# FAT-GEMs: (Field Assisted) Transparent Gaseous-Electroluminescence
Multipliers

S. Leardini  A. Saá-Hernández  M. Kuźniak  D. González-Díaz  C. D. R. Azevedo
F. Lucas  P. Amedo  A. F. V. Cortez  D. Fernández-Posada  B. Mehl  G. Nieradka
R. de Oliveira  V. Peskov  T. Sworobowicz  S. Williams

###### Abstract

The idea of implementing electroluminescence-based amplification through
transparent multi-hole structures (FAT-GEMs) has been entertained for some
time. Arguably, for such a technology to be attractive it should perform at
least at a level comparable to conventional alternatives based on wires or
meshes. We present now a detailed calorimetric study carried out for 5.9 keV
X-rays in xenon, for pressures ranging from 2 to 10 bar, resorting to
different geometries, production and post-processing techniques. At a
reference voltage 5 times above the electroluminescence threshold
($E_{EL,th}\sim 0.7$ kV/cm/bar), the number of photoelectrons measured for the
best structure was found to be just 18% below that obtained for a double-mesh
with the same thickness and at the same distance. The energy resolution stayed
within 10% (relative) of the double-mesh value.

An innovative characteristic of the structure is that VUV-transparency of the
PMMA substrate was achieved, effectively, through TPB-coating of the
electroluminescence channels combined with ITO-coating of the electrodes. This
resulted in a $\times 2.25$-increased optical yield (compared to the bare
structure), that was found to be in good agreement with simulations if
assuming a TPB wavelength-shifting-efficiency at the level of WLSE=0.74-1.28,
compatible with expected values. This result, combined with the stability
demonstrated for the TPB coating under electric field over 20 h of continuous
operation, shows great potential to revolutionize electroluminescence-based
instrumentation.

##  1 Introduction

The term electroluminescence (EL) is often used, among others, to refer to the
detection principle introduced by Conde and Policarpo in the 60’s [1, 2, 3].
In its simplest description, within this context, it might be seen as the
mechanism by which to enhance the ionization response of a gaseous detector,
converting ionization electrons (difficult to count) into photons (easy to
count) by means of an electric field. Since the accelerated swarm of electrons
experiences different energy thresholds for excitation and ionization, the net
result is the appearance of an electric field regime where it is possible to
have the former without the latter. In noble gases, specifically, the high
VUV-scintillation probability per excited state [4, 5] results in strong
scintillation yields ($Y$) of up to easily 1000’s of ph/e, yet in the absence
of avalanche multiplication [6, 7]. These are the conditions under which EL
exhibits its most remarkable features and finds widespread use: in the
avalanche-free regime, as noble gases possess no inelastic degrees of freedom
other than excitations, nearly all energy gained by electrons in the electric
field ($qV$) turns into scintillation photons, leading to an approximately
linear response [8]. This can be expressed handily as:

$\displaystyle Y$ $\displaystyle\simeq K(V-V_{th})$ (1.1) $\displaystyle
Y_{z}/N$ $\displaystyle\simeq K(E^{*}-E^{*}_{th}).$ (1.2)

The second expression conveys the fact that, when the density-reduced electric
field ($E^{*}=E/N$, a measure of the characteristic electron energy) is above
a threshold value needed to excite the medium ($E^{*}_{th}$), any additional
energy gained in the field goes into new excitations. In the above equations
$K$ is a proportionality constant, $Y$ refers to the scintillation yield,
$Y_{z}$ to the yield per unit length and $N$ is the number of atoms per unit
volume. The high efficiency of the EL process has a second consequence, that
represents perhaps one of its best known properties: the relative variance of
the electroluminescence signal ($Q=(\sigma_{Y}/Y)^{2}$) is very small. Its
contribution to the calorimetric response of a gaseous detector propagates
into the energy resolution (FWHM) as:

$\mathcal{R}=2.355\sqrt{F+Q+\frac{1}{n_{pe}}\left(1+\frac{\sigma_{{}_{G}}^{2}}{G^{2}}\right)}\sqrt{\frac{1}{n_{e}}}.$
(1.3)

In the above expression $F$ represents the Fano factor of the medium (0.1-0.2
in noble gases [9]), $n_{pe}$ is the number of detected photons
(‘photoelectrons’) per electron, and $\sigma_{G}/G$ refers to the relative
width of the single-photon distribution function of the photosensor. The last
term involves the number of ionization electrons, $n_{e}=\varepsilon/W_{I}$,
with $\varepsilon$ being the energy deposited in the medium and $W_{I}$ the
average energy needed to release an electron [10]. The term $Q$ is generally
so small [8, 11] that it has eluded experimental determination except in the
presence of electronegative gases such as CO2 [12]. Due to the smallness of
$Q$, as soon as the number of detected photons per primary electron is of the
order of $n_{pe}=10$ or more, the energy resolution will approach the
intrinsic limit of the gas medium [13].

