###### Abstract

The Wavelength-shifting Optical Module (WOM) is a novel photosensor concept
for the instrumentation of large detector volumes with single-photon
sensitivity. The key objective is to improve the signal-to-noise ratio which
is achieved by decoupling the photosensitive area of a sensor from the cathode
area of its photomultiplier tube (PMT). The WOM consists of a transparent tube
with two PMTs attached to its ends. The tube is coated with wavelength-
shifting paint absorbing ultra-violet photons with nearly 100% efficiency.
Depending on the environment, e.g. air (ice), up to 73% (41%) of the
subsequently emitted optical photons can be captured by total internal
reflection and propagate towards the PMTs where they are recorded. The optical
properties of the paint, the geometry of the tube and the coupling of the tube
to the PMTs have been optimized for maximal sensitivity based on theoretical
derivations and experimental evaluations. Prototypes were built to demonstrate
the technique and to develop a reproducible construction process. Important
measurable characteristics of the WOM are the wavelength dependent effective
area, the transit time spread of detected photons and the signal-to-noise
ratio. The WOM outperforms bare PMTs especially with respect to the low
signal-to-noise ratio with an increase of a factor up to 8.9 in air (5.2 in
ice). Since the gain in sensitivity is mostly in the UV-regime, the WOM is an
ideal sensor for Cherenkov and scintillation detectors.

###### keywords:

neutrino detectors; photon detection; wavelength-shifting; UV sensitivity; low
noise; large sensitive area; photomultiplier tubes

xx 1 5 Received: date; Accepted: date; Published: date The Wavelength-shifting
Optical Module Benjamin Bastian-Querner1 ,Lucas S. Binn2, Sebastian Böser2 ,
Jannes Brostean-Kaiser1,3, Dustin Hebecker1,3 , Klaus Helbing4 , Timo Karg3 ,
Lutz Köpke2, Marek Kowalski1,3 , Peter Peiffer2, Anna Pollmann4* , John Rack-
Helleis2 , Martin Rongen2 , Lea Schlickmann2 , Florian Thomas2 , Anna Vocke2
Benjamin Bastian-Querner, Lucas S. Binn, Sebastian Böser, Jannes Brostean-
Kaiser, Dustin Hebecker, Klaus Helbing, Timo Karg, Lutz Köpke, Marek Kowalski,
Peter Peiffer, Anna Pollmann, Yuriy Popovych, John Rack-Helleis, Martin
Rongen, Lea Schlickmann, Nick Jannis Schmeisser, Florian Thomas, Anna Vocke
Correspondence<EMAIL_ADDRESS><EMAIL_ADDRESS>
##  1 Introduction

Many detectors for rare events in particle and astroparticle physics require
large interaction volumes, ranging up to cubic kilometers, in order to achieve
a reasonable detection rate. However, the larger the volume, the smaller the
feasible density of instrumentation. A viable method to read out detectors
with transparent target media is the detection of optical photons emitted by
incident particles (or their secondaries) in form of Cherenkov emission or
scintillation light. The prevailing sensor type, which is capable of detecting
_single photons_ , are photomultiplier tubes (PMT). They are, for example,
deployed in neutrino telescopes, neutrino detectors and dark matter
experiments such as IceCube Aartsen and et al (2017), Super-Kamiokande Fukuda
and et al (2003), Borexino Alimonti and et al (2009), SNO Boger and et al
(2000), JUNO An and et al (2016), XENONAprile and et al (2012), LUX Akerib and
et al (2013), DARWIN Aalbers and et al (2016), and many others. The
photosensitive area of the PMT scales approximately linearly with the area of
its photocathode, so does the dark current – the dominant source of noise. The
peak quantum efficiency of conventional PMTs is around $450\,\mathrm{nm}$
which is suboptimal for Cherenkov light as well as for scintillation emissions
from common liquid scintillators based on linear alkylbenzene (LAB) at
approximately $340\,\mathrm{nm}$ Tseung and Tolich (2011), or liquid noble
gases such as Xenon or Argon at around $178\,\mathrm{nm}$ and
$128\,\mathrm{nm}$, respectively.

Figure 1: A schematic drawing of the WOM. UV photons are absorbed in the WLS
paint layer and are re-emitted as optical photons. If the emission angle of
the photons is larger than the critical angle, they are trapped by total
internal reflection and are guided along the tube to small, low-noise PMTs.

The Wavelength-shifting Optical Module (WOM) has been developed as an
alternative sensor for large volume detectors. The WOM, schematically shown in
Figure 1, consists of a transparent tube with photosensors attached to its
ends. The tube is coated with a paint containing wavelength-shifting (WLS)
organic luminophores and acts as a light collector. The delayed isotropic
emission of the WLS molecules circumvents the conservation of phase space as
required by Liouville’s theorem (etendue), that otherwise forbids the
concentration of a homogeneous light distribution on a smaller area using
refractive and reflective optics.

The performance of the WOM is determined by a number of efficiency factors
which are discussed throughout this work. The overall efficiency of the WOM
$\epsilon_{\mathrm{tot}}$ is defined as the number of detected photons $N_{\rm
det}$ compared to the number of incident photons $N_{\rm inc}$ as follows:

$\displaystyle\epsilon_{\mathrm{tot}}=\frac{N_{\rm det}}{N_{\rm
inc}}=\epsilon^{\mathrm{WLS}}_{\mathrm{LY}}\left(\lambda_{\rm
inc}\right)\cdot\epsilon_{\mathrm{TIR}}\left(x_{0}\right)\cdot\epsilon_{\mathrm{TP}}\left(z\right)\cdot\epsilon^{\mathrm{PMT}}_{\mathrm{QE}}\left(\lambda_{\rm
em}\right)\cdot\epsilon_{\mathrm{IF}}\cdot\epsilon_{\mathrm{TM}}\left(\lambda_{\rm
inc}\right)$ (1)

UV photons incident on the WLS tube are absorbed in the paint layer and re-
emitted isotropically as optical photons with the light yield
$\epsilon^{\mathrm{WLS}}_{\mathrm{LY}}$. This efficiency depends on the
wavelength of the incident photons $\lambda_{\rm inc}$ as well as the
thickness of the paint layer $d$ and the concentration of wavelength-shifting
molecules $c_{\rm WLS}$. Values close to unity can be achieved over a large
part of the absorption spectrum. A fraction $\epsilon_{\mathrm{TIR}}$ of the
re-emitted photons has an angle with the tube wall smaller than the critical
angle for total internal reflection (TIR). The radial symmetry of the
configuration ensures that the photon incidence angle on the surface remains
constant for each interaction. Therefore subsequent surface interactions also
fulfill the TIR criterion, such that the photons are trapped and guided
towards the ends of the tube, see Figure 2. The TIR fraction
$\epsilon_{\mathrm{TIR}}$ depends on the fraction of the tubes radius $x_{0}$,
at which the photons are emitted, as well as on the refractive indices of the
tube $n_{\rm tube}$ and the environment $n_{\rm env}$ which define the
critical angle.

While the captured photons are propagating towards the ends of the tube, they
can be absorbed or scattered out of the material. This attenuation effect,
denoted as $\epsilon_{\mathrm{TP}}$, depends on the distance $z$ between the
emission point and the end of the tube as well as the scattering $\lambda_{\rm
scatt}$ and absorption length $\lambda_{\rm abs}$ (merged into the attenuation
length $\lambda_{\rm att}$). Attached to the tube are PMTs which are
characterized by their wavelength dependent quantum efficiency
$\epsilon_{\mathrm{QE}}^{\mathrm{PMT}}$ which depends on the wavelength of the
re-emitted photons $\lambda_{\mathrm{em}}$. A small fraction of photons is
lost at the tube-PMT interface denoted as $\epsilon_{\mathrm{IF}}$.

In some environments it is necessary to encapsulate the WOM with a housing,
e.g. in deep water or ice to protect the WOM from pressure. The probability
for transmission into the housing through an optional filling into the WOM
$\epsilon_{\mathrm{TM}}$ depends on the wavelength $\lambda_{\rm inc}$ of the
incident photons and the refractive indices $n_{\rm env},n_{\rm
housing},n_{\rm fill}$ of the materials enclosing the WLS tube.

All these efficiencies, described above, are used to characterize the WOM in
this paper. As a baseline in this paper, the following _prototype design_ is
discussed: the tube, coated on the inside surface with wavelength-shifting
paint, is $700\text{\,}\mathrm{mm}$ long, made of quartz Her (2021) with an
outer diameter of $60\text{\,}\mathrm{mm}$ and a wall thickness of
$2.5\text{\,}\mathrm{mm}$. Two 3.5 inch PMTs Ham (2021) are attached to the
ends with optical gel Elj (2021). An optional quartz pressure vessel111The
dimension of this pressure vessel are given by availability in the laboratory.
The dimensions of the WOM tube and the PMT diameters are derived from these.
is added around the WOM with $1200\text{\,}\mathrm{mm}$ length,
$110\text{\,}\mathrm{mm}$ outer diameter and $10\text{\,}\mathrm{mm}$ wall
thickness. Dimensions and materials of any setup discussed in this text
corresponds to this prototype design – apart from a few exceptions which are
described accordingly.

In this paper, the different optical processes required to describe and
optimize the WOM efficiency are discussed in Section 2. The optimized
production of the main component of the WOM, the coating of the wavelength-
shifting tube, is described in Section 3. Finally, characterization and
performance measurements of the WOM are presented in Section 4.

##  2 Performance factors

The efficiencies of the WOM components, which make up the overall efficiency
of the WOM, introduced in Equation 1, are derived in this chapter.

###  Section 2.1 Total internal reflection

Figure 2: Visualization of several photons paths propagating in the wall of
the WOM tube simulated with a GPU-based ray tracing algorithm Thomas (2019).
The photons are generated inside the paint layer of the tube in response to
the incident UV photon(s) (blue). Their attenuation probability depends on the
effective path length which in turn depends on the emission angle. With the
inset a UV photon (blue) is shown, which is absorbed and re-emitted in the
material (green) or lost (red). The critical angle for the re-emitted photon
defines a _loss cone_ (grey dashed lines).

