# Large-Scale Detector Testing for the GAPS Si(Li) Tracker

Mengjiao Xiao, Achim Stoessl, Brandon Roach, Cory Gerrity, Ian Bouche, Gabriel
Bridges, Philip von Doetinchem, Charles J. Hailey, Derik Kraych, Anika Katt,
Michael Law, Alexander Lowell, Evan Martinez, Kerstin Perez, Maggie Reed,
Chelsea Rodriguez, Nathan Saffold, Ceaser Stringfield, Hershel Weiner, Kelsey
Yee M. Xiao, B. Roach, I. Bouche, A. Katt, K. Perez, and K. Yee were with the
Massachusetts Institute of Technology, Cambridge, MA 02139, USA.A. Stoessl, C.
Gerrity, P. von Doetinchem, and H. Weiner were with the University of Hawai’i
at Mānoa, Honolulu, HI 96822, USA.G. Bridges, C. Hailey, D. Kraych, M. Law, E.
Martinez, K. Perez, M. Reed, C. Rodriguez, N. Saffold, and C. Stringfield were
with Columbia University, New York, NY 10027, USA.A. Lowell was with the Space
Sciences Laboratory, University of California, Berkeley, Berkeley, CA 94720,
USA.GAPS is supported in the U.S. by the NASA APRA program (Grant Nos.
NNX17AB44G, NNX17AB46G, and NNX17AB47G), in Japan by the JAXA/ISAS Small
Science Program FY2017, and in Italy by the ASI/INFN agreement No.
2018-22-HH.0: “Partecipazione italiana al GAPS — General AntiParticle
Spectrometer.” M. Xiao, B. Roach, and K. Perez are supported by Heising-Simons
Foundation award 2018-0766. C. Gerrity is supported by NASA under award No.
80NSSC19K1425 of the Future Investigators in NASA Earth and Space Science and
Technology (FINESST) program. K. Yee is supported through the U.S. National
Science Foundation Graduate Research Fellowship under grant 2141064.

###### Abstract

Lithium-drifted silicon [Si(Li)] has been used for decades as an ionizing
radiation detector in nuclear, particle, and astrophysics experiments, though
such detectors have frequently been limited to small sizes
($\boldmath{\text{few\,cm}^{2}}$) and cryogenic operating temperatures. The
10-cm-diameter Si(Li) detectors developed for the General Antiparticle
Spectrometer (GAPS) balloon-borne dark matter experiment are novel
particularly for their requirements of low cost, large sensitive area
($\boldsymbol{{\sim}10\text{\,m}^{2}}$ for the full 1440-detector array), high
temperatures (near –40$\boldsymbol{\,{}^{\circ}}$C), and energy resolution
below 4 keV FWHM for 20–100-keV x-rays. Previous works have discussed the
manufacturing, passivation, and small-scale testing of prototype GAPS Si(Li)
detectors. Here we show for the first time the results from detailed
characterization of over 1100 flight detectors, illustrating the consistent
intrinsic low-noise performance of a large sample of GAPS detectors. This work
demonstrates the feasibility of large-area and low-cost Si(Li) detector arrays
for next-generation astrophysics and nuclear physics applications.

##  I Introduction

First employed as an ionizing radiation detector in the 1950s, lithium-drifted
silicon [Si(Li)] detectors have since found wide use in a variety of nuclear,
particle, and astrophysics applications as charged-particle and photon
detectors (e.g., [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]). The introduction of
lithium ions into p-type silicon compensates impurities in the crystal
lattice, producing nearly-intrinsic regions up to a few millimeters in
thickness. Early Si(Li) detectors were generally limited to active areas of a
few cm2 by the size and purity of available monocrystalline silicon wafers, by
the increase in capacitance with detector area, and by the uniformity in
lithium drifting across the detector (e.g., [12]). In time, improvements in
production methods enabled the development of larger Si(Li) detectors with
energy resolutions suitable for x-ray spectroscopy (e.g., [13, 14]).