The aforementioned characteristics make electroluminescence, nowadays, the
workhorse of many experiments based on Time Projection Chambers (TPCs) in the
field of Rare Event Searches, such as XENON [14], LZ [15], PandaX [16], and
DarkSide [17] (aimed at direct WIMP Dark Matter detection) or NEXT [18] (aimed
at measuring $\beta\beta 0\nu$ decay). Its use is foreseen in upcoming
experiments such as RED [19] and GANESS [20] (aimed at precision studies of
coherent neutrino scattering), and it can be found, too, in applied research
for instance in proposals for Compton cameras [21] and Compton dispersion at
next-generation Light Sources [22]. In such experiments, the single-electron
detection capabilities of electroluminescence are essential to extend WIMP
sensitivity down to very low masses (e.g. [23]), while near-Fano energy
resolution is required for precise calorimetry in $\beta\beta 0\nu$ searches,
thus avoiding contamination from $\beta\beta 2\nu$ decays and natural
radioactivity [24]. High-rate environments like [21] and [22] benefit from the
absence of ion feedback and subsequent high rate capability stemming from the
avalanche-free nature of the electroluminescence process.

For all their beauty, the electroluminescence process in presently running
experiments is invariably implemented based on early designs relying on wires
or meshes, and suffer from the inevitable scaling-up limitations due to
electrostatic sagging and deformation [25] and, chiefly, defects [26]. During
the operation of the NEXT-NEW detector, for instance, the pressure-reduced
electric field was 1.2 kV/cm/bar at 10 bar, a mere 0.5 kV/cm/bar above the EL
threshold and 3 times below the values achieved in the present work and,
generally, on small R&D setups. Thus, when possible, the commissioning of the
EL-region becomes a separate endeavour, requiring purposely-built chambers
several square meter in size, essentially as large as the final operating
conditions demand [27]. Given that experiments keep increasing in size to
achieve sensitivity, it seems very unlikely that the situation will improve
except if new production techniques are introduced.

Lately, over the last 5-10 years, there has been interesting progress on the
development of optically-enhanced structures, and we follow this lead.
Transparent substrates like glass, for instance, have been successfully carved
into gaseous electron multipliers (GEMs), be it by photolitography [28] or
sand-blasting [29]. They are sturdy and immune to sagging or deformation, and
can be easily tiled to cover large areas [30]. At the thicknesses and hole
sizes needed for efficient electroluminescence (several mm), structures based
on the highly VUV-reflective Teflon [31] or relying on the transparency of
PMMA (polymethyl methacrylate) [32] have been manufactured by CNC drilling. In
order to achieve VUV-transparency, the solid wavelength-shifter PEN was
proposed as a bulk material and successfully machined and operated under Xe
and Ar for the first time in [33]. A natural continuation of the previous
works was to resort to tetraphenylbutadiene (TPB) coating of the (PMMA-based)
GEM channels, theoretically enabling higher wavelength-shifting yields
compared to polyethylene naphthalate (PEN) plates. Aiming at wide range of
applications, in particular those related to Rare Event Searches, the core
materials of such EL-structures are chosen to be radiopure.

Here we present a comprehensive performance study of different FAT-GEM
structures under 5.9 keV X-rays, involving different fabrication procedures,
different processing (adding wavelength-shifting coating or an internal
reflective layer), different geometries (hole sizes), different gases (xenon
and argon), and different pressures (2-10 bar). Comparisons with simulations
and with a simple 2-mesh configuration are given too.

##  2 FAT-GEMs

###  2.1 Fabrication process

Results from micropattern gas detectors (MPGDs) operated in avalanche mode in
gaps as small as 50 µm (typical GEM thickness) suggest that they can
potentially produce a high optical output in a noble gas [34].
Electroluminescence, on the other hand, benefits from electrified regions
where the product of the number density, $N$, times gas gap, $d$, is much
larger (up to $P\cdot d\sim 10$ bar${\cdot}$cm at room temperature, compared
to $P\cdot d\sim 5\times 10^{-3}$ bar${\cdot}$cm for GEMs at around
atmospheric pressure). Geometries with larger values of the product $N\cdot d$
can sustain higher breakdown voltages [35] and therefore provide higher
optical gains in avalanche-free conditions (eq. 1.2). In regard to the
electric field configuration, an uniform field region is preferable in terms
of intrinsic energy resolution [11] and maximum optical throughput before the
onset of multiplication (e.g. [7, 36]). Coincidentally, a high $N\cdot d$
enhances neutral bremsstrahlung radiation below the $E_{EL}$ threshold, too
[37, 38]. The main objection against employing large EL gaps is the presence
of sagging and deformation when such uniform fields are created by means of
meshes or wires suspended on m2 areas and beyond [11, 25].

