# Comparison of different sensor thicknesses and substrate materials for the
monolithic small collection-electrode technology demonstrator CLICTD

K. Dort111Also at University of Giessen, Germany<EMAIL_ADDRESS>R.
Ballabriga  J. Braach222Also at University of Hamburg, Germany E. Buschmann
M. Campbell  D. Dannheim  L. Huth  I. Kremastiotis  J. Kröger333Also at
University of Heidelberg, Germany L. Linssen  M. Munker  W. Snoeys  S.
Spannagel  P. Švihra  T. Vanat  CERN, Geneva, Switzerland  Deutsches
Elektronen-Synchrotron DESY, Notkestr. 85, 22607 Hamburg, Germany  University
of Geneva, Geneva, Switzerland

###### Abstract

Small collection-electrode monolithic CMOS sensors profit from a high signal-
to-noise ratio and a small power consumption, but have a limited active sensor
volume due to the fabrication process based on thin high-resistivity epitaxial
layers. In this paper, the active sensor depth is investigated in the
monolithic small collection-electrode technology demonstrator CLICTD. Charged
particle beams are used to study the charge-collection properties and the
performance of devices with different thicknesses both for perpendicular and
inclined particle incidence. In CMOS sensors with a high-resistivity
Czochralski substrate, the depth of the sensitive volume is found to increase
by a factor two in comparison with standard epitaxial material and leads to
significant improvements in the hit-detection efficiency and the spatial and
time resolution.

###### keywords:

High-resistivity Czochralski silicon , Inclined particle tracks , Monolithic
silicon sensor , Small collection-electrode design

††journal: Nucl. Instr. Meth. A

##  1 Introduction

In monolithic CMOS sensors the readout electronics are integrated into the
active sensor volume, which offers the potential for fine pixel pitches and a
low mass. Profiting from the commercial CMOS industry, these devices are
particularly suited for large-scale production. Monolithic sensor designs
featuring a small collection electrode benefit from a reduced capacitance,
which enables an improvement in signal-to-noise ratio and reduced power
consumption [1]. Several sensors have been fabricated in a modified 180 nm
CMOS imaging process implementing the small collection-electrode design with a
25 - $30\text{\,}\mathrm{\SIUnitSymbolMicro m}$ high-resistivity epitaxial
layer on a low-resistivity substrate, such as the ALPIDE [2], (Mini-)MALTA
[3], FASTPix [4] and CLICTD [5] sensors. They have exhibited promising results
regarding radiation tolerance, a time resolution down to hundreds of
picoseconds, a spatial resolution of a few micrometers and full efficiency
over a wide threshold range.

Although sensor optimisations enable a full lateral depletion [6] in the small
collection-electrode design, the devices are only partially depleted in depth.
The active sensor depth, from which charge carriers contribute to the signal,
extends further than the depletion depth but is limited by the thickness of
the epitaxial layer due to the short charge carrier lifetime in the low-
resistivity substrate. High-resistivity substrate materials are therefore
investigated as a possible replacement, extending both the depletion and
active sensor depth thus leading to a higher measured signal. In this
document, a high-resistivity Czochralski substrate as alternative wafer
material is assessed, which has already proven to increase efficiency after
irradiation in the small collection-electrode design [7].

An in-depth comparison of 40 - $300\text{\,}\mathrm{\SIUnitSymbolMicro m}$
thick sensors in the original epitaxial-layer design with
$100\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick Czochralski sensors is
presented for the CLICTD technology demonstrator. To this end, the performance
and charge-sharing characteristics of different CLICTD sensors are studied
using charged particle beams with perpendicular and inclined incidence
relative to the sensor surface. Most notably, in-pixel studies are presented
that allow for a two-dimensional mapping of charge-collection properties. The
effective active sensor volume is determined as well by employing the grazing
angle technique [8] for the different sensor thicknesses and materials.

##  2 The CLICTD Sensor

(a) Continuous n-implant

(b) Segmented n-implant

Figure 1: Schematics of the CLICTD pixel design for the pixel flavour with (a)
continuous and (b) segmented n-implant. The readout circuitry is placed in the
nwell and pwell above the deep pwell. Not to scale.

The CLICTD sensor features a matrix of $16\times 128$ detection channels with
a size of $300\text{\times}30\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{m}$
in column $\times$ row direction. Each channel is segmented along the column
direction into 8 sub-pixels with a size of
$37.5\text{\times}30\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{m}$. The
following section gives a brief overview of the main features of the CLICTD
sensor. Additional details can be found in [5] and [9].

###  2.1 Sensor Design

The CLICTD sensor is fabricated in a modified 180 nm CMOS imaging process [6]
using two different pixel flavours, as shown schematically in Fig. 1. The
sensor is characterised by a small n-type collection electrode on top of a
$30\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thin high-resistivity (few
k$\Omega$cm) p-epitaxial layer, that is grown on a low-resistivity ($\sim
10^{-2}$\text{\,}\mathrm{\SIUnitSymbolOhm}\text{\,}\mathrm{cm}$$) p-type
substrate. The on-channel front-end electronics is placed in the n-well and
p-well above the deep p-well, which shields the circuitry. A low-dose n-type
implant below the p-wells allows for full lateral depletion of the epitaxial
layer [6]. In the second pixel flavour, the n-implant is segmented at the
pixel edges, which causes an increase in the lateral electric field. As a
consequence, an accelerated charge collection and reduced charge sharing is
achieved with this design. In the CLICTD sensor, the segmentation is only
introduced in the column direction. In the row direction, a high degree of
charge sharing is desired in order to improve the spatial resolution.

A reverse bias voltage is applied to nodes in the p-wells and the substrate.
The bias voltage at the p-wells is limited to -6 V to prevent breakdown of the
on-channel NMOS transistors [10].

