average, lower time residual values, i.e. negative deviation
from the mean, are associated to smaller clusters while higher time residuals
are associated to larger ones. In other words, a slower DUT response is
observed when a track hits the pixel edges or corners, where the probability
of charge sharing with neighboring pixels, hence cluster size, is enhanced.
The correlation between time residual values and associated cluster size is
further highlighted by Fig. 13. It shows the different contributions coming
from signals associated with single pixel clusters (green histogram) and from
signals associated with multiple pixel clusters (red histogram). As already
pointed out for Fig. 12, the signals associated to single pixel clusters are
on average faster and contribute to a narrower distribution than signals from
clusters of larger size. Moreover, the distribution associated to the latter
explains the asymmetric feature of the time residuals.
The arguments presented above suggest a correction to compensate for the
dependence of the time residuals on the seed signal charge and on the
associated cluster size, as proposed in Ref. [8].

Figure 12: Map of the deviation from the time residuals mean value (left) and
cluster size map (right) for in-pixel track incidence positions for the DUT
based on modified with gap process operated at
V${}_{\textrm{sub}}$=$-4.8\text{\,}\mathrm{V}$. The tracking resolution is
represented by the white circle ($r=\sigma_{\textrm{track}}=$
$1.8\text{\,}\mathrm{\SIUnitSymbolMicro m}$) in the bottom left corner of both
maps. Figure 13: Distributions contributing to non corrected time residuals
(blue histogram) divided according to the associated cluster size for the DUT
implementing modified with gap process operated at
V${}_{\textrm{sub}}$=$-4.8\text{\,}\mathrm{V}$. The green distribution
represents the time residual values related to single pixel clusters, while
the red one describes the contribution of clusters with pixel multiplicity
larger than one.

For this correction, a clustering threshold of $100\text{\,}\rm{e^{-}}$ (cf.
Sec. 3.2) is adopted and the data are divided in two subsets: the first one
with single pixel clusters and the second with clusters of multiplicity larger
than one. For both subsets, to avoid introducing any bias in calculating the
correction, the mean time residuals for each signal charge bin of one half of
the dataset are interpolated with a quadratic function. The latter is then
subtracted from the time residuals of the other half of the data set, and vice
versa.
Figure 11 (bottom) shows the time residuals as a function of seed pixel signal
charge after the correction discussed above. As intended, it reduces the
dependence on the seed signal charge and removes its asymmetric feature, as
also highlighted by the corrected time residual distribution shown in Fig. 10
(orange histogram).
Three estimators for the time residual distribution width are finally derived:
the RMS of the entire data set, the RMS evaluated on the central 99.7
percentiles of the distribution and, for the corrected data, the standard
deviation $\sigma$ of a Gaussian fit within a 3$\sigma$ interval. The fit is
performed on the corrected data only, as, without the correction, the residual
distribution is not symmetric around the maximum. The RMS of the corrected
distribution gives $76\text{\,}\mathrm{p}\mathrm{s}$ $\pm$
$3\text{\,}\mathrm{p}\mathrm{s}$ and is higher than the width $\sigma$=
$67\text{\,}\mathrm{p}\mathrm{s}$ $\pm$ $1\text{\,}\mathrm{p}\mathrm{s}$ of
the Gaussian fit. The fit is comparable with the RMS99.7%=
$70\text{\,}\mathrm{p}\mathrm{s}$ $\pm$ $1\text{\,}\mathrm{p}\mathrm{s}$. All
the reported uncertainties are statistical only. The time resolution of the
APTS-OA is calculated according to Eq. 3 by considering RMS99.7% as the width
of the time residual distribution.
Since the correction requires a large data sample to be effective, only the
data taken with the modified with gap structure operated at
V${}_{\textrm{sub}}$ = [list-units=single]-1.2;-2.4;-4.8 can be corrected.

The dependence of the time resolution on the reverse substrate bias voltage
V${}_{\textrm{sub}}$, for both modified and modified with gap sensors, is
shown in Fig. 14.

Figure 14: Non-corrected (open symbols, orange dotted line and green dashed
line) and corrected (full symbols, blue solid line) time resolution measured
for modified and modified with gap DUT process variants. A time walk-like
correction, described in Sec. 3.2, is applied only to high statistical
significance data sets, namely those measured with the modified with gap
structure.