Thus, in order to create a large-gap, uniform-field, sagging-free structure,
PMMA plates of about 5 mm-thickness were procured, drilled at different hole
diameters (1-4 mm) on an hexagonal pattern, with a pitch of 5-6 mm. Two
additional structures were prepared based on the 2 mm-hole geometry, this time
having TPB coated inside the holes. One of them had an additional 3M™ Enhanced
Specular Reflector (ESR) layer [39, 40] placed underneath the cathode. A
compilation of the structures studied is provided in table 1.

Regular (uncoated) structures were produced in the RD51 workshop at CERN: a
bare PMMA plate (7 cm $\times$ 7 cm) was thermally bonded to two circular
copper electrodes (6 cm diameter).111The metallization area was increased with
respect to the structures used earlier in [32], leaving the active area
unchanged, to eliminate possible fringe-fields stemming from charging-up.
Holes were then CNC-drilled, and a rim around them (0.2 mm) was created in a
chemical bath, to mitigate corona discharges. Finally, a hatched pattern
(inner square side 0.35 mm, trace width 0.1 mm) was made through
photolithography on the cathode of the structure. Two things were noticed: on
the positive side, electric field simulations showed a negligible change in
the electric field compared to the geometry with a solid cathode; on the
negative side, thermal-bonding rendered the structure translucent and sub-
optimal for further optical treatment, something that was pursued through an
alternative fabrication process that is discussed below. Two microscope photos
of the resulting structures are provided in Figure 1, and the fabrication
procedures are sketched in Figure 2a.

Descriptor |  Hole size (mm) |  Pitch (mm) |  Thickness (mm) |  Number of holes |  TPB |  ESR
---|---|---|---|---|---|---
A |  1 |  5 |  4.5 |  30 |  No |  No
B |  2 |  5 |  4.7 |  30 |  No |  No
C |  3 |  5 |  4.75 |  30 |  No |  No
D |  4 |  6 |  4.8 |  18 |  No |  No
E |  2 |  5 |  5.33 |  31 |  Yes |  No
F |  2 |  5 |  5.47 |  31 |  Yes |  Yes
Table 1: Compilation of the FAT-GEM structures characterized in this work.

Figure 1: Uncoated FAT-GEM ‘B’ (the hatched-electrode technique was employed
in this particular case).

The TPB-coated structures were produced at AstroCeNT (Poland), starting from
the application of thin PET films coated with indium tin oxide (ITO) to the
two faces of the bare tile, by means of an adhesive film. Compared to the
thermally-bonded hatched electrode (transparency 60%), the PET+ITO resulted in
a larger transparency of 79% (according to the producer [41]), with the
benefit of preserving the optical properties of the plate. Once the PET-ITO
films were adhered, holes were drilled and finally TPB evaporated inside them
(Figure 2b). In order to further increase light collection, an ESR layer was
interleaved in between the PMMA and the ITO electrode for one of the
structures (Figure 2c). The thickness of the plates was around 4.7 mm for the
uncoated structure and 5.4 mm for the coated ones.

Figure 2: Sketch of the fabrication process for FAT-GEMs produced at CERN
($a$) and at AstroCeNT ($b$ and $c$). FAT-GEMs produced at CERN have thermal-
bonded copper electrodes, one of them made semi-transparent through chemical
etching of a hatched pattern. For the structures produced at AstroCeNT, ITO
electrodes were applied in order to increase the structure transparency;
moreover, TPB was coated inside the holes. Procedures $b$ and $c$ differ for
the presence of a reflecting ESR layer.

###  2.2 Radiopurity

A mid-size FAT-GEM of 18 cm diameter was purposely-built at the CERN-RD51
workshop and screened mainly to show that the production process did not
result in strong contamination. The raw PMMA material was Polycast provided by
Spartech (as used in the DEAP-3600 detector), with measured activities as low
as 0.11 mBq/kg of 235U [42]. The radiopurity screening was performed at
Laboratorio Subterráneo de Canfranc over a practical time of a bit over a
month (50.76 days at GeAnayet for the bare PMMA plate, 47.7 days at GeTobazo
for the FAT-GEM). The sensitivity of the measurements, presented in Table 2,
was mainly limited by the mass of the amplification structure. While
competitive radiopurity levels would still need to be demonstrated (especially
for a structure that is expected to face the interaction volume), in the light
of our current measurements the present fabrication techniques seem promising.