###  2.2 Sensor Material

CLICTD sensors with different thicknesses were produced using backside
grinding. The total device thickness ranges from
$40\text{\,}\mathrm{\SIUnitSymbolMicro m}$ to
$300\text{\,}\mathrm{\SIUnitSymbolMicro m}$, including a metal stack of
approximately $10\text{\,}\mathrm{\SIUnitSymbolMicro m}$ on top of the sensor
[11].

The size of the active sensor volume is limited by the thickness of the
$30\text{\,}\mathrm{\SIUnitSymbolMicro m}$ epitaxial layer. To increase the
active volume, an alternative substrate material is studied, which consists of
high-resistivity (few
$\text{\,}\mathrm{k\SIUnitSymbolOhm}\text{\,}\mathrm{cm}$) p-type Czochralski
silicon [7]. The implants are introduced directly on the Czochralski wafers
and no additional epitaxial layer is grown on top. Henceforth, the term
Czochralski substrate is used to refer to the sensors fabricated on high-
resistivity Czochralski wafers.

The advantages of the high-resistivity Czochralski material are twofold:
Firstly, the isolation between p-well and substrate bias nodes is improved,
allowing for a larger difference between the two voltages. Secondly, the
depletion can evolve further in depth owing to the larger size of the high-
resistivity volume.

The benefits of the larger active volume depend on the aspect ratio of the
pixel cell and the target applications of the sensor. For instance, sensors
with a comparably large pixel pitch that aim for a good spatial resolution,
profit from a larger active depth by tuning the depth such that an optimal
degree of charge sharing and an enhanced signal are achieved. Sensors with a
pixel pitch considerably smaller than the active depth are less suited for the
Czochralski substrate, since the cluster size increases considerably, which
typically does not lead to additional improvements of the performance.
Likewise, in designs where the charge collection within the sensor is subject
to a high degree of charge sharing, thick sensors with Czochralski substrate
are less suited. Therefore, the Czochralski substrate is only investigated for
CLICTD sensors with segmented n-implant, since charge sharing is suppressed
for this pixel flavour.

It should be noted that the availability of high-resistivity Czochralski
substrates for silicon sensor fabrication depends on foundry specifications,
since it is not a standard material for the investigated CMOS process.

###  2.3 Analogue and Digital Front-End

Each sub-pixel has an analogue front-end that consists of a voltage amplifier
connected to a discriminator, where an adjustable detection threshold is
compared to the input pulses. Effective threshold variations are corrected
using a 3-bit threshold-tuning DAC.

The discriminator output of the eight sub-pixels in a detection channel are
combined with a logical OR in the on-channel digital front-end. The binary hit
pattern of the sub-pixels is recorded as well as the 8-bit Time-of-Arrival
(ToA) and the 5-bit Time-over-Threshold (ToT) for time and energy
measurements, respectively. As a consequence of combining the sub-pixel
discriminator outputs, the ToA is set by the earliest sub-pixel timestamp and
the ToT is determined by the number of clock cycles in which at least one sub-
pixel is above the detection threshold.

No conversion from ToT to physical units is applied for the measurements shown
in this paper, since the conversion was found to have a limited precision
owing to non-linearities in the analogue front-end [5].

###  2.4 Sensor Operation

The front-end and operation settings were optimised in laboratory studies
detailed elsewhere [9, 5]. Most importantly, for each sensor a minimum
operation threshold is defined as the lowest possible threshold at which a
noise free operation ($<1\times 10^{-3}$ hits/s for the full pixel matrix) is
achievable with up to 10 noisy pixels masked, which is less than one per mille
of the entire matrix. The sensors presented in this paper are compared at
their respective minimum operation threshold. It should be noted that
measurements below the minimum operation threshold are nevertheless feasible,
since a small noise contribution can be tolerated.

The difference between the substrate and p-well bias voltages is limited by
the punch-through between the two nodes. Whereas this requirement constraints
the difference to a few volts for sensors with epitaxial layer, for the
Czochralski sensors, the difference can easily exceed tens of volts. For the
sensors with epitaxial layer, a high substrate bias voltage has a negligible
impact, since the depletion depth is limited by the thickness of the epitaxial
layer itself. Therefore, the bias voltage is fixed to -6 V/-6 V at the
p-well/substrate nodes for measurements presented in the following sections.
For the Czochralski sensors, the depletion region can evolve further into the
substrate, thus justifying measurements with increased substrate bias voltage.

###  2.5 Front-End Optimisation for Large Substrate Voltages

The CLICTD front-end is optimised for sensors with a
$30\text{\,}\mathrm{\SIUnitSymbolMicro m}$ epitaxial layer. Sensors fabricated
on Czochralski substrates are subject to a higher sensor leakage current, if
the difference between p-well and substrate voltage exceeds 5 V. The increased
current can saturate the leakage current compensation circuit, which renders
parts of the pixel matrix insensitive to incoming particles. To counteract the
saturation, the front-end settings are adapted such that a faster return to
baseline at the input node is achieved. With these settings, the sensor can be
operated up to -20 V substrate and -6 V p-well bias voltage before any
saturation effects set in. However, the adaptations reduce the signal gain,
which leads to coarser steps in the threshold settings and a larger minimum
operation threshold, since the front-end is operated in conditions it was not
designed for. The higher thresholds have important implications for the sensor
performance, as presented in Section 4.

The total power consumption of the device has been studied elsewhere [9]. As
the adapted settings at the input node only increase the range of the leakage
current compensation, the current and power consumption of the main circuit is
not affected.

##  3 Test-Beam and Analysis Setup

Figure 2: Test-beam setup with a rotated DUT

Test-beam measurements were performed in a two-week test-beam period at the
DESY II Test-Beam Facility [12] using a MIMOSA-26 telescope [13] equipped with
an additional Timepix3 [14] plane for improved track-time resolution, as
schematically depicted in Fig. 2. The beam consisted of 5.4 GeV electrons and
data for different incidence angles between the beam and the sensor surface
were recorded. To this end, the Device-Under-Test (DUT) was mounted on a
rotation stage to allow for inclinations relative to the beam axis.