The concept of the WOM evolves around the idea of total internal reflection of
photons if the difference of refractive indices between the tube $n_{\rm
tube}$ and the surrounding environment $n_{\rm env}$ is large222Since a hollow
tube is coated on one surface side, it is the lower of the refractive indices
of the wavelength-shifting paint $n_{\rm paint}$ and the coated substrate
$n_{\rm substrate}$ that determines the critical angle, i.e. $n_{\rm
tube}={\rm min}(n_{\rm paint},n_{\rm substrate})$. Using the Fresnel equation
for the reflectivity of an electromagnetic wave $R(\theta,n_{\rm paint},n_{\rm
env})$ for a re-emitted photon incident on the surface, the fraction of
captured photons after $N$ interactions with the surface can be determined as

$\epsilon_{\rm TIR}=\frac{1}{2}\int\left(R(\theta,n_{\rm paint},n_{\rm
env})\right)^{N}\sin\theta\,d\theta$ (2)

where $\theta$ is the angle of the photon trajectory $\vec{p}$ to the surface
normal $\vec{n}$, thus $\cos\theta=\vec{p}\cdot\vec{n}$. In contrast to
mirroring surfaces that achieve typical average reflectance of 90-99% if
employed over larger wavelength range, the TIR above the critical angle
$\sin\theta_{\rm crit}={n_{\rm env}}/{n_{\rm tube}}$ reaches 100% reflectance
independent of the wavelength. In the limit of a large number of interactions,
the reflectance $R$ can be approximated by a step-function $\Theta$ and
Equation 2 simplifies to

$\lim\limits_{N\to\infty}\varepsilon_{\rm
TIR}=\frac{1}{2}\int\Theta(\cos\theta-\cos\theta_{\rm
crit})\sin\theta\,d\theta=\cos\theta_{\rm crit}$ (3)

The critical angle thus defines two sharp loss cones while all other photons
are captured, see Figure 2. In the configurations discussed here, neither the
tube material nor the wavelength-shifting paint or surrounding environment
exhibit strong dispersion, so that $\epsilon_{\rm TIR}\simeq 73\,\mathrm{\%}$
($\theta_{\rm crit}\simeq 43.2^{\circ}$) for a WOM tube
(${n_{\mathrm{tube}}}\simeq 1.46$) operated in air ($n\simeq 1.0$) and
$\epsilon_{\rm TIR}\simeq 41\,\mathrm{\%}$ ($\theta_{\rm crit}\simeq
65.6^{\circ}$) for a WOM tube operated in water ($n\simeq 1.33$). The surface
curvature given by the radius of the tube $r_{\rm tube}$ has been neglected
which is a good approximation as long as the radius of the emission point
$r_{\rm em}$ is close to the surface $r_{\rm tube}-r_{\rm em}\ll r_{\rm tube}$
(denoted as _no-curvature_ approximation later on). In resorting to the ray-
like description of reflectance, evanescence was also neglected which is a
good approximation as long as the emission point is further away from the
surface than the typical wavelength $r_{\rm tube}-r_{\rm em}\gg\lambda_{\rm
em}$. Both conditions are well satisfied in the given configuration with
typical emission wavelength of
$400\text{\,}\mathrm{nm}500\text{\,}\mathrm{nm}$, coating thicknesses $r_{\rm
tube}-r_{\rm em}$ in the range of several micrometers and tube radii $r_{\rm
tube}$ of several centimeters. The TIR efficiency $\epsilon_{\rm TIR}$ is thus
independent of the tube radius $r_{\rm tube}$ in good approximation.

Figure 3: Illustration of the solid angle under which the photons are captured
as a function of the relative fraction of the radius
$x_{0}={\left|\vec{r}\right|}/{R}$ at which the photons are emitted (indicated
by the yellow dot). The orange (blue) line in the upper plot indicates photons
that encounter the surface under the critical angle as a function of the
azimuth angle $\phi$ ($\phi_{0}$) relative to the emission point (center of
the cylinder). In the upper and middle plots the blue shaded areas indicate
solid angle regions under which photon trajectories captured by total internal
reflection while red shaded areas show those that are not captured. In the
middle plot yellow arrows indicate directions of incident photons, while green
arrows depict surface normals. In this example, the critical angle is chosen
as $\theta_{c}={\pi}/{4}$.

While the general working principle of the WOM is similar to that of a
wavelength-shifting fiber, the different geometry makes a noteworthy
difference in the fraction of photons that can be captured by total internal
reflection. Following a purely geometrical argument, there is no difference
between a hollow tube and a solid cylinder, as for any photon trajectory the
incidence angle on the inner surface of a hollow tube will always be larger
than the incidence angle on the outer surface. Total internal reflection in
the first interaction on the outer surface is thus a fully sufficient
criterion to determine whether a photon is captured and guided along the tube.
In a full cylinder the no-curvature approximation $r_{\rm tube}-r_{\rm em}\ll
r_{\rm tube}$ no longer applies and Equation 3 needs to be generalized to

$\varepsilon_{\rm
TIR}=\frac{1}{4\pi}\int\Theta(\left|\vec{p}\cdot\vec{n}\right|-\cos(\theta_{\rm
crit}))\,d\Omega$ (4)

If the emission point $\vec{r}_{\rm em}$ sits in the center of the cylinder -
as would approximately be the case in a wavelength-shifting fiber - this
results in two symmetrical _capture cones_ along the symmetry axis of the
fiber while most of the photons are lost even for large values of $\theta_{\rm
crit}$ (left-most case in Figure 3). As the emission point is moved outward by
a fraction $x_{0}={r_{\rm em}}/{r_{\rm tube}}$, the incidence angle for
photons orthogonal to the offset vector of the emission point
$\vec{p}\perp\vec{r}_{\rm em}$ increases, thus increasing the overall capture
fraction. Moving the emission point out to
$x_{o}=\sin\left(\theta_{c}\right)$, even horizontal photons
$\vec{p}\perp\vec{r}_{\rm em}\perp\vec{z}$ also perpendicular to the cylinder
axis $\vec{z}$ subtend an angle larger than the critical angle with the
surface, so that under some azimuthal angle all photons are captured
independent of their polar angle. This region is maximized for emission on the
surface, $\lim x_{0}\to 1$, where again only the two cones around the surface
normal vector are lost. This is the edge-case depicted in Figure 2 close to
which the WOM is operated. In Figure 5 the fraction of the solid angle
$\epsilon_{TIR}$ is shown under which the light is captured in the first
surface interaction. For the ease of handling and to protect the coating from
the environment, the coating is applied on the inside of the prototype
discussed here. In this case, $x_{o}$ and thus the wall thickness of the tube
become a relevant parameter. For the particular geometry of the prototype
significant losses due to $x_{0}$ only occur if the module is immersed in
water or ice.

###  Section 2.2 Light propagation

Once the photons are trapped in the tube, absorption and scattering are the
two mechanisms which contribute to light losses along the photon path with
characteristic lengths $\lambda_{\rm abs}$ and $\lambda_{\rm scatt}$. While
absorbed photons are lost directly, scattered photons may no longer be
confined by total internal reflection, leading to a total attenuation
characterized by the attenuation length ${\lambda_{\rm att}}$. Both
attenuation mechanisms depend on the photon path length which in turn depends
on the initial emission direction (see Figure 2).

Using the no-curvature approximation from above as basis, the path length
distribution can be described in an analytical model – the so-called flattened
model. Therein, the tube mantle is approximated as a flat rectangle with
periodic boundary conditions on the long sides.333Figuratively, the mantle is
’cut open’, flattened out and photons reaching one of the long sides of the
rectangle enter it again from the opposite side. In addition to the (polar)
surface incidence angle $\theta$, the azimuthal angle $\phi$ is defined, with
$\phi=0$ denoting the direction towards one end of the flattened tube (see
Figure 2). Due to the symmetry of the situation it is sufficient to consider
photons that travel towards one end, limiting $\phi$ to the range
$[-\pi/2,\pi/2]$. In the flattened model, the path length to the end of the
tube becomes $z/(\cos(\phi)\cos(\theta))$ and the one-sided efficiency (i.e.
the fraction of re-emitted photons reaching one end of the tube) is calculated
as

$\displaystyle\epsilon_{\rm one-sided}(z,\lambda_{\rm att}):$
$\displaystyle=\epsilon_{\rm TIR}\cdot\epsilon_{\rm TP}(z,\lambda_{\rm att})$
(5)
$\displaystyle=\frac{1}{4\pi}\,\cdot\,\int_{-\pi/2}^{\pi/2}\,\int_{-\theta_{C}}^{\theta_{C}}\exp\left(-\frac{z}{\cos(\phi)\cos(\theta)\,\lambda_{\mathrm{att}}}\right)\,\cos(\theta)\,d\theta\,d\phi$
(6)

Since $\epsilon^{\mathrm{WLS}}_{\mathrm{LY}}\approx
1\approx\epsilon_{\mathrm{IF}}$ in Equation 1, the one-sided efficiency
becomes the predominant performance measure differentiating the WOM from the
operation of a bare PMT. The shape of this distribution can be seen in Figure
13 where it is fit to measurements.

To verify this simplistic model, it is compared to a _Monte Carlo_ (MC)
simulation of the photon propagation in the tube. The GPU based implementation
incorporates the full 3D geometry as well as an accurate model of absorption
and scattering Thomas (2019), see the visualization in Figure 2. The model and
the simulation agree with less than < 1% deviation for a tube length of
$20\,\mathrm{mm}$ to $1200\,\mathrm{mm}$. Therefore further MC simulation,
used in this work, use the model instead of the GPU simulation.

Figure 4:  Fraction $\epsilon_{\rm TIR}$ of the solid angle under which
emitted photons are captured by total internal reflection as a function of the
offset radius $x_{0}$ of the emission point. The two lines represent a module
immersed in air (solid) or water (dashed). The green dots indicate the
captured efficiency for the prototype module, which is coated on the inside of
tube. Minimal values for the emission point in the center of the tube and
maximal values for emission on the outside of the tube are indicated by
triangles.

Figure 5:  The combined efficiency for WOM operation in ice (or water), air,
and LAB derived by simulating the propagation of $5\cdot 10^{5}$ photons that
are incident isotropically. The maximum achievable efficiency is 38.3 % in ice
at $n\approx 1.32$, 70.3 % in air at $n\approx 1.18$, and 24.5 % in LAB at
$n\approx 1.32$ (refractive index for LAB taken from Ref. Tseung and Tolich
(2011)). For the geometry, the prototype design is used, as specified in
Section 1.

###  Section 2.3 Light transmission

If the WOM is operated in a pressure housing with refractive index
$n_{\mathrm{housing}}$, the transmission of light from the environment with
refractive index $n_{\mathrm{env}}$ into the modules needs to be taken into
account. In order to preserve the UV sensitivity, quartz glass can be used.
The extinction coefficients is less than 0.1 % per centimeter down to a
wavelength of $\lambda_{\rm inc}\sim 180\,\mathrm{nm}$ for fused silica and
down to $\lambda_{\rm inc}\sim 240\,\mathrm{nm}$ for fused quartz Her (2021),
so that the dependence on the photon wavelength $\lambda_{\rm inc}$ can be
neglected in most cases.