Figure 3: Bare PMMA plate (left) and FAT-GEM (right) inside the copper shielding of the setups used for radioactivity screening at Laboratorio Subterráneo de Canfranc. Isotope |  PMMA (mBq/kg) |  FAT-GEM (mBq/kg) [(mBq/cm2)] |  PMMA, DEAP-3600 (mBq/kg)
---|---|---|---
U-238/Pa-234m |  $<$340 |  $<$791 [$<$0.741] |
U-238/Pb-214 |  $<$2.8 |  $<$6.9 [$<$0.006] |
U-238/Bi-214 |  $<$2.3 |  $<$7.0 [$<$0.007] |
U-238/Ra-226 |  |  |  $<$0.1
U-238/Th-234 |  |  |  $<$9.0
Th-232/Ac-228 |  $<$8.8 |  $<$22 [$<$0.021] |
Th-232/Pb-212 |  $<$2.9 |  $<$7.4 [$<$0.007] |
Th-232/Tl-208 |  $<$6.3 |  $<$15 [$<$0.014] |
Th-232 |  |  |  $<$0.3
U-235/U-235 |  $<$1.9 |  $<$6.1 [$<$0.006] |  $<$0.6
K-40 |  $<$17 |  $<$38 [$<$0.036] |  $<$1.1
Co-60 |  $<$0.74 |  $<$2.5 [$<$0.002] |
Cs-137 |  $<$1.1 |  $<$1.9 [$<$0.002] |
Table 2: Measurements of radiopurity performed at the Canfranc Underground
Laboratory for the bare PMMA (second column) and for a FAT-GEM with thermally-
bonded copper electrodes (third column). The last column shows the
measurements of the PMMA light guide from the DEAP-3600 detector [42].

###  2.3 Working principle

Having a cutoff typically in the range of 300 nm [43], PMMA is not a VUV-
transparent material. Therefore, without further treatment, it is not optimal
for use under noble gas scintillation as the amount of light detected would be
limited by the solid angle defined by the holes’ walls. In principle, coating
the walls with TPB should allow to make use of such a ‘lost’ light at near
100% efficiency [44], re-emitting it isotropically in a band (peaked at
$\lambda\sim$420 nm, with a cutoff around $\lambda\sim$350 nm [45]) to which
the PMMA is fully transparent. Additionally, a reflective layer would help
recovering part of the wavelength-shifted light that is emitted in the
opposite direction with respect to the light sensor (Figure 4).

Figure 4: Illustration of the FAT-GEM concept. The electron enters from above
into the channels due to the intense electric field, and produces
electroluminescence (VUV). The light is subsequently wavelength-shifted into
the visible range through TPB-coating of the holes’ walls, reflected at the
cathode inner surface and transmitted through the transparent anode until it
reaches the photosensor.

##  3 Experimental methods

###  3.1 Setup

The setup used was the same as in previous works [32, 33]: the
electroluminescent structures served as the anode of a drift/conversion region
of 1.5 cm in length, closed by an aluminum cathode with an x-ray source (55Fe)
placed behind it (Figure 5). Initially, a high-transparency mesh was placed
covering the anode of the amplification structures, but it was removed once
assessed that it had a negligible impact on the performance. At 1.5 cm from
the FAT-GEM anode, a Hamamatsu R7378 PMT was placed, covered with a grounded
mesh to eliminate fringe-fields from the gas region leaking into the PMT
vacuum. The PMT was then connected to a pre-amplifier (ORTEC 142), an
amplifier (ORTEC 572A) and finally to an MCA (Amptek 8000D) to collect the
spectra. In order to convert from MCA channels to photoelectrons, a
calibration run was performed by connecting the PMT directly to an acquisition
card (CAEN DT5725), as described later.

A sketch of the experimental setup and a description of the acquisition system
can be seen in Figure 5. The container vessel was connected to a
pressure/vacuum system and, before filling, it was pumped down to 10-4 mbar.
During operation the gas was circulated through a cold getter (Entegris GPU80)
specified to trap H2O and O2, with a KNF compressor (N286.15) at around 20
Nl/min.

Figure 5: Sketch of the experimental setup and the two acquisition modes
employed during the measurements. The central one was used regularly for most
measurements, while the right one was employed to calibrate from MCA channels
to photoelectrons.

During the argon measurements, high-purity fresh gas (6N bottle, i.e., ppm-
level contamination) was used for each run (namely, for each EL-field series).
During the measurements with xenon, on the other hand, the gas was
cryorecovered after each run and residual impurities were pumped away.
Variations in the yields were observed during the measurements and estimated
to represent a 15%, at maximum. They were attributed to gas contamination and
PMT drifts.