Two different telescope plane spacings were used to optimise the tracking
performance for the respective measurements: For measurements with
perpendicular incidence between the beam and the sensor surface, the innermost
telescope planes are as close as physically possible to the DUT. When the DUT
is rotated, the telescope planes are adjusted such that the DUT can be tilted
to $\leq 70^{\circ}$ without touching the telescope planes.

A trigger signal, consisting of a coincidence between two scintillators in
front of the first telescope plane, is provided by the AIDA Trigger Logic Unit
(TLU) [15]. The EUDAQ2 data acquisition framework is used to control and read
out the telescope and the DUT [16].

###  3.1 Reconstruction and Analysis

The software framework Corryvreckan [17, 18] is used to perform offline
reconstruction and analysis of the test-beam data. Individual events are
defined by CLICTD readout frames. The start of each frame is marked by opening
the acquisition shutter and the end by closing the shutter 200 ns after
receiving a trigger signal from the TLU. The Timepix3 hit timestamp and the
TLU trigger timestamp associated to MIMOSA-26 hits determine their allocation
to a specific event by requiring that the timestamp is within a CLICTD frame.
The subsequent analysis is performed on an event-by-event basis.

For each telescope plane and the DUT, adjacent pixel hits are combined into
clusters and the cluster position is calculated by a ToT-weighted centre-of-
gravity algorithm. For the CLICTD sensor, the cluster position in row
direction is corrected using the $\eta$-formalism to take non-linear charge
sharing between pixel cells into account [19, 20, 5]. In addition, split
clusters are considered for measurements with rotated DUT i.e. a gap of one
pixel is permitted between pixel hits to account for single pixels within a
cluster that fall below the threshold. The risk of having merged clusters from
two distinct particles is considered to be negligible, since less than one
percent of all events contain more than one reconstructed track.

Track candidates are formed from clusters on each of the seven telescope
planes. For track fitting the General Broken Lines (GBL) formalism [21] is
used to account for multiple scattering in the material. The telescope
alignment is performed by minimising the track $\chi^{2}$ distribution. Tracks
with a $\chi^{2}$ per degree of freedom larger than three are discarded. The
telescope track resolution at the position of the DUT is
$2.4\text{\,}\mathrm{\SIUnitSymbolMicro m}$ for the close telescope plane
spacing and $5.6\text{\,}\mathrm{\SIUnitSymbolMicro m}$ for the wide rotation
configuration, as estimated from analytical calculations based on [22, 23].

A reconstructed track is associated with a CLICTD cluster by requiring a
spatial distance of less than 1.5 pixel pitches between the global track
intercept position on the DUT and the reconstructed cluster position as well
as a track timestamp within the same CLICTD frame as the cluster. It has been
verified that the spatial cut is sufficiently large even for the larger track
resolution at the position of the DUT in the wide telescope-plane
configuration. Clusters adjacent to the edge of the pixel matrix are rejected
to exclude edge effects. The following observables are considered to
characterise the DUT:

#### Cluster size

The cluster size is defined as the number of pixels in a given cluster.
Correspondingly, the cluster size in column/row direction is given by the size
of the cluster projected onto the respective axis. The systematic uncertainty
on the cluster size arises from uncertainties in the threshold calibration, as
detailed in [5]. At the minimum operation threshold, the systematic
uncertainty evaluates to $\pm 0.01$ for the mean cluster size and the
statistical uncertainty is of the order of $10^{-4}$.

#### Hit-detection efficiency

The hit-detection efficiency is calculated as the number of associated tracks
divided by the total number of tracks. The considered tracks are required to
pass through the acceptance region of the DUT, excluding one column/row at the
pixel edge as well as masked pixels and their direct neighbours. The
statistical uncertainty is calculated using a Clopper-Pearson interval of one
sigma [24] and the systematic uncertainty arises from the threshold
calibration as mentioned above.

#### Spatial resolution

The unbiased spatial residuals are calculated as the difference between the
reconstructed cluster position and the track intercept on the DUT. The RMS of
the central $3\,\sigma$ of the distribution is extracted and the spatial
telescope track resolution of $2.4\text{\,}\mathrm{\SIUnitSymbolMicro m}$ for
the close and $5.6\text{\,}\mathrm{\SIUnitSymbolMicro m}$ for the wide
telescope configuration is quadratically subtracted, which yields the spatial
resolution of the DUT.

At the minimum operation threshold, the statistical uncertainty on the spatial
resolution is of the order of $10^{-2}$\text{\,}\mathrm{\SIUnitSymbolMicro
m}$$. The systematic uncertainties result from uncertainties in the telescope
single-plane resolution given in [23]. In addition, the plane positions in
z-direction are shifted independently by $\pm$1\text{\,}\mathrm{mm}$$ and the
calculation of the track resolution at the position of the DUT is repeated.
Propagating the deviations to the spatial resolution yields an uncertainty of
$\pm$0.1\text{\,}\mathrm{\SIUnitSymbolMicro m}$$. The propagated threshold
uncertainty evaluates to $\pm$0.1\text{\,}\mathrm{\SIUnitSymbolMicro m}$$ as
well and the total systematic uncertainty is given by the quadratic sum of the
two.

#### Time resolution

Similar to the spatial residuals, the time residuals are defined as the
difference between the DUT timestamp and the track timestamp. Signal-dependent
time-walk effects are corrected by exploiting the ToT information. The mean
time difference between the DUT and the track timestamp are subtracted for
each ToT bin separately. After correction, the RMS of the central $3\,\sigma$
of the time residuals distribution is calculated and the track time resolution
of 1.1 ns [25] is quadratically subtracted.