The time resolution is found to be independent of the process variant, for
this $10\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pitch. An improvement in
timing performance with increasing reverse bias is observed, resulting in a
resolution $\sigma_{t}$ = $63\text{\,}\mathrm{p}\mathrm{s}$ $\pm$
$3\text{\,}\mathrm{p}\mathrm{s}$ (stat.) and $\sigma_{t}$ =
$82\text{\,}\mathrm{p}\mathrm{s}$ $\pm$ $3\text{\,}\mathrm{p}\mathrm{s}$
(stat.) at V${}_{\textrm{sub}}$=$-4.8\text{\,}\mathrm{V}$ for corrected and
not corrected data, respectively.

The uniformity of timing performance along the pixel surface can be studied by
looking at the correlation of the time resolution with the in-pixel track
position. Figure 15 shows the map of corrected time resolution of the modified
with gap DUT operated at V${}_{\textrm{sub}}$=$-4.8\text{\,}\mathrm{V}$, with
hits from all the pixels grouped per associated track hit position and
projected onto one pixel area. As expected, the lowest time resolution
$\sigma_{t}$ = $52\text{\,}\mathrm{p}\mathrm{s}$ $\pm$
$4\text{\,}\mathrm{p}\mathrm{s}$ is measured for tracks hitting the pixel
center, where the distance to the collection electrode is minimal and the
electric field is maximum, and it deteriorates for incident tracks on the
pixel edge ($\sigma_{t}$ = $58\text{\,}\mathrm{p}\mathrm{s}$ $\pm$
$4\text{\,}\mathrm{p}\mathrm{s}$) and corner ($\sigma_{t}$ =
$72\text{\,}\mathrm{p}\mathrm{s}$ $\pm$ $4\text{\,}\mathrm{p}\mathrm{s}$),
marked by the points A, B, and C of Fig. 15, respectively. The reported
uncertainties are statistical only.

Figure 15: Left: corrected in-pixel time resolution of the modified with gap
structure operated at V${}_{\textrm{sub}}$=$-4.8\text{\,}\mathrm{V}$. Right:
time resolution variation along the path from the pixel center to the edge,
and to the corner.

The obtained results demonstrate the improvement in particle detection timing
performance brought by the TPSCo $65\text{\,}\mathrm{n}\mathrm{m}$ CMOS
technology with respect to the $180\text{\,}\mathrm{n}\mathrm{m}$ CMOS
technology. In fact, the best time resolution, after the correction, measured
for monolithic pixel sensors implemented in $180\text{\,}\mathrm{n}\mathrm{m}$
CMOS imaging technology is $106\text{\,}\mathrm{p}\mathrm{s}$ [8], while a
time resolution of $63\text{\,}\mathrm{p}\mathrm{s}$ is achieved, after time
walk correction, for the structures implemented in
$65\text{\,}\mathrm{n}\mathrm{m}$ CMOS technology discussed here when operated
at reverse substrate voltage V${}_{\textrm{sub}}$=$-4.8\text{\,}\mathrm{V}$.
However, it is worth noticing that the study presented in this publication
concentrates on the time resolution of the sensor only, while the time
resolution of a full detector system will also be affected by other
components, such as the readout circuitry.

##  4 Conclusions

The performance of the analog pixel test structures realized in the 65 nm
TPSCo CMOS imaging technology is presented in this publication. The APTS-OA
was successfully integrated in a telescope for the evaluation of its time
resolution, spatial resolution, and detection efficiency. The modified pixel
processes achieved a remarkable time resolution of
$63\text{\,}\mathrm{p}\mathrm{s}$ with over 99% detection efficiency and a
spatial resolution of $2\text{\,}\mathrm{\SIUnitSymbolMicro m}$ when tested at
a substrate voltage V${}_{\textrm{sub}}$ of $-4.8\,\textrm{V}$ and
$100\text{\,}\rm{e^{-}}$ threshold, without any observed process dependence.
These results not only underline the potential of the 65 nm CMOS imaging
technology in advancing high-energy physics also for applications demanding
precise timing information in combination with full detection efficiency and
spatial resolution.