###  3.2 Data taking and analysis

For each structure, the electroluminescence field ($E_{EL}$) was kept fixed
while scanning the drift field ($E_{Dr}$), to achieve the highest electron
transmission. With the drift field fixed at that value, a scan for different
electroluminescence field values was performed. MCA spectra were then stored,
rebinned, background-subtracted and finally fitted to a gaussian (Figure 6).
Apart from the electronic noise at low channel count, there was a second
source of background correlated with activity in the buffer region (between
the structure and the PMT-mesh) when the anode of the FAT-GEM was positively
biased (Figure 6-a). The source of background was assessed by a dedicated run
with the 2-mm structure, taking spectra at the same drift and
electroluminescence fields, but with the anode of the structure grounded
(Figure 6-b). Figure 6-c shows for reference a spectra taken close to the
optimal electric field. At the highest pressures, when bipolar biasing of the
FAT-GEMs was unavoidable due to feedthrough limitations, the background
subtraction was implemented to extract the energy resolution.

Figure 6: a) and b): exemplary spectra taken with the MCA (2 mm structure,
$P$=2 bar, $E_{Dr}$=167 V/cm/bar, $E_{EL}$ = 4.6 kV/cm/bar), with a Gaussian
fit superimposed (22.4% FWHM -a), and 22.0% FWHM -b), respectively). This run
corresponds to a control measurement performed with bipolar bias (a) and
grounded anode (b). The difference in background activity is attributed to the
buffer region and was subtracted during analysis. c): MCA spectrum taken for
the 2 mm structure at $P$=2 bar, $E_{Dr}$=167 V/cm/bar, $E_{EL}$ = 6.9
kV/cm/bar, corresponding to an energy resolution of 18% FWHM. The PMT voltage
was lower for this point than for the spectra in a) and b), in order to match
the MCA range.

In order to convert from MCA channels to photoelectrons, a two-step procedure
was followed: first, the PMT was calibrated according to the procedure
described in [36]: a green LED was powered with a fast pulser (Agilent
81130A), setting an intensity estimated to be at the single-photon level. Data
was then taken with an acquisition card (CAEN DT5725) and fitted with
gaussians, whose integral values were bound by Poisson statistics. Second, a
dedicated run with the 2-mm uncoated structure was performed, setting the same
values of drift and electroluminescence fields as for the data taken with the
MCA. Through a pulse-shape analysis and fitting routine, and resorting to the
single-photon calibration, the number of photoelectrons/electron was obtained.
Finally, the slope between the number of photoelectrons/electron and the peak
position in the MCA data was found by performing a linear fit, providing the
calibration value (Figure 7, left).

Since different PMT biases were used during the measurements, the relation
between gain and voltage was assessed with an LED. The data was then fitted to
a power-law, showing agreement with the data-sheet from the manufacturer
(Figure 7, right).

Figure 7: Left: calibration of the MCA spectra for the 2-mm uncoated
structure: $P=8$ bar, VPMT=550 V. The $y$-axis shows the 55Fe X-ray peak
position obtained from pulse shape analysis, and the $x$-axis the one from the
peak obtained from the MCA. Right: average amplitude of the PMT signals as a
function of the bias voltage for three LED intensities. Each LED intensity
series was taken so as to keep the PMT charge per pulse within the same range,
and re-scaled afterwards.

##  4 Simulations

Simulations were performed according to the following steps. First, the
electric field maps ensuing from an elementary amplification cell were created
with Ansys [46], (Figure 8a). Field and geometry maps were then imported into
Garfield++ [47] and extended in the $x$ and $y$ axis (axes parallel to the
electrode plane), building the FAT-GEM structure (Figure 8b). The position of
the primary electrons was generated following an uniform $x$, $y$ distribution
centered at the middle of the detector, extending over a $\pm 5$ mm region and
placed at 0.1 mm from the cathode plane. The impact of considering a
distributed ionization source corresponding to the X-ray mean free path
(around 2.7 mm/bar) was evaluated but the differences dimmed too small. In
Figure 8c the path of an electron is shown: as expected, most of the
collisions that produce an excited state happen inside the FAT-GEM hole.

The Garfield++ simulation provided the 3D-distribution of excited states over
the entire array of holes. This was then imported into Geant4 [48] and used to
sample the initial positions of the scintillation photons, that were
subsequently launched isotropically.222A control simulation considering
excited states produced only in the central hole yielded little differences.
Photon ray-tracing was handled by a Geant4 model with optical properties
implemented for all materials, extending the model used in Ref. [33]. New
wavelength-dependent optical properties added to the model included the
transparency of ITO (approx. 79%, based on the suppliers’ specification [41]),
measured reflectivity for the laminated ESR foil, and TPB properties as in
[49]. This allowed us to estimate the geometrical efficiency of the
experimental setup (Figure 8d). A two-mesh configuration was simulated using
similar techniques, except that the mesh transparency was introduced as an
effective number and the reflectivity of the aluminum cathode [50] was
included too (yielding about a 10% increase, an effect negligible for FAT-
GEMs).

Figure 8: Simulations steps: (a) elementary cell in Ansys, (b) Ansys field
maps loaded in Garfield++, (c) electron tracking in Garfield++, and (d)
photon-tracing in Geant4.