The statistical uncertainties are of the order of 0.01 ns. The systematic
uncertainties are composed of the threshold uncertainty evaluating to $\pm
0.1$ ns and sub-pixel by sub-pixel variations. To quantify the latter, the
analysis is repeated for every sub-pixel in a detection channel individually
and the spread of the time resolution is used to define the systematic
uncertainty, which yields $\pm 0.1$ ns at the minimum operation threshold.

#### Studies with inclined particle tracks

The inclination angle of the DUT with respect to the beam is taken from the
alignment procedure. The angle agrees with the nominal rotation angle set for
the rotation stage apart from a constant offset. It was confirmed that the
alignment has converged by manually modifying the plane orientation by $\pm
0.5^{\circ}$ and repeating the alignment. A deviation of less than $\pm
0.01^{\circ}$ is found with respect to the initial alignment.

##  4 Performance for Perpendicular Particle Tracks

First, measurement results for perpendicular beam incidence are presented.
Here, CLICTD sensors with different thicknesses and wafer materials are
compared for the two different pixel flavours. A comparison of the pixel
flavours themselves can be found elsewhere [5].

Table 1: Mean cluster size (Cls. Size), spatial resolution (Spat. Res.) in row direction and time resolution (Time Res.) at the minimum operation threshold (Thd.) for both pixel flavours, different sensor thicknesses and wafer materials. C - continuous n-implant, S - segmented n-implant, Epi - epitaxial layer, Cz - Czochralski substrate. Thickn. [$\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{m}$] | Material | Flavour | Thd. [e] | Cls. Size | Spat. Res. (row) [$\text{\,}\mathrm{\SIUnitSymbolMicro m}$] | Time Res. [ns]
---|---|---|---|---|---|---
300 | Epi | C | $139^{+4}_{-5}$ | $1.99\pm 0.01$ | $4.6\pm 0.2$ | $6.5\pm 0.1$
100 | Epi | C | $136^{+4}_{-5}$ | $1.94\pm 0.01$ | $4.6\pm 0.2$ | $6.4\pm 0.1$
50 | Epi | C | $140^{+4}_{-5}$ | $1.91\pm 0.01$ | $4.6\pm 0.2$ | -
40 | Epi | C | $138^{+4}_{-5}$ | $1.86\pm 0.01$ | $4.9\pm 0.2$ | $6.4\pm 0.1$
300 | Epi | S | $136^{+4}_{-5}$ | $1.82\pm 0.01$ | $4.6\pm 0.2$ | $5.6\pm 0.1$
100 | Epi | S | $140^{+4}_{-5}$ | $1.81\pm 0.01$ | $4.5\pm 0.2$ | $5.5\pm 0.1$
50 | Epi | S | $131^{+4}_{-5}$ | $1.83\pm 0.01$ | $4.6\pm 0.2$ | -
40 | Epi | S | $130^{+4}_{-5}$ | $1.73\pm 0.01$ | $4.8\pm 0.2$ | $5.3\pm 0.1$
100 | Cz | S | $151^{+4}_{-5}$ | $2.36\pm 0.01$ | $3.9\pm 0.2$ | $4.8\pm 0.1$

###  4.1 Cluster Size

(a) Continuous n-implant

(b) Segmented n-implant

Figure 3: Mean cluster size as a function of the detection threshold using
sensors with different sensor thicknesses and wafer materials for the pixel
flavour with (a) continuous and (b) segmented n-implant using a bias voltage
of -6 V/-6 V at the p-well/substrate.

(a) Epitaxial layer

(b) Czochralski substrate

Figure 4: In-pixel representation of the total cluster size at the minimum
operation threshold for a sensor with (a) epitaxial layer and (b) Czochralski
substrate. Both sensors have a segmented n-implant and are biased at -6 V/-6 V
at p-wells/substrate.

Comparing the cluster size of different sensors is sensitive to the total
amount of induced charge and its distribution among adjacent pixel cells. The
mean cluster size for the two pixel flavours as a function of the detection
threshold is presented in Fig. 3 and the mean size at the minimum detection
threshold is listed in Table 1. The shaded band represents the uncertainties
discussed in the previous section.

For both pixel flavours, the mean cluster size is the same within the
uncertainties for sensor thicknesses between
$50\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and
$300\text{\,}\mathrm{\SIUnitSymbolMicro m}$. The results imply that only the
fraction of the low-resistivity substrate is removed from which charge carrier
do not contribute to the measured signal. Thus, thinning the sensor to
$50\text{\,}\mathrm{\SIUnitSymbolMicro m}$ still leaves the active sensor
material intact.

On the other hand, the mean cluster size for the
$40\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick sensor is reduced by
approximately $10\text{\,}\mathrm{\char 37\relax}$ at the minimum operation
threshold. As the $40\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick sensor
consists of approximately $10\text{\,}\mathrm{\SIUnitSymbolMicro m}$ of metal
layers and $30\text{\,}\mathrm{\SIUnitSymbolMicro m}$ sensor material, it can
be assumed that the substrate is fully removed. Damage to the epitaxial layer
by the thinning procedure [26] is expected to affect the signal as well, which
results in a lower cluster size.

The decrease in mean cluster size for the
$40\text{\,}\mathrm{\SIUnitSymbolMicro m}$ sensors is more pronounced for the
pixel flavour with segmented n-implant (cf. Fig. 3(b)), which is consistent
with the reduced charge sharing expected for this flavour. A high degree of
charge sharing leads to the distribution of the total signal to several
adjacent pixel cells, thus reducing the amount of charge collected per pixel.
In particular, charge carriers generated at the lower border of the active
sensor region are subject to intense charge sharing, since their longer
propagation path allows for a stronger contribution of diffusion processes. If
the induced signal on a given pixel is not enough to surpass the threshold,
the charge carriers that propagated to this cell are effectively lost.
Therefore, this phenomenon is particularly important for the flavour with
continuous n-implant and affects mostly charge carriers from the lower part of
the active sensor volume. A removal of this volume is thus less severe, since
a fraction of charge carriers are anyway lost due to sub-threshold effects.
The stronger concentration of charge carriers for the pixel flavour with
segmented n-implant mitigates the charge-sharing-induced signal loss and this
flavour is consequently more sensitive to the thinning.