There are two processes which compete while optimizing the refractive index of
the filling material $n_{\rm fill}$ between the housing and the WOM tube: (i)
materials with low refractive index will optimize the capture efficiency
$\epsilon_{\rm TIR}$ (see Equation 3) while (ii) they reduce the the
efficiency of photon transmission $\epsilon_{\mathrm{TM}}$ into the module due
to total internal reflection at the housing-filling material boundary. In the
co-planar model with isotropic illumination, the capture efficiency
$\epsilon_{\mathrm{comb}}^{\mathrm{co-planar}}$ is derived from the Fresnel
equations

$\displaystyle\begin{split}\epsilon_{\mathrm{comb}}^{\mathrm{co-
planar}}(n_{\rm env},n_{\rm fill}):&=\epsilon_{\mathrm{TM}}(n_{\rm env},n_{\rm
housing},n_{\rm fill})\cdot\epsilon_{\mathrm{TIR}}(n_{\rm fill},n_{\rm
tube})\\\
&=\int_{0}^{\pi/2}T(n_{\mathrm{env}},n_{\mathrm{housing}},\theta_{\rm
inc})\cdot T(n_{\mathrm{housing}},n_{\mathrm{fill}},\theta_{j}(\theta_{\rm
inc}))\\\
&\qquad\quad\cdot\,T(n_{\mathrm{fill}},n_{\mathrm{tube}},\theta_{k}(\theta_{j}))\sin\theta_{\rm
inc}\,d\theta_{\rm inc}\\\ &\times\cos{\theta_{\mathrm{crit}}}\end{split}$ (7)

where $T(n_{i},n_{j},\theta_{l})$ is the transmission probability at the
interface between two media of refractive indices $n_{i}$ and $n_{j}$ for an
incident angle $\theta_{l}$ determined by Snell’s law on the previous layer.
There is an optimal value for the refractive index of the filling already in
this simplified approach. However, the radii of the cylinders have a non-
negligible impact here because the curved pressure housing can have a focusing
or defocusing effect in the transverse plane and the inner tube could be
missed altogether.

Therefore, in order to find the optimal refractive index of the filling
material for the prototype geometry, the cylindrical geometry of the WOM is
modelled in a MC simulation444In this ray tracing algorithm, written in
Python, photons start from a rectangular plane which is uniformly rotated
around the WOM. The photons are propagated through the WOM surfaces taking
Fresnel losses and angular changes via Snell’s law into account. The number of
photons captured by total inner reflection are counted and divided by the
total number of photons as well as the area of the generation plane to get the
combined capture efficiency., propagating incident photons with Fresnel
equations and Snell’s law in three dimensions. The wavelength dependence of
the refractive indices is negligible and it is assumed that all refractive
indices are fixed at a wavelength of $\lambda=589\,\mathrm{nm}$. The capture
efficiency derived from this simulation is shown in Figure 5 and compared to
the co-planar model. The optimal refractive index of the filling increases
with larger refractive indices of the environment to a maximum at $n\approx
1.32$ with $\epsilon_{\mathrm{comb}}=38.3\%$ for water and ice. For water and
ice, the filling could be ethanol or methanol, which have the disadvantage
that they dissolve the WLS paint, or perfluoropolyether (PFPE), which is
comparatively expensive.

##  3 Coating

In addition to the optimization of the WOM design based on theoretical
considerations, as presented in the previous section, some components are
optimized empirically.

The absorption probability for photons incident on a WLS paint layer is given
by

$\displaystyle\begin{split}\epsilon^{\mathrm{WLS}}_{\mathrm{LY}}&=\left(1-e^{-d\cdot\sigma_{\mathrm{WLS}}(\lambda)\cdot
n(c)}\right)\cdot\epsilon_{\rm QY}^{\rm PL}\\\
&\simeq(1-10^{-\delta_{\mathrm{OT}}})\cdot\epsilon_{\rm QY}^{\rm PL}\\\
&=(1-e^{-{d}/{\lambda_{\rm abs}^{\rm inc}}})\cdot\epsilon_{\rm QY}^{\rm
PL}\end{split}$ (8)

Here, $d$ denotes the distance of a photon travelling inside the WLS matrix –
i.e. the thickness of the coating and $\sigma_{\mathrm{WLS}}(\lambda)$ stands
for the cross section of the wavelength-shifter with incident photons of
wavelength $\lambda$. The number density of WLS particles along the incident
photons path $n(c)$ solely depends on the concentration of WLS in the matrix
$c$. The effectiveness of the light absorption can be expressed either in the
form of an optical thickness $\delta_{\rm OT}(\lambda)$ or in terms of an
absorption length $\lambda_{\rm abs}^{\rm inc}(\lambda)=1/\left(\sigma_{\rm
WLS}(\lambda)\cdot n\right)$. The emission efficiency of the WLS paint is
denoted as $\epsilon_{\rm QY}^{\rm PL}$.

In this chapter, the steps taken along the development of the WLS coating are
outlined as well as the considerations on the coupling of tube and PMT. First
the test setup is presented which was build to aid the optimization as well as
to measure the WOM characteristics presented in the next section.

###  Section 3.1 Test stand

The scope of the test stand is to measure the local sensitivity of a WLS tube
and its timing characteristics. The setup is schematically depicted in Figure
6. In the test stand, a Xenon arc lamp Qua (2022a) serves as light source for
wavelengths between $250\text{\,}\mathrm{nm}700\text{\,}\mathrm{nm}$. The lamp
is coupled to a monochromator Qua (2022b) of which the slit width is set in a
way that the bandwidth of the selected wavelength is
$\sigma_{\lambda}=$1.06\text{\,}\mathrm{nm}$$.

The monochromatic beam is chopped to allow for a signal read out via _lock-in_
amplifier Zur (2021). The chopper frequency is fed into two lock-in amplifiers
which demodulate a PMT signal. Subsequently the light is passing a diffusor
which shapes the beam to a homogeneous Gaussian profile. The beam is split up
by a beam splitter. The reflected fraction of the beam illuminates a reference
photodiode Ham (2022) to correct for lamp intensity variations, while the
transmitted fraction is guided into a dark box to illuminate an WLS-tube using
a liquid light guide Tho (2021). The end of the light guide in the dark box
can be moved along the symmetry axis (the $z_{\mathrm{Tube}}$ position) and
the azimuthal angle $\phi_{\mathrm{Tube}}$555Note that this is a different
definition than the the variable $\phi$ in the flattened model in Equation 6.
The size of the illumination spot is around $1\text{\,}\mathrm{cm}$ in
diameter. Thereby, selected points in $\phi_{\mathrm{Tube}}$ and
$z_{\mathrm{Tube}}$ on the tube surface can be illuminated to determine the
local efficiency. The light is detected at both tube ends using PMTs Ham
(2021). The PMT surface is described in polar coordinates with the radius $r$
and the angle $\psi_{\mathrm{PMT}}$.

Figure 6: Schematic of the WOM test stand with a photograph of the darkbox.

In this _lock-in_ setup, the efficiency of the WOM for a given light source
position and incident wavelength is calculated as

$\displaystyle\epsilon_{\mathrm{lock-
in}}(\lambda,\phi_{\mathrm{Tube}},z_{\mathrm{Tube}})=\frac{I^{\mathrm{corr}}_{\mathrm{sig}}(\lambda,\phi_{\mathrm{Tube}},z_{\mathrm{Tube}})}{\frac{1}{N_{\rm
steps}}\sum_{i}I^{\mathrm{corr}}_{\mathrm{ref}}(\lambda,\psi_{\mathrm{PMT,i}})}\qquad$
(9)

Here $I^{\mathrm{corr}}_{\mathrm{sig}}$ refers to the PMT output current
corrected by the reference diode signal. For the reference measurement, the
light source illuminates the PMT directly. The current
$I^{\mathrm{corr}}_{\mathrm{ref}}$ is measured on the tube radius by varying
$\psi_{\rm PMT}$ in a total of $N_{\rm steps}$ steps around the circumference,
in our case $N_{\rm steps}=36$. The mean of these measurements is calculated
to take the PMT sensitivity variations on the photocathode into account. The
resulting currents of signal and reference measurement are corrected for the
wavelength dependent quantum efficiency of the PMT as well as for intensity
variations of the light source.

An overview of systematic uncertainties on the efficiency determination in the
test stand is given in Ref. Rack-Helleis (2019). The largest uncertainty is
the coupling of the WOM tube to the PMT using optical gel instead of a gel
disc. An overall systematic error of approximately $4\text{\,}\%$ on the
efficiency determination for the prototype tube is obtained. This value was
obtained by repeatedly coupling the tube and PMT with gel to measure the
variance of the one sided efficiency induced by the losses at the interface
$\epsilon_{\rm IF}$. Additionally the variation of the paint layer is taken
into account (compare Figure 11). The values for the currents
$I^{\mathrm{corr}}_{\mathrm{sig}}$ and $I^{\mathrm{corr}}_{\mathrm{ref}}$ are
averaged over a time window of $2\,\mathrm{sec}$ at a chopping frequency of
$120\,\mathrm{Hz}$ and the standard deviation is used as uncertainty.

The described setup can be adjusted for _single photon_ read-out by replacing
Xe-Lamp, monochromator and chopper with a $375\text{\,}\mathrm{nm}$ pico-
second pulser Rongen and Schaufel (2018). The pulser is dimmed so that $\sim
6\text{\,}\%$ of the waveforms recorded with a triggered fast ADC Tel (2021)
include one photon signal within the expected time window. For the _single
photon_ read-out, the collection efficiency of the tube
$\epsilon_{\mathrm{single}}$ is determined by the ratio:

$\epsilon_{\mathrm{single}}=\frac{n_{\mathrm{sig}}(\lambda,\phi_{\mathrm{Tube}},z_{\mathrm{Tube}})-n_{\mathrm{bkg}}}{\frac{1}{\mathrm{N_{\rm
steps}}}\sum_{\mathrm{i}}\left(n_{\mathrm{ref}}(\lambda,\psi_{\mathrm{PMT,i}})-n_{\mathrm{bkg}}\right)}$
(10)

where $n_{\mathrm{sig}}$ denotes the number of photons detected when
illuminating the point $(\phi_{\mathrm{Tube}},z_{\mathrm{Tube}})$ with
wavelength $\lambda$. The number of photons detected when directly
illuminating the PMT is denoted by $n_{\mathrm{ref}}$ and $n_{\mathrm{bkg}}$
is the number of photons falsely reconstructed from background light. The
stability of the pulser has been measured over a $12\text{\,}\mathrm{h}$
cycle, and the light output variance was found to be smaller than
$2\text{\,}\%$, thus a subdominant contribution to the overall systematic
error . The statistical error is calculated based on the number of measured
photons $n$ for each measurement. Since the same systematics as in the lock-in
amplifier setup apply, the estimated systematic error for this setup amounts
to approximately $4\text{\,}\%$.