Finally, photon detection efficiency (PDE) curves were considered for four
illustrative sensors: Hamamatsu R7378 [51] (employed in these measurements),
R11410-21 (used in XENON1T [52]) PMTs, and two representative SiPMs: FBK NUV-
HD-SF [54] and Hamamatsu VUV4 (S13370) [55].

##  5 Results

###  5.1 Untreated FAT-GEMs

In Figure 9, the characterization of the uncoated 2 mm-structure is reported.
Data were taken with xenon gas at 2, 4, 6, 8, and 10 bar. The top row refers
to the drift-scan measurements: on the left the energy resolution (FWHM), on
the right the light yield normalized to the maximum (‘transmission’ curve).
The decrease of transmission at high drift fields can be explained by the loss
of field-focusing: the electron, under a strong drift field, hits the surface
of the structure instead of being channeled into the holes. The decrease of
transmission at low fields is qualitatively reproduced by simulations too
(Figure 10) and can be attributed partly to electroluminescence extending
outside of the hole region and increasing as the drift field increases.
However the much stronger trend in data suggests the presence of additional
contributions (presumably due to attachment to impurities).

The bottom row in Figure 9 shows the results of the electroluminescence scan:
on the left the energy resolution, on the right the detected number of
photons/electron, namely photoelectrons/electron ($n_{pe}$). One can see that
the scintillation yield increases with pressure as expected, except for 10 bar
where the voltage limit of our power supplies is reached. The voltage drop
across the FAT-GEM amounts to 15 kV in those conditions.

Figure 9: Drift field (top) and EL field (bottom) scans for the uncoated 2 mm-
hole FAT-GEM. The lines for the energy resolution and the transmission curves
are splines meant to guide the eye. Figure 10: Experimental (left) and
simulated (right) electron-transmission curve for the uncoated 2-mm-hole FAT-
GEM. The decrease of transmission is reproduced at high fields and partially
at low fields. An extra contribution is suspected to come from attachment to
impurities.

The ‘typical’ best energy resolution was 17-17.5%, obtained for virtually any
structure and pressure, at high EEL fields (Figure 11). A dedicated run with
xenon at 4 bar and meshes (electroluminescence gap of 5 mm) yielded an energy
resolution a bit over 15% despite the much increased scintillation (the mesh
results are shown through the continuous line in Figure 11).

Figure 11: Energy resolution at 4 bar for FAT-GEM structures of different hole
dimensions (blue - 2 mm ‘B’, purple - 3 mm ‘C’, light blue - 4 mm ‘D’). For
reference, the splines corresponding to the double-mesh data (black,
continuous) and 10 bar data (blue, dot-dashed) are given too (and data-points
can be found elsewhere in this document).

In Figure 12 (left) the pressure-reduced yields are shown for the three
uncoated structures and all pressures. All points fall on a line, showing that
operation takes place in pure EL-mode, i.e., largely free from avalanche
multiplication. Comparing the results with simulations (Figure 12, right), the
latter predict slightly larger yields: 15% (2 mm), 22% (3 mm), 30% (4 mm).
Remarkably, both in simulation and measurements, the threshold to have
scintillation light is observed to be 1 kV/cm/bar (above the canonical 0.7
kV/cm/bar for uniform-field conditions in xenon [37]) for all structures. The
increase can be interpreted as the lower effective field in the central axis
of the hole (where electrons are field-focused) compared to a parallel-
electrode configuration. In data, a small deviation is observed for 2 mm
structures, providing a hint that the yields at high $E_{EL}/P$ and low $P$
might have a small contribution from avalanche multiplication, biasing the
linear fit towards higher threshold values.

Figure 12: Left: pressure-reduced scintillation yields measured for FAT-GEM
structures of different hole dimensions (dark blue 2 mm - ‘B’, purple 3 mm -
‘C’, light blue 4 mm - ‘D’). Right: pressure-reduced scintillation yields
simulated for FAT-GEM structures of different hole dimensions. (Measurements
and simulations performed for drifts fields corresponding to the transmission
plateau).

An additional structure with 1 mm hole size was characterized, yielding a
factor $\times 3$ less light than the 2 mm structure. This seems to support
the expectation from simulation, where a minimum diameter size of 1.75 mm is
needed in order to reach 100% ‘entrance $\times$ transmission’ probability for
the impinging electron, on a 5 mm-long xenon channel at typical EL fields.

###  5.2 TPB-coated FAT-GEMs

A direct assessment of the impact of TPB at the holes’ walls was made for the
2 mm structure under argon, since our PMT has a fused-silica window and is
therefore blind to its scintillation. As expected, no signal was observed
before coating with TPB, however a clear spectrum was formed after doing so
(Figure 13, dark-blue circles).