The mean cluster size for a $100\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick
sensor fabricated on a Czochralski substrate is shown in Fig. 3(b). At the
minimum threshold, the mean cluster size is increased by approximately
$30\text{\,}\mathrm{\char 37\relax}$ compared to sensors with epitaxial layer.
The in-pixel representation of the cluster size allows for a detailed
investigation of the cluster size difference, as presented in Fig 4. In this
representation, the cluster size is depicted as a function of the particle
incident position within the pixel cell by folding data from a full CLICTD
pixel matrix into a single cell. The largest clusters originate from the pixel
corners owing to geometrical effects and the low electric field in this region
resulting in a high contribution from charge carrier diffusion. For the sensor
fabricated on Czochralski substrate, the cluster size is larger regardless of
the incident position. Especially in the pixel centre, the map exhibits mean
cluster size values well above one, even though the lowest degree of charge
sharing is expected from this region. The results are thus indicative of an
overall higher signal resulting from a larger active sensor volume.

The depletion region within the Czochralski substrate is not expected to
extend to the sensor backside at a bias voltage of -6 V/-6 V, which still
limits the active sensor depth. An increase in substrate bias voltage,
increases the depletion depth and therefore also affects the active depth, as
illustrated in Fig. 5, where the mean cluster size as a function of the
substrate bias voltage is displayed for the pixel flavour with segmented
n-implant. The p-well voltage is fixed to -6 V and a higher detection
threshold of 348 e is applied to the sensor due to the different front-end
operation settings as explained before.

Figure 5: Mean cluster size as a function of the substrate bias voltage at a
threshold of 348 e for a Czochralski sensor with segmented n-implant. The
p-well voltage is fixed to -6 V.

###  4.2 Hit-Detection Efficiency

(a) Continuous n-implant

(b) Segmented n-implant

Figure 6: Hit-detection efficiency as a function of the detection threshold
using sensors with different sensor thicknesses and wafer materials for the
pixel flavour with (a) continuous and (b) segmented n-implant using a bias
voltage of -6 V/-6 V at the p-well/substrate.

The hit-detection efficiency is closely related to the maximum single-pixel
charge (seed charge) in a cluster and is thus correlated with the total signal
and the degree of charge sharing. The efficiency is determined as a function
of the detection threshold as presented in Fig. 6 for both pixel flavours.
While efficiencies well above $99\text{\,}\mathrm{\char 37\relax}$ are
achieved at low detection thresholds, the efficiency deteriorates for values
greater than 500 e, since all single-pixel signals in a cluster can fall below
the detection threshold. The degradation is stronger for the pixel flavour
with continuous n-implant due to the enhanced charge sharing, which leads to a
smaller charge per pixel, as discussed in detail in [5].

For high thresholds, inefficient regions start to form at the pixel borders,
as illustrated in Fig. 7(a), where the in-pixel efficiency is shown at a
threshold of 1950 e for a $300\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick
sensor with segmented n-implant and epitaxial layer. As the diffusion of
charge carriers to neighbouring pixels is enhanced at the edges, a smaller
seed signal and consequently a lower efficiency is associated with these
regions.

For the $40\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{m}$ thick sensors, the
high-efficiency plateau is noticeably reduced compared to the thicker sensors.
In agreement with the smaller cluster size observed in the previous section,
the degraded efficiency indicates an overall reduction in signal compared to
the thicker sensors. These results support the assumption of a smaller active
depth due to the removal of sensitive sensor volume. The degradation in
efficiency is less severe for the pixel flavour with continuous n-implant as
discussed above. A slight trend towards smaller efficiencies is also visible
for $50\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{m}$ thick sensors, although
it is covered by the systematic uncertainties. The results indicate that parts
of the active material are potentially already damaged in the
$50\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{m}$ thick sensors.

The sensor fabricated on a Czochralski substrate exhibits a larger efficiency
at high detection thresholds compared to sensors with epitaxial layer as a
direct consequence of the higher signal. The in-pixel representation of the
efficiency is depicted in Fig. 7(b) at a detection threshold of approximately
1950 e and confirms that the efficiency is larger especially in the pixel
edges, where the highest degree of charge sharing is expected.

The impact of the substrate voltage for samples with Czochralski substrate is
illustrated in Fig. 8, where the detection threshold corresponding to an
efficiency of $80\text{\,}\mathrm{\char 37\relax}$ is presented as a function
of the substrate bias voltage. The threshold increases by about
$30\text{\,}\mathrm{\char 37\relax}$ from -6 V to -20 V. At -20 V, the value
is about $85\text{\,}\mathrm{\char 37\relax}$ higher compared to the
corresponding threshold for samples with epitaxial layer, which evaluates to
approximately 1400 e.

(a) Epitaxial layer

(b) Czochralski substrate

Figure 7: In-pixel representation of the hit-detection efficiency at a
threshold of 1950 e for a sensor with (a) epitaxial layer and (b) Czochralski
substrate. Both sensors have a segmented n-implant and are biased at -6 V/-6 V
at p-wells/substrate. Figure 8: Detection threshold corresponding to an
efficiency of $80\text{\,}\mathrm{\char 37\relax}$ as a function of the
substrate bias voltage for a Czochralski sample with segmented n-implant. The
p-well voltage is fixed to -6 V.