###  Section 3.2 Chemical composition

Wavelength-shifting is a special case of photofluorescence. The WLS molecules
are excited when absorbing short wavelength photons. After a decay time on the
order of $1\text{\,}\mathrm{ns}2\text{\,}\mathrm{ns}$ Kuzniak and Szelc (2020)
depending on the specific wavelength-shifter, the molecule returns to the
ground state and a photon of larger wavelength is emitted. A fraction of the
energy is dissipated non-radiatively.

The WLS paint for the WOM is selected from a large number of variants with
regard to the following criteria as treated in detail in Ref. Hebecker (2014):

  * •

maximal overlap of the emission spectrum and the sensitivity of the readout
PMT

  * •

large Stokes shift, i.e. minimal overlap of the absorption and emission
spectrum

  * •

maximal transparency of the WLS paint for re-emitted photons

  * •

similar refractive index of the coating and the WLS tube material

  * •

good adhesiveness and mechanical properties

  * •

optical thickness to enable reaching high concentration of WLS film to absorb
100% of the light for a broad spectrum

Best results are obtained with a solution of Toluene containing 213 g/l of the
plastic polyethylmethylacrylate (PEMA) Pre (2021), which provides the matrix
for the wavelength-shifting molecules, and a wavelength-shifting dye mix of
1.3 g/l Bis-MSB and 2.6 g/l p-Terphenyl per liter666The proportions given
apply to the mixing process of the paint. In the paint layer of a coated tube,
proportions differ as the toluene evaporates during drying.. The absorption
spectrum of p-Terphenyl lies well below the Bis-MSB absorption spectrum. Since
the emission spectrum of p-Terphenyl lies within the absorption spectrum of
Bis-MSB, adding p-Terphenyl yields a sensitivity enhancement in the lower UV
region.

###  Section 3.3 Coating process

For the tube material, PMMA (Polymethylmethacrylate) and quartz glass are
considered due to their optical properties with attenuation lengths for
photons of multiple metres Beise (2019); Her (2021). PMMA and PEMA are both
soluble in toluene, which yields a transit region in which the two materials
are mixed. This guaranties a strong bond, able to withstand shearing forces
generated by the different coefficients of thermal expansion over a wide
temperature range. Since quartz glass is not soluble in toluene, the paint is
bonded by van der Waals forces only.

Since the bond between quartz glass and the paint is purely of van der Waals
nature, any contamination on the tube surface affects the bonding strength of
the paint. When the tube surface is treated with a sequence of citric acid,
acetone and isopropanol, we find good adhesion in the subsequent coating. An
alternative method is the usage of caustic soda and cleaning agent Car (2021).
Both methods yield satisfying results. Current versions of coated quartz tubes
have proven to be stable over time. We found no signs of delamination in
several freezing cycles. Additionally, no significant deterioration of the
paint layer when exposed to laboratory light was observed.

The coating can be applied to the inside or outside of the cylinder. It is
also possible to coat both sides, but generally high enough absorptivity for
the incident UV light can be obtained with a single coating. Some major
differences between in and outside coating are summarized as follows:

  * •

Coating on the inside shifts the light emission point towards the center,
resulting in a reduced capture efficiency, as discussed in Section 2.1. The
performance loss will increase with the thickness of the tube and the
refractive index of the environment in which the coated tube is deployed.

  * •

While quartz glass has high transmission down to wavelengths of
$180\text{\,}\mathrm{nm}$, PMMA is generally opaque to light below
$300\text{\,}\mathrm{nm}$ Abdel-Mottaleb and Ahmed (2009) but in commercial
products it is often doped with additional UV-absorbers to reduce aging in sun
light, thus limiting the UV light yield. Quartz glass can therefore be coated
on either side, while PMMA performs best when coated outside.

  * •

Coating a tube on the inside allows for easier handling. Impurities such as
fat or dirt act as scattering centers for photons travelling inside the tube.
Under UV light illumination, contaminated areas are clearly visible presumably
because photons couple out of the tube at these sites. The WLS paint is
hydrophilic and therefore delaminates as a whole when immersed in water
rendering the tube opaque to light.

  * •

In an assembly, an inside coated tube will not interact chemically with the
medium surrounding it, allowing for the surrounding medium to be chosen
freely. While embedding the module in a housing can alleviate the problem in a
similar way for outside coated tubes, a filling material is in general
required between the housing and the tube (see Figure 5), transferring the
problem to chemical compatibility with the filling material.

Figure 7: Profilometer measurements of two different paths on a slide, coated
with the wavelength shifter, are shown. In each row the measured profile is
shown on the left and a 3 dimensional profile is shown in the middle. The path
in the bottom row comprises a scratch in order to measure the thickness of the
coating. A photograph of this slide is shown on the far right in which the
approximate measurement points are indicated.

In order to apply coatings to tubes, two simple techniques have been
developed, which are both based on the industrially employed dip-coating
method Brinker (2013); Rio and Boulogne (2017). For an external coating, the
tube is vertically immersed in the paint and removed at a controlled speed, to
yield a homogeneous coating of adjustable thickness. Plugs are used to keep
the inside of the tube paint free. In order to achieve an internal coating,
the tube is filled completely with paint which is then released at a constant
flow rate using a valve. Due to the viscosity of the WLS solution, a higher
velocity of extracting the paint in the coating process leads to a thicker
paint layer (see Equation 11). Both coating procedures are performed at a
temperature of $20\pm 1\text{\,}\mathrm{\SIUnitSymbolCelsius}$ and the tubes
stay immersed in the paint for $90\text{\,}\mathrm{s}$ before paint or tube
are extracted at a fixed velocity. Both processes are operated in the Landau-
Levich-Derjaguin (LLD) regime Derjaguin (1993) where for sufficiently high
viscosity $\eta$ and coating speed $v_{\rm coating}$ the wet-film thickness is
given as Brinker (2013); Rio and Boulogne (2017)

$d_{0}=0.8\cdot\sqrt{\frac{v_{\rm coating}\eta}{\rho g}}$ (11)

Here $\rho$ denotes the density of the paint and $g$ is the gravitational
acceleration. As the solvent evaporates, a dry film of constant thickness
$d=\epsilon_{d}\cdot d_{0}$, with $\epsilon_{d}={\rho_{\rm PEMA}}/{\rho_{\rm
paint}}=0.198$ is deployed on the surface. The relative factor $\epsilon_{d}$
corrects for the paints density before and after coating. Besides its
simplicity, it is found that these methods yields excellent surface quality.
Using profilometer measurements on microscope slides coated with this
technique, a small-scale surface roughness of $<5\,{\rm nm}$ and a wavyness of
$50-100\,{\rm nm}$ on scales of $10\,\mu\mathrm{m}$ was found, see Figure 7.

Figure 8: Absorption efficiency for different coating velocities
$v_{\mathrm{coating}}$ and concentrations $c$ of Bis-MSB in a WLS paint
mixture of $400\,\mathrm{ml}$ anisole and $85.1\,\mathrm{g}$ PEMA (the second
WLS was not used here). The methodology of the experiment is described in Ref.
Hebecker (2014). Shown in purple are fits to the different absorption
efficiencies using Equation 8 multiplied by a normalization constant.

Figure 9: One-sided efficiency at $375\text{\,}\mathrm{n}\mathrm{m}$ versus
the coating speed for quartz tubes and PMMA tubes. Efficiencies are read out
by a PMT 150 mm away from the illumination point. The solid lines show a fit
with the thickness and absorption model from Equations 8 and 11.

In Figure 9 the effect of the variation of coating velocity
$v_{\textrm{coating}}$ and concentration of the wavelength-shifter Bis-MBS
$c_{\textrm{Bis-MBS}}$ on the absorption of the paint layer as a function of
the wavelength is shown. To verify, that the absorption efficiency follows
Equation 8, we use the $\sigma_{\mathrm{WLS}}(\lambda)$ dependency from the
lowest absorption curve to estimate the optical depth for the other coating
speeds and concentrations. Fit and data values are in good agreement.
Comparing the different variations, it can be observed that high paint layer
thicknesses lead to an overall broadening of the absorption spectrum up to a
maximum where all incident photons are absorbed. In this way, the absorptive
properties of the WLS paint can be optimized.

In Figure 9, the relative light yield of PMTs at the end faces of quartz and
PMMA tubes coated on the outside is shown as a function of the coating
velocity. The incident light has a wavelength of $375\text{\,}\mathrm{nm}$.
For quartz the same tube is coated, measured and the coating removed again.
This procedure is repeated at different velocities and twice for the highest
velocity. For PMMA tubes the coating can not be removed, so a different
individual PMMA tube is coated for each measurement. As soon as nearly
complete absorption of the injected light is achieved, a further increase in
the coating thickness yields no further increase in efficiency. For the
highest velocity, the two efficiencies obtained in the two coatings of quartz
glass differ by significantly less than the measurement error, indicating that
the coating process is well reproducible. In comparison, the results achieved
for PMMA tubes show a larger spread and significantly lower efficiency values
(see Figure 9), indicating a less reliable coating process. The larger value
simultaneously obtained for the absorption length for incident light
$\lambda^{\rm inc}_{\rm abs}$ possibly suggests that the tube surface is
partly dissolved by the toluene in the coating process, thus locally diluting
the wavelength-shifter concentration.
The obtained absorption length $\lambda^{\rm inc}_{\rm abs}$ for quartz can be
transformed into an optical depth using Equation 8 and the estimated paint
thickness of $2\times 17\,$$\text{\,}\mathrm{\SIUnitSymbolMicro m}$ (paint
layer on both sides of the tube contribute) to be
$\delta_{\mathrm{OT}}=1.83\pm 0.30$. This number lies well within the
different optical thicknesses obtained in Figure 9.

In Figure 11 a measured relative efficiency over half the surface of a quartz
tube is shown. The current $I_{\mathrm{sig}}(z,\phi)$ is measured in steps of
$10^{\circ}$ in azimuth angle $\phi$ and $10\text{\,}\mathrm{mm}$ in cylinder
height $z$. The intensity value at a given position $z$ is divided by the
corresponding value at $\phi=0$. Concluding an overall relative variation of
the paint layers efficiency of $\pm 5\text{\,}\%$ was obtained.

Figure 10: A 2D-scan of the relative efficiency of a quartz tube. For a given
longitudinal position, the efficiency is relative to the corresponding value
at $0^{\circ}$, in order to correct for the longitudinal intensity dependence.
The angular variation of the efficiency is less than $\pm 5\,\mathrm{\%}$.