A run with xenon at 4 bar showed a 125% average increase of detected light
with respect to the uncoated structure, resulting on a mere 25% deficit with
respect to meshes at the maximum operating field of 3.5 kV/cm/bar (Figure 13,
light-blue circles). Such a field was significantly lower than the 5 kV/cm/bar
applied to the uncoated structures and was chosen simply to fully preserve the
structure for further studies, avoiding risk of discharges and TPB damage. At
that field, the energy resolution was comparable with the one provided by the
two-mesh setup (Figure 13, left).

A structure with ESR was also tested in xenon at 4 bar (pink circles),
providing just 6% more light than the coated structure without reflector. As
discussed later in text, such a modest increase can be understood largely due
to the presence of internal reflection inside the PMMA, due to the specular-
reflection characteristics of ESR, and/or a bad optical coupling. A path to
improve this performance is discussed later in text.

Figure 13: Performance studies of the TPB-coated FAT-GEMs (light and dark blue
- ‘E’, pink - ‘F’), including results for the uncoated structure (‘B’), and
two parallel meshes (black circles). These studies were performed at 4 bar, in
xenon and argon.

Short-term aging of the TPB-coated FAT-GEMs was studied in xenon at 4 bar,
operating the structure with $\Delta V$=6.8 kV continuously over 20 hours
(event rate $\sim$5 Hz). Non-monotonous variations within a maximum of 25%
were observed, attributed mainly to PMT drifts (Figure 14). No indication of
permanent damage was evident after the test.

Figure 14: Study of possible TPB-damage induced by sustained operation under
high voltage ($\Delta{V}=6.8$ kV). The optical gain of the FAT-GEM was
monitored over 20 h in xenon at 4 bar and, except for a non-monotonous
variation (attributed to the PMT drift), no strong short-term deterioration
could be seen.

##  6 Discussion

The best energy resolution that was measured for FAT-GEMs in this work was 17%
(FWHM), at the 5.9 keV peak of 55Fe. This represents almost a factor two
increase with respect to the value expected from the Fano factor alone [56,
57, 58, 59, 60, 61]. The measurement is not photon statistics -limited, as
similar asymptotic values were obtained for different optical gains (up to a
number of detected photoelectrons per electron $n_{pe}=10$). Further, similar
results were obtained both with a double-mesh and with a drift-less
configuration (the latter being more immune to attachment). The deviation from
the Fano limit can be qualitatively understood from the afterpulsing of this
PMT model (as observed during the LED characterization): it appears with a
delay of about 250 ns, and can reach about 10% of the signal; as the
ionization cloud spreads over at least a few µs due to the combined effects of
the photoelectron range and diffusion, afterpulsing can not be removed and its
event-by-event fluctuations are not correctable.

Notwithstanding, an extrapolation of present results up to the
$Q_{\beta\beta}$-scale of 136Xe (2.45 MeV) indicates that the achieved energy
resolution is competitive with the ones reached by current experiments and
other R&D efforts (Figure 15). The recent result of 0.73% at 1.836 MeV (star),
reported for Teflon-based perforated structures in [63], gives further support
to the notion that, in practical applications, this type of EL-structures are
already within the double-mesh performance limit in terms of optical gain and
energy resolution.

Figure 15: Energy resolution in this work (dark-blue circle) and comparison
with other experiments (Figure adapted from [62], with data from [63, 65, 66,
67, 68, 69, 70]). The Fano factor represented by the dashed line is an average
value from [56, 57, 58, 59, 60, 61], while the band shows the region
comprising the highest and lowest values, considering the entire energy range
involved.

To better understand the present technology limits, it is relevant to estimate
the wavelength-shifting-efficiency (WLSE) achieved for the TPB-coating process
inside the structure channels. The ratio of the TPB-coated structure to the
non-coated one has been used for this purpose, as the ratio should be more
immune to mis-modeling effects (Figure 16). The uncertainty band was taken to
be 15%. As shown, the estimated WLSE of the TPB lies within the 74% to 128%
range, centered at 105%, in line with the literature results [64, 44].
Simulations performed for the structure with ESR produced slightly lower
values of the WLSE of around 94%, that could point to a bad optical coupling
(or modeling) of the ESR reflector.

Figure 16: Ratio of the light yield of the TPB-coated FAT-GEM to the uncoated
one (purple circles), as a function of the pressure-reduced electric field,
obtained in xenon at 4 bar. The light-red band accounts for the systematic
uncertainty in data. Wavelength-shifting-efficiency (WLSE) has been estimated
by comparison with the ratio predicted in simulations (WLSE values indicated
by dashed lines).