###  4.3 Spatial Resolution

(a) Continuous n-implant

(b) Segmented n-implant

Figure 9: Spatial resolution as a function of the detection threshold using
sensors with different thicknesses and wafer materials for the pixel flavour
with (a) continuous and (b) segmented n-implant using a bias voltage of -6
V/-6 V at the p-well/substrate. Figure 10: Spatial resolution as a function of
the substrate bias voltage at a threshold of 348 e for a Czochralski sample
with segmented n-implant. The p-well voltage is fixed to -6 V.

The spatial resolution in row direction as a function of the detection
threshold is presented in Fig. 9 for both pixel flavours and the results at
the minimum threshold are listed in Table 1. For thresholds above 1200 e, no
$\eta$-correction is applied, since the application of the algorithm becomes
challenging due to the small number of two-pixel clusters.

As the modifications to the n-implant are not applied in row direction, the
charge sharing behaviour is similar for both pixel flavours and the spatial
resolution is thus in good agreement within the uncertainties. Although the
resolution degrades with increasing threshold due to the decrease in cluster
size, the binary resolution of $8.7\text{\,}\mathrm{\SIUnitSymbolMicro m}$ is
never exceeded. For high threshold values, an improvement of the spatial
resolution is caused by the formation of inefficient regions at the pixel
edges, as displayed in Fig. 7(a). These inefficiencies lead to an effectively
smaller pixel pitch that results in an artificial improvement in spatial
resolution.

Within the uncertainties, the spatial resolution for the
$\geq$50\text{\,}\mathrm{\SIUnitSymbolMicro m}$$ thick sensors are in good
agreement owing to the similar cluster size at a given threshold.

The spatial resolution of the $40\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick
sensor degrades for thresholds smaller than $1000$ e owing to the smaller
cluster size at a given threshold (cf. Fig. 3). For the flavour with
continuous n-implant, the degradation is as high as $7\text{\,}\mathrm{\char
37\relax}$ at the minimum detection threshold. The difference vanishes at high
thresholds, where single-pixel clusters dominate for all sensor thicknesses.

The higher signal from the Czochralski sensors leads to a larger cluster size
and consequently an improved spatial resolution. The difference is
particularly noticeable at small threshold values in accordance with the
larger difference in cluster size that was presented in Fig. 3(b). At the
minimum operation threshold listed in Table 1, the resolution improves by
about $15\text{\,}\mathrm{\char 37\relax}$. At high thresholds, the mean
cluster size converges to one resulting in an identical resolution within the
uncertainties.

With increasing substrate bias voltage, the depleted region expands evoking a
higher signal that leads to a larger cluster size and consequently an improved
spatial resolution, as illustrated in Fig. 10 for a Czochralski sensor with
segmented n-implant at a comparably high threshold of 348 e. Between -6 V and
-20 V, the spatial resolution improves by approximately
$13\text{\,}\mathrm{\char 37\relax}$. While the comparably high threshold
limits the absolute performance improvement, the potential of the Czochralski
substrate is still distinguishable.

###  4.4 Time Resolution

(a) Continuous n-implant

(b) Segmented n-implant

Figure 11: Time resolution as a function of the detection threshold using
sensors with different thicknesses and wafer materials for the pixel flavour
with (a) continuous and (b) segmented n-implant using a bias voltage of -6
V/-6 V at the p-well/substrate.

The time resolution after time-walk correction is depicted in Fig. 11 as a
function of the detection threshold for both pixel flavours. The results at
the minimum operation threshold are listed in Table 1. With increasing
threshold, the time resolution degrades owing to a stronger contribution of
amplitude noise causing a time jitter. The jitter is inversely proportional to
the slope of the signal at the threshold-crossing point, which flattens
towards the peak of the signal.

It is expected that the time resolution is limited by the binning of the ToA
clock as well as the time-walk procedure [5], which obscure sensor effects
related to the device thickness. Nevertheless, a $14\text{\,}\mathrm{\char
37\relax}$ improvement is visible for the Czochralski sensor owing to a larger
seed signal, which facilitates the time-walk correction and suppresses time
jitter. The different front-end settings for the Czochralski sensors only
concern the input node and are therefore not expected to have a significant
impact on the time resolution. An increase in substrate bias voltage leads to
an additional improvement in time resolution, as presented in Fig. 12 at a
threshold of 348 e. Between -6 V and -20 V, the time resolution improved by
approximately $9\text{\,}\mathrm{\char 37\relax}$.

Figure 12: Time resolution as a function of the substrate bias voltage at a
threshold of 348 e for a Czochralski sensor with segmented n-implant. The
p-well voltage is fixed to -6 V.

##  5 Studies with Inclined Particle Tracks

In the following, the sensor performance is assessed for inclined particle
tracks and the active sensor depth is investigated.

###  5.1 Performance

In many HEP applications, particles enter the sensor under an oblique angle,
due to e.g. mechanical rotation of detector modules or helical particle
trajectories in a magnetic field. Therefore, the sensor performance for
inclined particle tracks merits detailed investigation. Here, a
$300\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick sensor with epitaxial layer
and continuous n-implant is used to exemplify the effects of the inclination
angle on the sensor performance.

#### Cluster Size

(a) Cluster size in row direction

(b) Cluster size in column direction

Figure 13: Cluster size as a function of the detection threshold for different
rotation angles for a $300\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick sensor
with epitaxial layer and continuous n-implant tilted in row direction. A bias
voltage of -6 V/-6 V is applied to the p-well/substrate.