## Acknowledgements

This project has received funding from the European Union’s Horizon Europe
research and innovation programme under grant agreement No 101057511. Funding
sources: (1) Project “Dipartimenti di eccellenza” at the Dept of Physics,
University of Turin, funded by Italian MIUR. (2) The National Research
Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No.
2022R1A6A3A03054907) Project 2022LJT55R, Concession Decree No. 104 of
02.02.2022 adopted by the Italian Ministry of University and Research, cup
D53D23002810006. The measurements leading to these results have been performed
at the SPS Test Beam Facility at CERN (Switzerland). We would like to thank
the coordinators at CERN for their valuable support of these test beams
measurements and for the excellent test beam environment. We would like, also,
to thank Federico Picollo for providing access to high brillance beam facility
for the detector characterization. ITS3 R&D and construction is supported by
several ITS3 project grants including LM2023040 of the Ministry of Education,
Youth, and Sports of the Czech Republic and Suranaree University of
Technology, the National Science and Technology Development Agency (JRA-
CO-2563-12905-TH, P-2050706), and the NSRF via the Program Management Unit for
Human Resources & Institutional Development, Research and Innovation (PMU-B
B47G670091) of Thailand.

## References

  * [1] G. Contin, et al., “The STAR MAPS-based PiXeL detector”, NIMA 907 (2018) 60–80. Advances in Instrumentation and Experimental Methods (Special Issue in Honour of Kai Siegbahn).
  * [2] F. Reidt, “Upgrade of the ALICE ITS detector”, NIMA 1032 (2022) 166632.
  * [3] O. Aberle, et al., High-Luminosity Large Hadron Collider (HL-LHC): Technical design report.  CERN Yellow Reports: Monographs. CERN, Geneva, 2020.  https://cds.cern.ch/record/2749422.
  * [4] G. Aglieri Rinella, et al., “Strategic R&D Programme on Technologies for Future Experiments - Annual Report 2021”, tech. rep.
  * [5] W. Snoeys, et al., “A process modification for CMOS monolithic active pixel sensors for enhanced depletion, timing performance and radiation tolerance”, NIMA 871 (2017) 90–96.
  * [6] M. Munker, M. Benoit, D. Dannheim, A. Fenigstein, T. Kugathasan, T. Leitner, H. Pernegger, P. Riedler, and W. Snoeys, “Simulations of CMOS pixel sensors with a small collection electrode, improved for a faster charge collection and increased radiation tolerance”, JINST 14 (May, 2019) C05013.
  * [7] T. Kugathasan, T. Ando, D. Dannheim, T. G. Etoh, M. Munker, H. Pernegger, A. Rivetti, K. Shimonomura, and W. Snoeys, “Monolithic CMOS sensors for sub-nanosecond timing”, NIMA 979 (2020) 164461.
  * [8] J. Braach, E. Buschmann, D. Dannheim, K. Dort, T. Kugathasan, M. Munker, W. Snoeys, P. Švihra, and M. Vicente, “Test-beam performance results of the FASTPIX sub-nanosecond CMOS pixel sensor demonstrator”, NIMA 1056 (Nov., 2023) 168641.
  * [9] CERN-EP-R&D, “MONOLITHIC PIXEL DETECTORS.”  https://ep-rnd.web.cern.ch/topic/monolithic-pixel-detectors.
  * [10] ALICE Collaboration, “Letter of Intent for an ALICE ITS Upgrade in LS3”, Tech. Rep. CERN-LHCC-2019-018. LHCC-I-034, CERN, Geneva, Dec, 2019.  https://cds.cern.ch/record/2703140.
  * [11] M. Šuljić, The Novel ALICE Inner Tracking System (ITS3) Based on Truly Cylindrical, Wafer-Scale Monolithic Active Pixel Sensors.  https://journals.jps.jp/doi/pdf/10.7566/JPSCP.34.010011.
  * [12] TowerJazz, “http://www.towersemi.com/.”  http://www.towersemi.com/. Last accessed on 25/01/2021.