Figure 11: Absorption (green) and emission spectrum (red) of a WLS-coated
quartz slide. The light yield efficiency
$\epsilon_{\mathrm{LY}}^{\mathrm{WLS}}$ measured on the prototype tube is
shown in blue and orange. The methodologies of the experiments are described
in Refs. Binn (2018); Hebecker (2014).

###  Section 3.4 Absorption and emission

In order to measure the properties of the WLS coating, quartz microscope
slides were coated with a thin film of WLS paint. The coated slides were then
illuminated by a 365 nm UV LED focused on the paint layer. The angular
distribution of the emission was measured in the UV band ($\lambda$ = 365
$\pm$ 10 nm) to test for a complete absorption of the UV light, as well as in
the optical range ($\lambda$ = 450 $\pm$ 40 nm) to investigate the re-
emission. In Figure 11 the measured absorption and emission spectrum of the
WLS paint are shown together with an absorption measurement of a fully coated
quartz tube.

Between $280\text{\,}\mathrm{nm}$ and $400\text{\,}\mathrm{nm}$, the paint is
around $92.7\text{\,}\%$ absorptive for a sufficiently thick paint layer. The
overlap between absorption and emission spectrum is a small band between
$400\text{\,}\mathrm{nm}420\text{\,}\mathrm{nm}$. Therefore, by calculating
the overlap, a re-emission and consecutive capture probability of
$99.61\text{\,}\%$ is expected in air. The emission spectrum peaks around
$440\text{\,}\mathrm{nm}$, which is the high quantum efficiency region for
standard PMTs that have a borosilicate window and a bialkali photocathode.

###  Section 3.5 Deterioration

The setup described in Section 3.4 was further used to explore possible
deterioration of the paint layer due to high UV exposure. It is found that
focusing the light output of the diode with 100 mW on a spot size of 1 mm2
over several hours leads to a deterioration of the paint layer. A diffuse
illumination of the entire slide with 1250 mm2 using the same light intensity
shows no damaging effect on a time scale of days. In conclusion, with a damage
threshold on the order of mW/mm${}^{2}\times$h deterioration of the paint due
to illumination is not a limiting factor. The UV light intensity in detector
experiments, in which the WOM is a suitable light sensor, will be orders of
magnitude lower.

Neither degradation of efficiency with time nor after exposing the tubes to
cold temperatures were found.

###  Section 3.6 Optical coupling

In order to minimize photon losses at the interface between end face of the
WOM tube and PMT glass, different methods of optically coupling the two
components are used. For repeatability of different experiments, an optical
coupling gel Elj (2021) was used in most experiments. However for a deployable
WOM, where a disassembly of the module is not desired, optical glue Nor (2021)
is the preferred choice. The refractive index of the cured glue is chosen to
lie between quartz glass ($n=1.46$) and borosilicate glass ($n=1.51$, used for
the PMT surface) to minimize Fresnel losses at the interface. It should be
noted that flat surface PMTs are preferable when using optical glue, since
spherical PMTs require chamfered ends of the WLS tubes to fit the curvature of
the PMT perfectly. If this is not the case, cracks in the glue layer are
observed which likely reduce bond strength and transmission efficiency of the
glue. Given the transmission from the datasheet and the Fresnel losses at the
interface (calculated using the angular distribution of the light output of
the WOM from simulation), a transmission probability of $\epsilon_{\rm
IF}$$>90\text{\,}\%$ is expected when using optical glue for the coupling.

It would be desirable to concentrate the light emission of the WOM from the
tube cross-section onto a compact area, allowing to further reduce the
photocathode area of the readout PMT. While conservation of etendue does not
prohibit this if the cross-sectional area is preserved, a viable solution was
not found. Starting from theoretical calculations Falke (2014), several
approaches have been investigated in simulation Thomas (2019); Schnur (2020)
and experiment Hebecker (2021). It is found that all lead to severe efficiency
losses777In simulation this is mostly due to photons being reflected back into
the tube and are therefore not suitable for the WOM design.

##  4 Characterization

In order to compare the WOM with other light sensors, measurements of its
characteristics are conducted, i.e. the one-sided efficiency $\epsilon_{\rm
one-sided}$, see Equation 6, the transit time spread, and the dark noise. The
effective area and the signal-to-noise ratio (SNR) are derived from these
values as well as the efficiencies discussed in the previous sections.

###  Section 4.1 Efficiency

In the absence of light reflected from the other end of the tube, the
efficiency measured with the test stand, described in Section 3.1, can be be
identified with the one-sided efficiency in Equation 6. The efficiency of the
WOM as a function of the $z$-position is determined using the _lock-in_ setup
(Equation 9) and the _single photon_ setup (Equation 10) independently for the
same WLS-tube. The results of both measurements overlap within their
respective uncertainties. In Figure 13 the measured efficiency is shown as a
function of the cylinder height $z$ obtained for the $700\text{\,}\mathrm{mm}$
long and $60\text{\,}\mathrm{mm}$ outer diameter prototype quartz tube
described in Section 1. The tube was coated on the inside at a speed of
$\leavevmode\nobreak\ 25\text{\,}\mathrm{mm}\text{\,}{\mathrm{s}}^{-1}$. Using
the obtained efficiency as a function of the distance $z$, the _flattened
model_ (see Section 2.2) is used as fit function in conjunction with a
normalization constant $N$ as additional fit parameter. The constant $N$
accounts for light losses independent of the position along the tube $z$.

Figure 12: Efficiency as a function of the distance from the ends of the tube
for a quartz tube Her (2021). The flattened model efficiency is used as fit
function to extract attenuation lengths. The injected light has a wavelength
of $375.00\pm 1.06\text{\,}\mathrm{nm}$. Systematic errors are shown as shaded
areas.

Figure 13: The measured transit time spread of a WOM tube with one attached
PMT is shown for different $z$-positions along the tube.

The respective fits lead to attenuation lengths of $2851\pm
55\text{\,}\mathrm{mm}$ and $3233\pm 37\text{\,}\mathrm{mm}$ and normalization
constants of $89.0\pm 0.4\text{\,}\mathrm{\char 37\relax}$ and $81.0\pm
0.2\text{\,}\mathrm{\char 37\relax}$. The mean and standard deviation obtained
for each PMT measurement result in an attenuation length of $\lambda_{\rm
att}=(3041\pm 191)\,\mathrm{mm}$ and a normalization constant of $N=(84\pm
4)\mathrm{\%}$. Several factors contribute to the deviation of $N$ from unity:

  * •

Overlap between absorption and emission spectrum of the WLS paint leads to re-
absorption of emitted photons with an estimated 0.39 % relative efficiency
loss.

  * •

Some efficiency is lost due to the inside coating of the tube (see Equation 4
and Figure 5). For the prototype, a reduction in capture efficiency
$\epsilon_{\rm TIR}$ compared to outside coating of 4.2 % is obtained.

  * •

Interface losses are calculated using the difference in refractive indices
between tube ($n_{\rm Tube}=1.46$) and glass of the PMT ($n_{\rm PMT}=1.51$)
together with the angular distribution on the end faces from simulation.
Averaging between s- and p-polarized transmission yields a relative loss of
$1-\epsilon_{\rm IF}=$5.5\text{\,}\%$$.

Concluding, besides the aspects discussed here, only minor additional
efficiency losses may occur and in air $\epsilon_{\rm one-sided}^{\rm
meas}=(46.4\pm 4.4)\,\%$ of photons can reach the end of the prototype tube.

###  Section 4.2 Transit time spread of photons

Using the _single photon_ setup, described in Section 3.1, the transit time
spread of photons coupling into the WLS tube is measured as a function of the
distance to the PMT $z$. Here the arrival time of each individual photon is
calculated as the first bin in which the recorded waveform amplitude reaches
half of the peak amplitude in the photon event (_constant fraction
discriminator_). The transit time spread is the distribution of the individual
arrival times. Measurements are taken on a $900\text{\,}\mathrm{mm}$ long
outside coated PMMA tube in increasing distance between PMT and light entry
point. The light pulser Rongen and Schaufel (2018) has a full width at half
maximum (FWHM) of $\sigma=$ $0.66\text{\,}\mathrm{ns}$ and the sampling time
step of the ADC digitizing the PMT output is $1\text{\,}\mathrm{ns}$. The time
resolution of the WOM is a convolution of three effects Schlickmann (2021):

  * •

time resolution of the PMT which is measured to be a Gaussian profile with
$\sigma\sim$6\text{\,}\mathrm{ns}$$.

  * •

absorption and re-emission of the WLS paint measured to be an exponential
decay with $\tau\approx$ $1.5\text{\,}\mathrm{ns}$ (in accordance with Ref.
Kuzniak and Szelc (2020)). For the lower UV $<280\,{\rm nm}$, where the light
needs to be absorbed and shifted by p-Terphenyl first (as mentioned in Section
3), an additional exponential decay with a time constant of around
$1\text{\,}\mathrm{ns}$ is expected.

  * •

photon trajectory path length distribution inside the tube depending on the
absorption length of the material

The final result together with the FWHM of the distribution is shown in Figure
13. The transit time spread of the full module has approximately a FWHM of
$\sim 18\text{\,}\mathrm{ns}$888A fit with a symmetric Gaussian gives
$\sigma=$$13.5\text{\,}\mathrm{ns}$.. The dominant contribution is caused by
the photon propagation in the tube. A trend towards larger time delays for
increasing distances $z$ between PMT and and light entry point for the
baseline response time can be observed.

###  Section 4.3 Noise

The background noise of the WOM comprises of the dark noise of the PMT as well
as the scintillation noise caused by radioactive decays in the tube glass and
optionally the glass of the housing. A climate chamber was used to measure the
PMTs dark noise rate at different temperatures. The PMTs were wrapped in black
cloth and enclosed in a metal box to prevent impact from background light and
radio frequency interference (RFI). To estimate the noise rate of the PMTs, a
single photo-electron (SPE) spectrum was obtained from a measurement over
time. An exponential together with a Gaussian was fitted to the data and the
number of photons under the Gaussian distribution was taken. The noise rate is
then estimated by dividing the number of photons by the dead time corrected
measurement length in seconds. The chosen PMTs have dark noise rates at
$-10^{\circ}\mathrm{C}$ of $r_{\rm DNR}^{-10^{\circ}}=\left(172.5\pm
27.7\right)\,\mathrm{Hz}$.