The amount of active silicon traversed by particles is varied by inclining the
sensor relative to the beam axis. For high inclination angles, particle tracks
cross several adjacent pixel cells, giving rise to a larger cluster size as
illustrated in Fig. 13 for a sensor tilted in row direction. The mean cluster
size at the minimum detection threshold is listed in Table 2. A considerable
increase in cluster size in row direction is distinguishable principally due
to the geometrical effect of charge deposition in several pixel cells. Between
$0^{\circ}$ and $70^{\circ}$, the increase is as high as
$250\text{\,}\mathrm{\char 37\relax}$ at the minimum operation threshold. The
simultaneous increase in cluster size in column direction is consistent with
an overall increase in the number of liberated charge carriers, whose
undirected diffusion also affects charge sharing in column direction. At the
minimum operation threshold, the mean cluster size in column direction is
approximately $6\text{\,}\mathrm{\char 37\relax}$ larger at $70^{\circ}$
compared to perpendicular incidence.

#### Efficiency

With increasing inclination angle, the total energy deposition in the sensor
increases due to the longer particle path in the active sensor region. As a
result, a higher signal is detected, which leads to an appreciable increase in
efficiency at high thresholds, as depicted in Fig. 14, where the efficiency as
a function of the detection threshold is shown for three different rotation
angles. At a threshold of 2300 e, the efficiency increases from about
$38\text{\,}\mathrm{\char 37\relax}$ at 0∘ to $70\text{\,}\mathrm{\char
37\relax}$ at 70∘.

Figure 14: Detection efficiency as a function of the detection threshold for
different rotation angles for a $300\text{\,}\mathrm{\SIUnitSymbolMicro m}$
thick sensor with epitaxial layer and continuous n-implant. The sensor was
tilted in row direction and the p-well/substrate was biased at -6 V/-6 V.

#### Spatial Resolution

The spatial resolution in row direction improves with increasing rotation
angle until approximately $40^{\circ}$, where it evaluates to
$3.6\pm$0.2\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{m}$$ after
$\eta$-correction, as illustrated in Fig. 15. The $\eta$-correction allows for
an improvement in spatial resolution for rotation angles below $40^{\circ}$.
At higher angles, an increase of cluster size $\geq 3$ complicates the
application of the reconstruction algorithms and no improvement with respect
to the centre-of-gravity algorithm is achievable.

Figure 15: Spatial resolution as a function of the rotation angle using a charge-weighted centre-of-gravity algorithm (CoG) and an $\eta$-correction (ETA) to reconstruct the cluster position on the DUT. A bias voltage of -6 V/-6 V was applied to the p-well/substrate. Table 2: Cluster size (CS) for different rotation angles (RA) using a sensor with epitaxial layer and continuous n-implant operated at a threshold of approximately 150 e. RA [∘] | CS (row) | CS (col.)
---|---|---
0 | $1.46\pm 0.01$ | $1.38\pm 0.01$
50 | $2.19\pm 0.01$ | $1.41\pm 0.01$
70 | $3.78\pm 0.01$ | $1.46\pm 0.01$

###  5.2 Determination of Active Sensor Depth

The extent of the active sensor volume is an essential ingredient to maximise
the signal and thus optimise the sensor performance. The results from the
previous sections imply that the active sensor volume only covers the upper
part of the sensors with epitaxial layer, since thinning the devices down to
$50\text{\,}\mathrm{\SIUnitSymbolMicro m}$ has no significant impact on the
performance.

To quantify the thickness of the active sensor volume, grazing angle
measurements [8] are performed, whereby inclined particle tracks are used to
determine an equivalent charge-collection depth for the observed cluster size.

Figure 16: Schematic representation of the cluster size dependence on the
inclination angle of the particle track.

The estimation of the active sensor depth is based on geometrical
consideration, as sketched in Fig. 16. The model relates the cluster size in
the tilt direction to the incident angle $\alpha$ and the active depth $d$.
Charge carriers created below the active depth are assumed to have no effect
on the cluster size. The following geometrical relation is considered to
extract the active depth $d$ for a sensor tilted in column direction:

$\textrm{column cluster size}=\frac{d\tan{\alpha}}{\textrm{pitch}}+s_{0},$ (1)

where $s_{0}$ is the cluster size in column direction for no rotation
($\alpha=0$). The active depth is extracted with a linear fit to the mean
cluster size as a function of the tangent of the rotation angle, as
exemplified in Fig. 17 for the pixel flavour with continuous n-implant using
sensors with different sensor thicknesses. The model neglects charge sharing
that is not induced by rotation, i.e. charge sharing via diffusion is not
accounted for. Since the cluster size at small rotation angles is dominated by
diffusion effects, data points below $40^{\circ}$ are excluded from the fit
[27]. The effect of diffusion-induced charge sharing is considered in the
systematic uncertainties by repeating the fit with varied fit ranges.

The fit results for both pixel flavours are summarised in Table 3. For all
sensor types, the estimated active depth of about
$30\text{\,}\mathrm{\SIUnitSymbolMicro m}$ is larger than the depletion depth
of $21\pm$1\text{\,}\mathrm{\SIUnitSymbolMicro m}$$ expected from simulation
studies [28]. A non-negligible contribution of charge carriers from the
undepleted region is possible, since there is still a residual electric field
below the depletion line.

The estimated active depth agrees well with the nominal thickness of the
epitaxial layer, which indicates that charge carriers from the undepleted low-
resistivity substrate are negligible due to their small lifetime. Only the
active depth for the $40\text{\,}\mathrm{\SIUnitSymbolMicro m}$ sensor is
clearly smaller compared to the other sensors, which is in agreement with the
results from the previous sections, where the reduced signal was attributed to
the removal of active material.