  * [13] G. A. Rinella, et al., “Characterisation of analogue Monolithic Active Pixel Sensor test structures implemented in a 65 nm CMOS imaging process”, 2024.
  * [14] W. Snoeys, et al., “Optimization of a 65 nm CMOS imaging process for monolithic CMOS sensors for high energy physics”, PoS Pixel2022 (2023) 083.
  * [15] G. Aglieri Rinella, et al., “Digital pixel test structures implemented in a 65 nm CMOS process”, NIMA 1056 (2023) 168589. https://www.sciencedirect.com/science/article/pii/S016890022300579X.
  * [16] R. M. Muenker, Test beam and simulation studies on High Resistivity CMOS pixel sensors.  PhD thesis, U. Bonn (main), 2018.
  * [17] W. Deng, et al., “Design of an analog monolithic pixel sensor prototype in TPSCo 65 nm CMOS imaging technology”, JINST 18 (Jan, 2023) C01065.
  * [18] A. D. Martin, R. Ballabriga, G. Borghello, M. Campbell, W. Deng, G. Hong, I. Kremastiotis, W. Snoeys, and G. Termo, “Measurements of total ionizing dose effects in TPSCo 65 nm and influence of NMOS bulk bias”, JINST 18 (Feb, 2023) C02036.
  * [19] V. Sarritzu and on behalf of the ALICE collaboration, “A readout system for monolithic pixel sensor prototypes towards the upgrade of the ALICE Inner Tracking System”, JINST 18 (Jan, 2023) C01047.
  * [20] D. Banerjee, J. Bernhard, M. Brugger, N. Charitonidis, N. Doble, L. Gatignon, and A. Gerbershagen, “The North Experimental Area at the Cern Super Proton Synchrotron”,. http://cds.cern.ch/record/2774716. Dedicated to Giorgio Brianti on the 50th anniversary of his founding the SPS Experimental Areas Group of CERN-Lab II and hence initiating the present Enterprise.
  * [21] M. Mager, “ALPIDE, the Monolithic Active Pixel Sensor for the ALICE ITS upgrade”, NIMA 824 (2016) 434 – 438. Frontier Detectors for Frontier Physics: Proceedings of the 13th Pisa Meeting on Advanced Detectors.
  * [22] F. Carnesecchi, et al., “Beam test results of 25 and 35 µm thick FBK ultra-fast silicon detectors”, EPJ+ 138 (Jan, 2023) .
  * [23] P. Žugec, et al., “Pulse processing routines for neutron time-of-flight data”, NIMA 812 (Mar., 2016) 134–144.
  * [24] J. Kröger, S. Spannagel, and M. Williams, “User Manual for the Corryvreckan Test Beam Data Reconstruction Framework, Version 1.0”, 2019.
  * [25] V. Blobel, “A new fast track-fit algorithm based on broken lines”, NIMA 566 (2006) 14–17.
  * [26] M. Mager, “The telescope optimizer”,. https://mmager.web.cern.ch/telescope/tracking.html.
  * [27] R. Bugiel, et al., “High spatial resolution monolithic pixel detector in SOI technology”, NIMA 988 (2021) 164897.
  * [28] R. Turchetta, “Spatial resolution of silicon microstrip detectors”, NIMA 335 (1993) 44–58.
  * [29] F. Carnesecchi, et al., “A new low gain avalanche diode concept: the double-LGAD”, EPJ+ 138 (2023) .
  * [30] A. Rivetti, CMOS Front-End Electronics for Radiation Sensors.  CRC Press, 2015.

##  App. A Analog front-end settings

The operating point used for measurements reported in this paper is summarized
in the Table. 3. The currents $I_{\textrm{reset}}$, $I_{\textrm{biasn}}$,
$I_{\textrm{biasp}}$ are shown in Fig. 3 while the biasing currents for the
operational amplifier $I_{\textrm{bias3}}$, $I_{\textrm{bias4}}$,
$V_{\textrm{casn}}$, and $V_{\textrm{casp}}$ are not depicted in Figure.
Finally, the value of $V_{\textrm{reset}}$ chosen depending on
$V_{\textrm{sub}}$ in order to operate in the most linear region of the front-
end is reported in Table 4.