For the choice of the pressure vessel, quartz glass samples from different
companies were tested. For the quartz glass of the prototype Her (2021) a dark
noise rate of $6\text{\,}\mathrm{Hz}\text{\,}{\mathrm{kg}}^{-1}$ was measured
at room temperature, thus $r_{\rm Tube}=4\,\mathrm{Hz}$ for the
$700\,\mathrm{g}$ tube and $r_{\rm Housing}=50\,\mathrm{Hz}$ for the
$8.3\,\mathrm{kg}$ housing in the prototype design.

###  Section 4.4 Effective area

The mean projected effective area is defined here by

$\left<A_{\rm eff}^{\rm proj}\left( \theta,\phi\right)\right>=\frac{N_{\rm
det}}{N_{\rm sim}^{\rm plane}}$ (12)

where $N_{\rm sim}^{\rm plane}$ photons are emitted from a plane that is
uniformly rotated around the detection device and of these $N_{\rm det}$ will
be recorded by the device.

The effective area of a single PMT with diameter 3.5 inch, see Ref. Ham
(2021), is obtained by deriving the sensitive projected area for isotropic
illumination using the MC simulation described in Section 2.3. Using a quantum
efficiency of 18% averaged over the WLS emission wavelengths
($400\,\mathrm{nm}$ to $500\,\mathrm{nm}$) and cathode area, the effective
area is approximately $A^{\rm PMT}_{\rm eff}=12.0\,\mathrm{cm}^{2}$ in water,
ice or air as environment.

For a WOM in the prototype geometry (see Section 1), all losses from optical
propagation into and in the WOM tube, summarized in Equation 1, are are
multiplied with the projected sensitive area. The WLS efficiency is taken from
the slide measurement in Figure 11. The fraction of captured photons
$\varepsilon_{\rm TIR}$ is derived using Equation 3. The attenuation during
propagation in the tube $\epsilon_{\mathrm{TP}}$ in dependence of the distance
to the tube end is taken from data shown in Figure 13 where the TIR effect is
factored out. The PMT efficiency is chosen as above and the loss at the tube
to glue or gel to PMT interfaces is chosen to be
$\epsilon_{\mathrm{IF}}=0.95$, compare Section 3.6. Then the effective area of
the WOM is approximately $A^{\rm ice}_{\rm eff}=78.6\,\mathrm{cm}^{2}$ in
water or ice and $A^{\rm air}_{\rm eff}=126.4\,\mathrm{cm}^{2}$ in air
averaged over the wavelength range of $250\,\mathrm{nm}$ to
$600\,\mathrm{nm}$.

In the evaluated design, the effective area of the WOM exceeds the effective
area of the single PMT by a factor of approximately $R_{\rm ice}=6.5$ in ice
and $R_{\rm air}=11.3$ in air. The wavelength dependent effective area of WOM
and a single PMT is shown in Figure 15. The Cherenkov spectrum (without
attenuation in medium) is shown in parallel, to illustrate the advantage of an
enhanced sensitivity at lower wavelength. The ratio of average effective area
improves to a factor of approximately $R^{\rm Cher}_{\rm ice}=10.4$ in ice and
$R^{\rm Cher}_{\rm air}=18.9$ when weighted with the Cherenkov spectrum.

The effective area scales linearly with the diameter of the tube. The scaling
of the effective area in dependence of the WOM length is saturating due to the
attenuation of photons during propagation in the tube, shown in Figure 15. In
reality the dimensions are further restricted by several limitations: the dip
coating station would need to be scaled; glass tubes of appropriate quality
are limited in diameter due to manufacturability; high weight and bulkiness of
the device complicates handling in the laboratory and during deployment.

Figure 14: Effective areas of the WOM in the prototype design and a single PMT
of this ensemble in dependence of wavelength estimated with the MC simulation
described in Section 2.3 assuming both devices are deployed in ice.

Figure 15: Scale of the effective area at low wavelengths in ice in dependence
of the WOM tube length obtained by MC simulation. Prototype specifications
were used for all other properties of the WOM.

###  Section 4.5 Signal-to-noise ratio

In order to calculate the signal-to-noise ratio (SNR) of the WOM in comparison
to a single PMT, the averaged effective area from Section 4.4 is used as
signal strength and the sum of the noise measurement in Section 4.3 of all
components is used for the denominator. In practice the noise of the WOM
components would not sum up, at least not for bright signals, because one
would add a coincidence requirement for photons hitting both PMTs which should
reduce the noise significantly. Here noise rates are summed up conservatively.

For the WOM SNR, this calculation yields improvement factors of approximately
$F_{\rm ice}=3.2$ or $F_{\rm air}=5.5$ compared to a single PMT embedded in
ice or air. Weighting the effective area with a Cherenkov spectrum (without
photon attenuation in medium) would improve the SNR even further. The
corresponding improvement factors are approximately $F^{\rm Cher}_{\rm
ice}=5.2$ in ice and $F^{\rm Cher}_{\rm air}=8.9$ in air.

##  5 Conclusion, applications, and outlook

In this work, a novel photosensor concept is described in which PMTs are
complemented with a tube with wavelength-shifting coating in order to enhance
the signal-to-noise ratio. It is demonstrated that consistent coatings can be
applied in a simple procedure to glass tubes which allows to effectively
convert the UV fraction of the incident spectrum. Theoretical studies and
experimental work were conducted to understand all features of this concept as
well as its performance in detail. In particular, it is shown that in air
$\epsilon_{\rm one-sided}^{\rm meas}=\left(46.4\pm 4.4\right)\%$ of the
converted photons can be detected at the end of the prototype tube. This
simple concept can thus be applied to significantly enhance the light
collection area of any light sensors. As the WLS tube does not add
significantly to the dark noise, for the prototype design this leads to
improvement factors in the Cherenkov weighted signal-to-noise ratio of $F_{\rm
air}^{\rm Cher}=5.2$ in ice, $F_{\rm ice}^{\rm Cher}=8.9$ in air,
respectively. As a side effect the sensitivity of the WOMs is improved in the
UV which is particularly beneficial for the detection of Cherenkov or
scintillation light by matching the emission spectrum of the WLS paint with
the PMT wavelength sensitivity. Besides the PMT, the cost of the module is
dominated by the coated glass tube while expenses of the paint and glue are
insignificant due to the small amounts required for each module. The transit
time spread of detected photons is wider than for bare PMTs because it is
smeared predominantly by the propagation time in the tube. While the
photosensors at the tube ends can be read out independently, only a single
photon is generated in the wavelength-shifting process so that in single-
photon detection mode no information about the incidence position along the
tube can be obtained.

The prototype design does not reach the maximal sensitivity possible in an
optimized geometry, due to practical considerations. A wider and longer tube,
if manageable, would improve the SNR. Silicone photomultipliers (SiPM) could
be chosen for the tube readout in bright conditions, e.g. when deploying in
liquid scintillator as detector medium. Light guides were evaluated to couple
smaller PMTs to wider tubes. However this has stringent theoretical
limitations and proved complicated in practice.

Figure 16: A demonstrator device made in the prototype configuration and
photographed under UV illumination (left). The electronics comprises of PMT
pulse readout, environmental sensors, and communication. After deployment a
photograph was taken by a robot in the Ocean Network Canada. (right). Right
picture: Courtesy of ONC.

One prototype module enclosed with a vessel was built using simple _of-the-
shelf_ electronics as _proof-of-concept_ following the prototype design
described in this work, see Figure 16. Hydrogel Bubeck (2020) was used as
filling material to improve the optical properties of the module. The module
was deployed in the Canadian sea at a depth of $2539\,\textrm{m}$ within the
Ocean Network Canada Rea and et al (2021). It operated stably at the given
conditions and providing data of the local bio-luminescence.

Another application, here prototypes are already at hand, is the envisioned
SHiP experiment Ehlert et al. (2019); Ahdida and et al (2021). SiPM are
coupled to the WLS tubes which are to be deployed in the veto chamber of the
experiment.

For the upcoming IceCube Upgrade, which extends the low-energy infill of
IceCube, a WOM with an improved design, adjusted to the environmental needs is
designed. Twelve modules with $1300\,\mathrm{mm}$ long pressure vessels, with
5 inch PMTs, and customized electronics are developed and will be deployed
Rack-Helleis et al. (2021).

Investigation and methodology: Benjamin Bastian-Querner, Lucas Binn, Sebastian
Böser, Jannes Brostean-Kaiser, Dustin Hebecker, Klaus Helbing, Timo Karg, Lutz
Köpke, Marek Kowalski, Peter Peiffer, Anna Pollmann, John Rack-Helleis, Martin
Rongen, Lea Schlickmann, Florian Thomas and Anna Vocke; Supervision: Sebastian
Böser, Klaus Helbing, Timo Karg, Lutz Köpke and Marek Kowalski; Writing –
review and editing: Sebastian Böser, Anna Pollmann and John Rack-Helleis.

We acknowledge the support from the following agencies: Bundesministerium für
Bildung und Forschung (BMBF), Deutsche Forschungsgemeinschaft (DFG) in
particular through the clusters of Excellence PRISMA and PRISMA+, Initiative
and Networking Fund of the Helmholtz Association, Deutsches Elektronen-
Synchrotron DESY. We acknowledge support from the Open Access Publication Fund
of the University of Wuppertal.

Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.

###### Acknowledgements.

We acknowledge the fruitful discussion with all the individuals involved in
establishing the WOM as sensor for the SHiP surround background tagger (SBT).
We are very grateful to ONC and the P-ONE Collaboration for the deployment of
the WOM prototype as part of the STRAW-b installation We would also like to
thank Andreas Best from the Max-Planck-Institute for polymer research for the
profilometer measurements which allowed us to estimate the thickness of our
WLS coatings. We are thankful to Jochen Schreiner and Hardy Simgen of the Max
Planck-Institute for Nuclear physics in Heidelberg, as well as Christoph
Düllmann from the Institute of Nuclear Physics in Mainz for the radioactive
impurity measurements on our glass samples. We further acknowledge the
numerous studies conducted by students in the context of the WOM which are not
explicitly presented in this publication. In particular, these are: Kristina
Sand2, Peter Falke1, Carl Fösig2, Esther del Pino Rosendo2, Jan Weldert2,
Elisa Lohfink2, Christian Matthe2, Lucas Binn2, Sandra Gerlach2, Alexandre
Portier4, Yuriy Popovych2, Daniel Popper2, Ronja Schnur2, Andreas Looft3,
Jakob Beise3, Maximillian Bubeck2, Maximillian Thiel2, Nich Jannis
Schmeisser5; from the institutions: 1Universtität Bonn, 2University of Mainz,
3DESY , 4PHELMA Grenoble, 5University of Wuppertal. The authors declare no
conflict of interest. yes References