The process of wavelength-shifting results in a different spectral content for
the FAT-GEM and double-mesh configurations, so it is interesting to perform a
comparison for different photosensors, based on the results achieved in this
work. Figure 17 shows the simulated number of photoelectrons (normalized to
cm$\cdot$bar) assuming the nominal PDE of each of the four exemplary
photosensors discussed here (meshes in black, FAT-GEM (present) in pink, FAT-
GEM (enhanced) in green). The ‘enhanced’ version of the FAT-GEM assumes a
diffuse reflector instead of ESR to minimize the effect of photon trapping due
to internal reflection inside the PMMA. Experimental data obtained in this
work are given by stars ($P=4~{}$bar). All comparisons have been made at a
pressure-reduced electric field of $E_{EL}=3.65$ kV/cm/bar for which
discharge-free operation of the FAT-GEM was comfortably achieved.
Extrapolations to a half-hemisphere photosensor plane are shown by the empty
bar.

Figure 17: Simulated light yields in phe/e/cm/bar when considering the PDE’s
of different photosensors, for a pressure-reduced field of 3.65 kV/cm/bar,
$P=4$ bar and a gas gap of 5 mm. The empty bars refer to a half-hemisphere
sensor, while the full bars assume the geometry in this work (2.1 cm diameter
photosensor at 1.5 cm distance). The structures considered are a double-mesh
(black), the FAT-GEM developed in this work (pink), and an ‘enhanced’ FAT-GEM
after the modifications discussed in text (green). The blue stars refer to
experimental data in this work.

##  7 Conclusions

The use of ‘ad hoc’ perforated structures for electroluminescence is reaching
maturity. Here we present performances for the FAT-GEM technology (Field-
Assisted Transparent Gaseous Electroluminescence Multipliers), that are
already matching those achievable for double-meshes, our proxy for the ‘ideal’
uniform-field situation. The optical gain achieved in xenon at 4 bar, at a
pressure-reduced electric field of 3.65 kV/cm/bar, is within 18% of the value
achieved in a double-mesh configuration with the same photosensor coverage, a
bit over the systematic uncertainty of present data (15%). Further, a good
description of the observed yields can be achieved if assuming a WLSE of 105%
for the TPB-coated channels. The structure is electrically stable at 3.65
kV/cm/bar (4 bar) and 2.8 kV/cm/bar (10 bar), the latter limited by the
maximum power supply of our equipment. Despite being in a high-field region,
no systematic TPB degradation was observed during 20 h of continuous
operation. Assuming complete hemispherical coverage, the above WLSE figure
extrapolates to a number of detected photoelectrons (at 4 bar) in the range
of: 29(41) for Hamamatsu R7378 PM, 43(57) for Hamamatsu R11410-21 PM, 60(92)
for FBK NUV-HD-SF SiPM and 66(99) for Hamamatsu VUV4 SiPM when considering the
present (or enhanced) FAT-GEM structures. Higher values are anticipated at
higher pressures. The observed energy resolution, on the other hand,
extrapolates to 0.84% (0.91%) FWHM for 4 bar (10 bar) at the $Q_{\beta\beta}$
of 136Xe, competitive for next-generation $\beta\beta 0\nu$ experiments.
Evidence has been presented, pointing to the intrinsic resolution of the
structure being better than that.

The FAT-GEM concept combines the properties of gas scintillation and light-
guides, being radiopure, versatile in design and intrinsically transparent
from the hard VUV up to visible and near-IR regions (1600 nm). It is called to
solve the scaling issues for large-volume chambers and perhaps offer an
universal technique to implement electroluminescence readouts in noble-
elements.

##  8 Acknowledgments

This research has been sponsored by RD51 funds through its ‘common project’
initiative, and has received financial support from Xunta de Galicia (Centro
singular de investigación de Galicia accreditation 2019-2022), and by the
“María de Maeztu” Units of Excellence program MDM-2016-0692. DGD was supported
by the Ramón y Cajal program (Spain) under contract number RYC-2015-18820.
This research was also partly funded by the Spanish Ministry (‘Proyectos de
Generación de Conocimiento’, PID2021-125028OB-C21), the National Science
Centre, Poland (Grant No. 2019/03/X/ST2/01560), the International Research
Agenda Programme AstroCeNT (MAB/2018/7) funded by the Foundation for Polish
Science from the European Regional Development Fund (ERDF), and the European
Union’s Horizon 2020 research and innovation programme under grant agreement
No 952480 (DarkWave project). The prototype construction was carried out with
the use of CEZAMAT (Warsaw) cleanroom infrastructures financed by the ERDF; we
thank Maciej Trzaskowski and CEZAMAT staff for technical support. We thank
Carlos Guerra (Spartech/Polycast) for kindly providing the acrylic samples for
this work; as usual, expert screening work by I. Bandac (Laboratorio
Subterráneo de Canfranc) was essential to the radiopurity results presented
here.

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