In-pixel
---
$I_{\textrm{reset}}$ | $100\text{\,}\mathrm{pA}$
$I_{\textrm{biasn}}$ | $-125\text{\,}\mathrm{\SIUnitSymbolMicro A}$
$I_{\textrm{biasp}}$ | $11.25\text{\,}\mathrm{\SIUnitSymbolMicro A}$
Out of pixel
$I_{\textrm{bias3}}$ | $212.5\text{\,}\mathrm{\SIUnitSymbolMicro A}$
$I_{\textrm{bias4}}$ | $2.6\text{\,}\mathrm{mA}$
$V_{\textrm{casn}}$ | $900\text{\,}\mathrm{mV}$
$V_{\textrm{casp}}$ | $270\text{\,}\mathrm{mV}$
Table 3: The operating point used for the measurement. See the details in Fig. 3. $V_{\textrm{sub}}($\text{\,}\mathrm{V}$)$ | $-1.2$ | $-2.4$ | $-3.6$ | $-4.8$
---|---|---|---|---
$V_{\textrm{reset}}($\text{\,}\mathrm{mV}$)$ | 380 | 420 | 440 | 440
Table 4: $V_{\textrm{reset}}$ settings at different $V_{\textrm{sub}}$

##  App. B APTS-OA detection efficiency as a function of the threshold with
different association window radius

Figure 16: Detection efficiency of the APTS-OA modified DUT as a function of
the threshold at V${}_{\textrm{sub}}$ = V${}_{\textrm{pwell}}$ =
$-1.2\text{\,}\mathrm{V}$, varying the association window (AW) radius.

A study on the association window radius was conducted, starting with a value
smaller than the pixel pitch and gradually increasing it to
$60\text{\,}\mathrm{\SIUnitSymbolMicro m}$. The detection efficiency improved
with larger association windows across all thresholds. However, the difference
in efficiency between the $15\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and
$60\text{\,}\mathrm{\SIUnitSymbolMicro m}$ radii was less than 0.05%.
Consequently, an association window of $15\text{\,}\mathrm{\SIUnitSymbolMicro
m}$ was selected for the analysis.

##  App. C APTS-OA noise

Figure 17: Noise RMS of the APTS-OA modified with gap at different
$V_{\textrm{sub}}$ = $V_{\textrm{pwell}}$ configurations.

In order to show only results not biased by noise, an analysis of the baseline
fluctuations was conducted and efficiency and spatial resolution were plotted
for thresholds above 3 times the RMS of the noise distribution, shown in Fig.
17.

##  App. D APTS-OA time residuals width at varying signal amplitude fraction

Figure 18: Time residuals distribution width for APTS-OA DUTs’ signal times
measured at different fractions of the signal amplitude for each operation
V${}_{\textrm{sub}}$. The values pertaining to the modified process DUT are
indicated with square markers and dashed lines, while those referring to the
modified with gap process DUT with circle markers and dotted lines. A slight
displacement in the x axis is added between the two curves to allow better
visibility.

The time residuals width, expressed as the RMS of the 99.7 central percentiles
of the distribution, has been evaluated for both measured DUTs at varying seed
signal amplitude fraction. Signal times measured at 10% of the signal
amplitude provide the lowest time residuals RMS, and are therefore used for
the analysis presented in this paper.

##  App. E APTS-OA detection efficiency at $100\text{\,}\rm{e^{-}}$ threshold

Figure 19: Detection efficiency of the APTS-OA modified and modified with gap
DUT at $100\text{\,}\rm{e^{-}}$ threshold at different $V_{\textrm{sub}}$ =
$V_{\textrm{pwell}}$ configurations.

Fig. 19 compares the efficiency measured at $100\text{\,}\rm{e^{-}}$ threshold
at different $V_{\textrm{sub}}$. No significant difference can be observed
between the modified and modified with gap process variants and the efficiency
is well above 99$\%$ for all the $V_{\textrm{sub}}$ configurations.

##  App. F APTS-OA correlation between seed signal charge and seed signal
leading edge time

Figure 20: Correlation between seed signal charge and signal leading edge time
for the APTS-OA modified with gap DUT operated at
V${}_{\textrm{sub}}$=$-4.8\text{\,}\mathrm{V}$.

The non-uniformity of the analog signal shape is investigated by studying the
correlation between the seed signal charge and the signal leading edge time,
expressed as the difference between the signal time at 50% of full amplitude
and the time at 10% of full amplitude. The leading edge time is used as a
proxy to evaluate the signal slope. Slower signals, i.e. longer leading edge
times, are observed for smaller collected charge.