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November 26, 2020

# Pixelated 3D sensors for tracking in radiation harsh environments

Jordi Duarte-Campderros1 on behalf of the RD50 Collaboration 1Instituto de
Fisica de Cantabria (IFCA (UC/CSIC))1Instituto de Fisica de Cantabria (IFCA
(UC/CSIC)) Av. de los Castros s/n Av. de los Castros s/n Santander 39005
Santander 39005 Spain Spain<EMAIL_ADDRESS>
###### Abstract

The High Luminosity upgrade of the CERN Large Hadron Collider will be able to
reach a peak instantaneous luminosity of
$5\text{\times}{10}^{34}\text{\,}{\mathrm{cm}}^{-2}\text{\,}{\mathrm{s}}^{-1}$.
The innermost detectors of the CMS and ATLAS experiments will have to cope
with unprecedented requirements on radiation hardness. At the end of the
operation period, radiation levels are expected to reach values above
$2.6\text{\times}{10}^{16}\text{\,}\mathrm{n_{eq}}\text{\,}{\mathrm{}}^{2}\text{\,}{\mathrm{cm}}^{-1}$.
Sensors based on 3D pixel technology, with intrinsic radiation tolerance, are
the baseline option for the innermost layers of the vertex detectors of
several HL-LHC experiments. This article gives an overview of the ongoing
characterization of the pixelated 3D sensor technology, their performance and
their current development status for tracking on radiation harsh environments.

particle tracking detectors,HL-LHC upgrade,3D silicon pixel detectors,
radiation-hard detector

##  1 Introduction

The High Luminosity Large Hadron Collider (HL-LHC) project[1] is going to push
their experiments to very stringent radiation environments. The innermost
detectors of the largest HL-LHC experiments, ATLAS and CMS, will have to cope
with unprecedented radiation levels and with extremely high track densities.
Their upgraded vertex detectors will have to be able to operate in a hostile
radiation environment, reaching hadron fluences up to about
$2.6\text{\times}{10}^{16}\text{\,}\mathrm{n_{eq}}\text{\,}{\mathrm{}}^{2}\text{\,}{\mathrm{cm}}^{-1}$
before being replaced [2, 3]. Sensors based on 3D pixel technology are
excellent candidates because of their inherent radiation tolerance.

A 3D sensor is built by inserting highly doped columns into the bulk to form
the P-N junctions, decoupling in that way the inter-electrode distance from
the active sensor thickness (see Fig. 1). The thickness is defining the amount
of charge generated but is in the case of 3D sensors independent of the
distance between the electrodes, respectively the depletion voltage. The
inter-electrode distance can thus be optimized independent of the amount of
charge deposited by an ionizing particle, as opposite to a planar sensor. The
small inter-electrode distance allows to reduce the charge carrier trapping
probability after irradiation, acquire the induced charge faster, and use low
voltages to fully deplete the sensor, among other benefits [4]. This low
depletion voltage enables to operate the 3D sensors with an extremely low
power consumption, especially compared with equivalent planar sensors.

Figure 1: Schematic simplified layout of a planar (left) and a 3D (right)
sensors, assuming a n-in-p layer structure. Read out electrodes are bonded to
the highly doped n+ thin region (colored in green). Electrodes bonded to the
ohmic layers p+ (colored in yellow) are needed to polarize the sensor. The
sensor thickness, $\Delta$, determines how many charges are created int the
sensor when a particle passes through, while the inter-electrode distance, L,
defines the maximum distance a charge carrier should travel before being
collected. It can be observed that in a planar sensor $\text{L}=\Delta$, but
in a 3D sensor $\text{L}<<\Delta$.

However, the columnar structure also presents some disadvantages. The electric
field is not uniform within the depleted region, and therefore the sensor
response cannot be uniform either. Indeed, there are charge losses inside the
electrodes and ohmic columns, as the columns themselves are not active
regions. Null points between same type of electrodes will delay the created
charges generated in there, as they have to diffuse first. As the inter-
electrode distance is smaller, the capacitance of a 3D sensor is order of 3-5
times higher than an equivalent planar, and consequently a 3D sensor is
noisier. The fabrication process is still in the development phase, being an
expensive and time consuming process made by just a few R&D institutions or
foundries (IMB-CNM in Barcelona, FBK in Trento or SINTEF in Oslo), especially
compared to the manufacturing of planar sensors. There are many companies
capable to produce planar sensors, and with a well-established production,
even for this small-pitch detector.

Several of these drawbacks can be or have been overcome. For instance, the
production processes have been simplified and improved over the past few
years, in particular by using single-sided processes as opposed to the double-
sided initially used for the first 3D batches [5]. The latest productions are
mature enough to achieve overall good yields [6]. Another example: the
response of the electric field can be _uniformed_ by tilting the detector so
that the particle passes through different electric field regions.

The 3D pixel technology has already been successfully used in some LHC
experiments as position tracking detectors in radiation environments such as
in the ATLAS IBL [7], the ATLAS Forward Proton (AFP) detector [8], and the
CMS-TOTEM Precision Proton Spectrometer (PPS) detector [9]; proving to be a
mature enough yet novel technology. For the HL-LHC, ATLAS already decided to
include 3D pixel detectors with
$50\text{\times}50\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and
$25\text{\times}100\text{\,}\mathrm{\SIUnitSymbolMicro m}$ pixel size in the
innermost layer of its new silicon inner tracker [3]. At the time of this
report, CMS is in the process of deciding the inclusion of this technology in
the two innermost layers of the barrel and in the inner ring of the end-cap of
its inner tracking detector.

The RD50 Collaboration has been involved in several activities related with
the 3D pixel technology, such as their time performance in order to be used as
timing detectors, the radiation hardness at extreme fluences larger than
$1\text{\times}{10}^{17}\text{\,}\mathrm{n_{eq}}\text{\,}{\mathrm{}}^{2}\text{\,}{\mathrm{cm}}^{-1}$,
and the qualification and characterization of the small-pitch 3D sensor with
the pre-production readout chip RD53A [10], as part of the sensor
qualification process for the ATLAS and CMS Phase-2 upgrade programs. The RD50
collaboration has also played an important role to bring 3D sensors to
industrial production. In this paper, a summary of the last line of work is
being reported. Information and results of the other work packages can be
found elsewhere [11, 12, 13].

##  2 Sensor characterization for the HL-LHC experiments upgrade

The inner tracker upgrade projects of ATLAS and CMS require small-pitch,
radiation-hard detector candidates, to be assembled with the readout
electronics and mechanics projected by the collaborations. The readout chip
(ROC) developed for CMS and ATLAS, the RD53A, is a demonstrator ROC for CMS
and ATLAS upgrades, based on $65\text{\,}\mathrm{nm}$ CMOS process [10]. This
is a common layout design developed by the RD53 collaboration, which included
several Analogs Front-Ends (AFE) to be tested. The CMS and ATLAS ROCs
prototypes, the CROC and the ITkPixV1, respectively, have finally chosen to
use different AFEs: the linear AFE for CROC and the differential AFE for
ITkPixV1. Fig. 2 shows a picture of the RD53A ROC with the linear and
differential front-end regions highlighted, and the single chip cards
assemblies used for the characterization.

Figure 2: A RD53A chip picture (top) with the linear and differential regions
highlighted in red and orange respectively. The chip bump-bonded to a sensor,
is wire-bonded to a single chip card as part of the characterization setup.
Two different single chip cards have been used, the RICE card (left, developed
by RICE University), and the Bonn card (right, developed by the SiLab group at
Bonn University).

###  2.1 Module description

The sensors used have been produced either by IMB-CNM in Barcelona (Spain) or
by the FBK in Trento (Italy). In both cases, the production was made with a
single-sided process on p-type substrates Silicon on Silicon (SiSi) or Silicon
on Insulator (SOI). The former has finally been chosen over the SOI, as it
does not need the removal of the handle-wafer for biasing, which simplifies
the production process and improves the yield. FBK used 6 inches Direct Bond
Wafers (DBW) with a support wafer made of
$500\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick Czochralski (CZ) silicon,
with less than $1\text{\,}\mathrm{\SIUnitSymbolOhm}\text{\,}\mathrm{cm}$
resistivity. The electrodes were implanted by a Deep Reactive Ion Etching
(DRIE) process, in a Float Zone (FZ) wafer of high resistivity (higher than
$3000\text{\,}\mathrm{\SIUnitSymbolOhm}\text{\,}\mathrm{cm}$) of
$130\text{\,}\mathrm{\SIUnitSymbolMicro m}$ (production with Mask Aligner
lithography) and $150\text{\,}\mathrm{\SIUnitSymbolMicro m}$ (production with
Stepper lithography) thickness. The columns have about
$5\text{\,}\mathrm{\SIUnitSymbolMicro m}$ of diameter.

For the case of the IMB-CNM, the p-type substrates were produced on 4 inches
SOI wafers or 4 inches SiSi wafers with a handle wafer of
$300\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick CZ silicon of low
resistivity. The electrodes are implanted on an active region with a nominal
resistivity between
1000-$5000\text{\,}\mathrm{\SIUnitSymbolOhm}\text{\,}\mathrm{cm}$ and
$150\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick. On the SiSi wafers, there
is no need to remove the handle wafer for bias, as the low-resistivity wafer
is conductive. The columns have a diameter of about
$8\text{\,}\mathrm{\SIUnitSymbolMicro m}$.

Fig. 3 summarizes schematically the described sensors.

(a) FBK

(b) IMB-CNM, SOI (left) and SiSi (right)

Figure 3: Sensor cross-section layout. The main components are schematized,
showing the active region (light gray, high-resistive layer), the support CZ
layer (dark gray), the highly-doped column implant (red) and the ohmic columns
(green, yellow).

The sensors were manufactured with rectangular and square geometries, matching
the layouts CMS and ATLAS are considering to use. The square
$50\text{\times}50\text{\,}\mathrm{\SIUnitSymbolMicro m}$ has an inter-
electrode distance of about $35\text{\,}\mathrm{\SIUnitSymbolMicro m}$, and is
the easiest to produce. Furthermore, they do not suffer from the cross-talk
originated in the metallic routes [14], needed to match the RD53A
$50\text{\times}50\text{\,}\mathrm{\SIUnitSymbolMicro m}$ bond matrix pattern.
However, a rectangular geometry allows to increase the resolution in the short
pitch side, and therefore were considered as well. Two rectangular geometries
$25\text{\times}100\text{\,}\mathrm{\SIUnitSymbolMicro m}$ have been tested:
with 2 electrodes (2E) per pixel cell with a very small inter-electrode
distance of $28\text{\,}\mathrm{\SIUnitSymbolMicro m}$ but difficult to
produce, and 1 electrode (1E), less problematic to produce but with larger
inter-electrode distance. The later has been proven to be enough radiation
hard, even with its $52\text{\,}\mathrm{\SIUnitSymbolMicro m}$ of inter-
electrode distance, and therefore the 2E flavour has already been discarded.
Fig. 4 summarizes all the pixel geometries used in the results presented in
this report.