Si(Li) detector technology is ideal to meet the unique performance
requirements of the General Antiparticle Spectrometer (GAPS) experiment. GAPS
is a balloon-borne particle tracker and x-ray spectrometer, optimized to
detect low-energy (${<}0.25$ GeV/nucleon) cosmic antinuclei (i.e.,
antiprotons, antideuterons, and antihelium) resulting from dark-matter decay
and/or annihilation in the Milky Way [15, 16, 17, 18, 19, 20, 21, 22]. At the
heart of the GAPS payload and particle identification scheme is a novel
exotic-atom technique. An incoming antinucleus first passes through plastic-
scintillator time-of-flight (TOF) panels, providing velocity and energy-
deposition (d$E$/d$x$) information. The antinucleus then experiences d$E$/d$x$
losses in the Si(Li) tracker before coming to rest and being captured by an
atomic nucleus in the Si(Li) detectors or surrounding support materials. This
exotic atom subsequently de-excites, emitting a cascade of characteristic
x-rays whose energies are related to the reduced mass and nuclear charge of
the nucleus-antinucleus pair. Finally, the nucleus and antinucleus annihilate,
producing a shower of pions and protons whose multiplicity scales with the
mass of the antinucleus. This combination of signatures provides strong
rejection power against the abundant protons, alpha particles, and other non-
antimatter cosmic-ray particles.

Deploying this particle-identification technique on a balloon experiment such
as GAPS presents several unique challenges. First, a large active detector
area (${\sim}$10 m2) is required to search for rare signals such as
antideuterons or antihelium. Second, the detectors must be sufficiently thick
to serve as a stopping target for low-energy antinuclei, while also being
sufficiently thin for characteristic x-rays with energies ${\sim}$20–100 keV
to escape. Third, mass and power constraints prevent the use of a cryostat
large enough to contain the full tracker, so the GAPS detectors must be
operable near –40$\,{}^{\circ}\text{C}$, achieved with a novel oscillating
heat pipe thermal system [23, 24]. These requirements motivate the use of
10-cm-diameter and 2.5-mm-thick Si(Li) detectors for the GAPS tracker, with
each detector segmented into eight strips. Previous works have described the
fabrication, passivation, and testing of several prototype detectors [25, 26,
27, 28, 29].

In this paper, we describe the low-noise and low-temperature characterization
of the more than 1100 Si(Li) detectors that will be used for the first GAPS
flight. Before integrating the Si(Li) detectors into GAPS, we must
characterize the performance of each detector at the operating temperatures
expected in flight. These tests serve several purposes. First, we must verify
that the detector is operable (i.e., that its current draw will not saturate
the flight high-voltage power system). Second, we must characterize the x-ray
energy resolution of each strip. From these x-ray measurements we construct
noise models (i.e., energy resolution as a function of peaking time) for each
detector, allowing us to verify that the detector is performing as expected
and to predict the detector performance using the flight readout system.
Third, we will use these measurements to determine the placement of detectors
within the tracker, with higher-quality detectors being placed in the upper
layers (where more anti-nuclei events are expected).

In Sec. II we describe the custom low-noise, low-temperature testing system
that was developed to allow fast characterization of this large sample of
detectors. In Sec. III, we describe our procedures for detector processing,
testing, and data acquisition. In Sec. IV, we characterize this large sample
of detectors using a physically-motivated noise model. We conclude in Sec. V,
demonstrating that large-area and low-noise Si(Li) detectors can be
economically mass-produced and tested.

(a)

(b)

(c)

Figure 1: Top: A GAPS flight module without the top polypropylene window. The
FEB is the green cross-shaped board, in the center of which is the custom ASIC
chip (black). Middle: A module mounted to the SUN chamber door for testing.
Two Faraday cages have been pulled to the side to show the discrete
preamplifier boards (green) mounted to the FR4 testing board (yellow). Bottom:
The MIT Si(Li) testing system, with major components labeled. A system using
identical components was constructed at UHM.

##  II Detector Testing System

###  II-A GAPS Detector Module

The basic functional unit of the GAPS Si(Li) tracker is the detector module
(hereafter simply module) shown in Fig. 1. Each module contains four Si(Li)
detectors mounted into an aluminum frame, to which the detectors are grounded
via their guard rings. Each detector is rigidly mounted into place using
several fluorosilicone O-rings and G10 clamps. These clamps also secure a gold
tab to the bottom ohmic contact of each detector to supply the bias voltage.
Finally, we secure polypropylene windows on the top and bottom of each
detector module, providing a sealed volume for the detectors. These windows
(aluminized on their exterior surface to prevent metal flakes within the
detector volume) allow us to shield the detectors from stray light,
environmental contamination, and electromagnetic interference, and to flush
the modules with dry N2 gas during payload assembly and testing to suppress
humidity. Each module also carries a front-end board (FEB) with several major
roles. First, each FEB carries a custom ASIC chip to which the Si(Li) strips
are wirebonded, and which is responsible for processing and digitizing Si(Li)
energy deposits over a large dynamic range of tens of keV to ${\gtrsim}$100
MeV [30, 31, 32, 33]. Second, the FEBs also provide the 250-V reverse-bias
voltage to each detector. Lastly, the FEBs facilitate a power and
communication link between the flight computer and the ASICs.