Table 3: Active depth ($d$) for both pixel flavours (Fl.) and different sensor thicknesses (Thickn.). Fl. | Thickn. [$\text{\,}\mathrm{\SIUnitSymbolMicro m}$] |  $d$ [$\text{\,}\mathrm{\SIUnitSymbolMicro m}$]
---|---|---
C | 300 | $31.4\pm 0.1\textrm{ (stat.)}^{+0.2}_{-2.4}\textrm{ (syst.)}$
C | 100 | $30.7\pm 0.1\textrm{ (stat.)}^{+0.3}_{-1.8}\textrm{ (syst.)}$
C | 50 | $29.4\pm 0.1\textrm{ (stat.)}^{+0.9}_{-1.0}\textrm{ (syst.)}$
C | 40 | $26.2\pm 0.1\textrm{ (stat.)}^{+0.8}_{-1.0}\textrm{ (syst.)}$
S | 300 | $30.8\pm 0.2\textrm{ (stat.)}^{+0.4}_{-1.2}\textrm{ (syst.)}$
S | 50 | $29.8\pm 0.1\textrm{ (stat.)}^{+0.6}_{-1.0}\textrm{ (syst.)}$

It can be concluded that the CLICTD sensors with an epitaxial layer of
$30\text{\,}\mathrm{\SIUnitSymbolMicro m}$ can be thinned down to a total
thickness of $50\text{\,}\mathrm{\SIUnitSymbolMicro m}$ without suffering from
a significant loss in sensor performance. Assuming that a MIP generates on
average about 65 – 80 electron-hole pairs per micrometer [29], the expected
signal evaluates to about 2000 – 2400 e for an active depth of approximately
$30\text{\,}\mathrm{\SIUnitSymbolMicro m}$. For thinner sensors, performance
degradations emerge due to the removal or damage of the active sensor volume.

Figure 17: Mean cluster size in column direction as a function of the tangent
of the rotation angle for a sensor with epitaxial layer and continuous
n-implant. A bias voltage of -6 V/-6 V was applied to the p-well/substrate.

Unlike for sensors with epitaxial layer, the depletion for the Czochralski
substrate is not limited in depth by the thickness of the epitaxial layer. The
increased depletion region gives access to a larger active sensor volume, as
illustrated in the measurements shown in Fig. 18, where the active depth as a
function of the substrate voltage is depicted for a Czochralski sensor with
segmented n-implant.

The active depth at a substrate voltage of -6 V evaluates to

$34.2\pm 0.1\textrm{ (stat.)}^{+1.5}_{-0.6}\textrm{ (syst.)}$

and is therefore slightly larger compared to the sensors with epitaxial layer.
With higher absolute substrate voltages, the active depth increases and
reaches

$65.4\pm 0.1\textrm{ (stat.)}^{+0.5}_{-0.7}\textrm{ (syst.)}$

at a substrate voltage of -16 V. At this voltage, the active depth is more
than twice as large as the depth for the sensors with epitaxial layer
resulting in a significant increase in signal, which is expected to be around
4200 – 5200 e. The higher signal translates into a better performance as shown
in the previous section.

However, the improvement is limited by the front-end, which is not optimised
for the large signal generated in the thick Czochralski substrate.

Figure 18: Active depth as a function of the substrate bias voltage for a
sensor with Czochralski substrate with segmented n-implant.

##  6 Summary & Outlook

The performance, charge-sharing properties and the active sensor depth were
investigated for the small collection-electrode monolithic CMOS sensor CLICTD.
Different thicknesses for samples with a thin epitaxial layer were studied and
the performance was found to be similar for sensors between
$50\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and
$300\text{\,}\mathrm{\SIUnitSymbolMicro m}$. Sensors thinned down to
$40\text{\,}\mathrm{\SIUnitSymbolMicro m}$ exhibited a degradation in
performance, which was attributed to a smaller active sensor depth as
determined by grazing angle measurements. The active depth of the thicker
sensors was found to correspond to the nominal thickness of
$30\text{\,}\mathrm{\SIUnitSymbolMicro m}$ of the epitaxial layer.

To achieve a larger active depth and thus a higher signal, CLICTD sensors
fabricated on $100\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick Czochralski
substrate were tested and a twofold increase in active depth was found using a
substrate bias voltage of -16 V. The total signal is expected to double as
well and is shared among more pixel cells. As a consequence, an improvement of
approximately $15\text{\,}\mathrm{\char 37\relax}$ in spatial and
$14\text{\,}\mathrm{\char 37\relax}$ in time resolution was determined in
combination with an improved efficiency at high detection thresholds. The
design of the front-end would have to be modified in order to exhaust the full
potential of the Czochralski substrate.

The sensor performance was also evaluated for inclined particle tracks and an
improved performance was found due to the longer particle path through the
active sensor volume resulting in a higher signal. The spatial resolution has
an optimum at an inclination angle of $40^{\circ}$, where it evaluates to
$3.6\pm$0.2\text{\,}\mathrm{\SIUnitSymbolMicro m}$$ after $\eta$-correction.

## Acknowledgements

The authors would like to thank the STREAM network for providing the high-
resistivity wafer material and coordinating the sensor production.

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). This project has received funding from the European Union’s Horizon
2020 research and innovation programme under grant agreement No 654168 and
under the Marie Skłodowska-Curie grant agreement No 675587 STREAM. This work
has been sponsored by the Wolfgang Gentner Programme of the German Federal
Ministry of Education and Research (grant no. 05E15CHA). This work was carried
out in the framework of the CLICdp Collaboration.

## CRediT authorship statement

R. Ballabriga Resources J. Braach Investigation E. Buschmann Investigation M.
Campbell Methodology, Resources D. Dannheim Investigation, Methodology,
Supervision, Writing - Review & Editing K. Dort Formal analysis,
Investigation, Software, Visualization, Writing - Original Draft L. Huth
Investigation, Software I. Kremastiotis Investigation, Resources J. Kröger
Investigation, Software L. Linssen Project administration, Funding acquisition
M. Munker Investigation, Methodology, Supervision W. Snoeys Conceptualization,
Resources S. Spannagel Investigation, Software P. Švihra Writing - Review &
Editing T. Vanat Investigation, Resources

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