Figure 4: Pixel geometries considered for CMS and ATLAS. Each pixel cell is
defined by the ohmic columns (blue) and the highly doped implant electrode
(red). The inter-electrode distance is also specified. The bottom row is
showing the different routing pattern used to connect the bond-bumps on the
sensor with the RD53A readout electrodes. Solid (for the FBK modules) and
dashed (for the IMB-CNM) lines are superimposed to stress a pixel cell.

Some sensors were also irradiated in order to emulate the damage produced by
irradiation after years of operation in the experiments. Irradiations have
been carried out at several facilities, with different particles and energies,
in several intermediate steps until reaching fluences up to
$1\text{\times}{10}^{16}\text{\,}\mathrm{n_{eq}}\text{\,}{\mathrm{}}^{2}\text{\,}{\mathrm{cm}}^{-1}$,
the expected fluence of the innermost layers of CMS or ATLAS after the two
first runs of the HL-LHC in the scenario of $3000\text{\,}{\mathrm{fb}}^{-1}$.
Details about the irradiations and methodology can be found in Ref. [15].

###  2.2 Test beam characterization

Electrical, TCT, TCT-TPA, or other characterizations techniques were used to
study the sensors, and results have already been extensively presented
elsewhere [16, 20, 13]. The sensors described in the previous section were
bump-bonded to the RD53A demonstrator chip and wire bonded to PCB cards as
explained before, and tested under a beam of particles. Two main facilities
were used: CERN [17], with hadron beams of
$120\text{\,}\mathrm{GeV}\text{/}\mathrm{\text{$c$}}$, and DESY [18], where
electrons of $5.6\text{\,}\mathrm{GeV}\text{/}\mathrm{\text{$c$}}$ are
delivered to the beam lines. Test beam experiments are useful to study the
behaviour and response of a sensor under similar conditions it will face when
it is mounted in the real experiment. The sensor response is measured with the
help of a telescope [19], where the incident particles are identified and
reconstructed. Telescope reconstructed particles are used to identify the
position in the sensor under study where a hit should appear, allowing to
measure hit-efficiency, charge, resolution, etc.

Figure 5: Hit efficiency per pixel cell in different sensors, shown from left
to right; 50x50 Linear and Differential front-end, and 25x100 Linear front-
end. From top to bottom are with increasing fluence ($\Phi$) and incident
angle of the tracks ($\phi$). Details are inserted in the figures, with
fluence in units of
$1\text{\times}{10}^{15}\text{\,}\mathrm{n_{eq}}\text{\,}{\mathrm{}}^{2}\text{\,}{\mathrm{cm}}^{-1}$
(0 for fresh sensors). The operating bias voltaged used is also shown in some
plots. Sensors were produced at IBM-CNM with SOI p-type substrates. Figure re-
adapted and composed from Ref. [20].

The first important observable reported is the efficiency per pixel cell,
measured for $25\text{\times}100\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and
$50\text{\times}50\text{\,}\mathrm{\SIUnitSymbolMicro m}$ fresh sensors. The
two plots in Fig. 5 show the hit efficiency drop in the ohmic columns at the
four corners when the incident particles enter perpendicular to the sensor
plane. This drop is the result of the incident particle passing inside the
non-active region of the columns. However, there is no significant drop
observed in the n-column at center, as the charge generated below the column
(see Fig. 3) is enough to create a hit (thresholds are tuned around 1000
electrons).

The drop in the n-column appears in the irradiated sensor as consequence of
two effects: thresholds are increased to deal with a noisier detector, and
trapping, lowering the amount of generated charge below the column. Fresh
sensors are exhibiting a 98% overall efficiency, including the ohmic column
losses. When tilted, a 99.5% overall efficiency is recovered with very low
bias voltages. As it can be observed from Fig. 6, fully depletion is reached
with a few volts for fresh sensors, and with a few hundred of volts for
sensors irradiated up to
$1\text{\times}{10}^{16}\text{\,}\mathrm{n_{eq}}\text{\,}{\mathrm{}}^{2}\text{\,}{\mathrm{cm}}^{-1}$.

(a) 50x50, fresh and
$5\text{\times}{10}^{15}\text{\,}\mathrm{n_{eq}}\text{\,}{\mathrm{}}^{2}\text{\,}{\mathrm{cm}}^{-1}$

(b) 25x100, fresh and
$5\text{\times}{10}^{15}\text{\,}\mathrm{n_{eq}}\text{\,}{\mathrm{}}^{2}\text{\,}{\mathrm{cm}}^{-1}$

(c) 50x50 and 25x100,
$1\text{\times}{10}^{16}\text{\,}\mathrm{n_{eq}}\text{\,}{\mathrm{}}^{2}\text{\,}{\mathrm{cm}}^{-1}$

Figure 6: Measured overall hit efficiency with respect the applied bias
voltage, for fresh and irradiated sensors. Figures extracted from [20].

Equivalent results have been obtained for FBK produced sensors [21], showing
similar performances (see Fig. 7), as well as similar depletion voltages:
sensors irradiated at
$1\text{\times}{10}^{16}\text{\,}\mathrm{n_{eq}}\text{\,}{\mathrm{}}^{2}\text{\,}{\mathrm{cm}}^{-1}$
fully depletes around $120150\text{\,}\mathrm{V}$.

Figure 7: Hit efficiency in pixel cell for fresh
$50\text{\times}50\text{\,}\mathrm{\SIUnitSymbolMicro m}$ (top-left)
$25\text{\times}100\text{\,}\mathrm{\SIUnitSymbolMicro m}$ (top-right); and
after irradiation up to
$1\text{\times}{10}^{16}\text{\,}\mathrm{n_{eq}}\text{\,}{\mathrm{}}^{2}\text{\,}{\mathrm{cm}}^{-1}$
for $50\text{\times}50\text{\,}\mathrm{\SIUnitSymbolMicro m}$ (bottom-left)
and $25\text{\times}100\text{\,}\mathrm{\SIUnitSymbolMicro m}$ (bottom-right).
Sensors produced by FBK.

The resolution of the sensor attached to the RD53A before and after
irradiation up to
$1\text{\times}{10}^{16}\text{\,}\mathrm{n_{eq}}\text{\,}{\mathrm{}}^{2}\text{\,}{\mathrm{cm}}^{-1}$,
has been recently measured in the short pixel direction of the
$25\text{\times}100\text{\,}\mathrm{\SIUnitSymbolMicro m}$ geometry [22]. The
sensor shows a resolution of $3\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and
there is almost no degradation after irradiation, with a resolution of
$5.7\text{\,}\mathrm{\SIUnitSymbolMicro m}$ evaluated at the optimal angle.
These results complement the previously obtained for the
$50\text{\times}50\text{\,}\mathrm{\SIUnitSymbolMicro m}$ geometry, with a
resolution of $5\text{\,}\mathrm{\SIUnitSymbolMicro m}$, evaluated at the
optimal angle and before irradiation.

A parameter of interest, especially important for the commissioning and
operation of the modules in the targeted experiment, is the power consumption.
The ATLAS specifications are requiring to be below
$10\text{\,}\mathrm{mW}\text{/}{\mathrm{cm}}^{2}$, while CMS requires less
than $1\text{\,}\mathrm{W}\text{/}{\mathrm{cm}}^{2}$ (included sensor and chip
consumption). The power consumption of the tested sensors after being
irradiated up to
$1\text{\times}{10}^{16}\text{\,}\mathrm{n_{eq}}\text{\,}{\mathrm{}}^{2}\text{\,}{\mathrm{cm}}^{-1}$,
has been measured below the ATLAS specifications in the full operational range
of the sensor, defined with an overall efficiency larger than 97%. Consumption
has been evaluated operating the sensors at around
$-25\text{\,}\mathrm{\SIUnitSymbolCelsius}$, and for both geometries
$50\text{\times}50\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and
$25\text{\times}100\text{\,}\mathrm{\SIUnitSymbolMicro m}$. Fig. 8 summarizes
the results detailed in [20, 23].

Figure 8: Sensor power dissipation with respect to the operating bias voltage
for 25x100 and 50x50 geometries, irradiated up to
$1\text{\times}{10}^{16}\text{\,}\mathrm{n_{eq}}\text{\,}{\mathrm{}}^{2}\text{\,}{\mathrm{cm}}^{-1}$
and operated with a temperature around
$-25\text{\,}\mathrm{\SIUnitSymbolCelsius}$. Figure on the left corresponds to
SOI IMB-CNM of $150\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick sensors; on
the right, FBK SiSi $150\text{\,}\mathrm{\SIUnitSymbolMicro m}$ thick using
the Stepper lithography mask.

##  3 Conclusions

Small-pitch 3D pixel sensors bump-bonded to the pre-production ROC RD53A have
proven to have an excellent radiation tolerance up to
$1\text{\times}{10}^{16}\text{\,}\mathrm{n_{eq}}\text{\,}{\mathrm{}}^{2}\text{\,}{\mathrm{cm}}^{-1}$,
keeping hit efficiency larger than 97% at particle normal incidence with
operational bias voltages below $200\text{\,}\mathrm{V}$. This allows to
fulfill the power dissipation specifications required by the ATLAS and CMS
detectors.

Both geometries being considered,
$25\text{\times}100\text{\,}\mathrm{\SIUnitSymbolMicro m}$ and
$50\text{\times}50\text{\,}\mathrm{\SIUnitSymbolMicro m}$, show similar
performance, in particular the
$25\text{\times}100\text{\,}\mathrm{\SIUnitSymbolMicro m}$ with 1 electrode is
able to deal with the radiation tolerance demanding conditions, therefore
there is no need for the 2 electrodes design. Their performance meets the
baseline requirements to be qualified for the HL-LHC inner tracker upgrades of
ATLAS and CMS.

A new set of test beam measurements is being planned for samples already
irradiated to
$2\text{\times}{10}^{16}\text{\,}\mathrm{n_{eq}}\text{\,}{\mathrm{}}^{2}\text{\,}{\mathrm{cm}}^{-1}$,
while further irradiation are planned to reach the expected fluences for the
LS5, i.e.
$2.6\text{\times}{10}^{16}\text{\,}\mathrm{n_{eq}}\text{\,}{\mathrm{}}^{2}\text{\,}{\mathrm{cm}}^{-1}$,
when is planned the replacement of the modules of the innermost layers of CMS.
New productions of sensors bump-bonded to the experiment-dedicated ROCs, the
ItkPixV1 (ATLAS) and the CROC (CMS) have already started.

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