As the FEBs and ASICs were being developed simultaneously with the Si(Li)
detector testing, we require a different method of detector readout for the
lab testing described in this work. To that end, we replace the FEB and top
polypropylne window with a single FR4 board. Each board contains a 1-M$\Omega$
resistor for overcurrent protection and a 10-nF capacitor for noise protection
as shown in Fig. 2. Spring-loaded conductive pins (“pogo pins”) mounted to the
underside of the window couple the Si(Li) strips to conductive pads on the top
surface of the window for signal readout via charge-sensitive discrete
preamplifiers.

Figure 2: Electrical connection diagram for the Si(Li) module testing system.
For clarity, only one of the four Si(Li) detectors is shown, with all four
detectors receiving the same –250-V bias via the 1-M$\Omega$ resistor. The
electrical ground for the Si(Li) module and preamplifier holder boards is
defined by the LVPS. The exterior electronics (LVPS, patch panel, and NIM
crate) receive clean AC power and grounding from the isolation transformer,
with the lab computer (PC) and cold chamber receiving AC power and grounding
from the building mains. For more details see Sec. II.

###  II-B Custom Si(Li) Module Testing System

The GAPS module testing systems at the Massachusetts Institute of Technology
(MIT) and the University of Hawai’i at Mānoa (UHM) use largely identical
systems and commercially-available components. The purpose of the tests was to
characterize the detector energy resolutions based on known x-ray lines with
energies in the range of the exotic-atom transition x-rays that GAPS is
uniquely designed to detect (${\sim}$20–100 keV). Each testing setup itself is
composed of several major subsystems: the environmental chamber, the cable
feedthrough system, the exterior electronics, the discrete preamplifiers, and
the radioactive source.

####  II-B1 Environmental Chamber

We use SUN Electronics EC13 chambers to provide a temperature- and humidity-
controlled environment during testing, as well as to facilitate the electrical
connections to the module. The GAPS Si(Li) detectors are expected to operate
at a temperatures lower than approximately –40$\,{}^{\circ}$C; therefore, we
test detectors at a conservative –37$\,{}^{\circ}$C. The chambers include
inlets for liquid and gaseous N2 for cooling and humidity suppression,
respectively, as well as a built-in temperature display and interior fan. The
SUN chamber doors were modified in-house to provide holes for cable
feedthrough (discussed later in this section) and detector module mounting to
the attached tray.

####  II-B2 Discrete Preamplifiers

We use custom charge-sensitive discrete preamplifiers to extract signals from
the Si(Li) strips and perform initial pulse shaping. The preamplifiers are
based on Ref. [34], with each preamplifier including a 100-M$\Omega$ feedback
resistor, a 0.5-pF feedback capacitor, and a low-noise JFET with capacitance
${\sim}$10 pF. The preamplifiers have a noise floor of ${\sim}$2 keV FWHM.
Each Si(Li) strip is connected to a single preamplifier, with eight
preamplifiers (i.e., the readout for each Si(Li) detector) mounted into a
holder board. The holder boards are mounted to the FR4 top window of the
module with conductive screws and standoffs, providing both mechanical and
electrical (i.e., ground) connections. Finally, to shield the preamplifiers
and Si(Li) detectors from external noise, we create custom Faraday cages from
0.6-mm-thick aluminum sheets, folded into five-sided rectangular prisms with
dimensions ${\sim}10\text{\,cm}\times 10\text{\,cm}\times 10\text{\,cm}$ to
place atop each detector/holder board, with small holes cut into each to
accommodate the signal and low-voltage power cables.

####  II-B3 Cable Feedthrough System

The cable feedthrough systems provide connections for the low-voltage discrete
preamplifiers, the high-voltage detector bias, the individual discrete
preampflifier signal channels (one per detector strip), and various backup
cables. They are composed of circular non-conductive black Teflon flanges
custom-machined for this purpose, with high-fidelity RG316 coaxial cables
potted through the flanges with the use of Torr Seal. The coaxial cables had
their exterior plastic insulation stripped at a small ($\sim$1-2 mm) length so
they could be to be bonded to the Teflon flange with cyanoacrylate adhesive
prior to the final application of Torr seal. Circular openings consistent with
the flange dimensions were machined into the cold chamber doors, and the
flanges screwed into place with a thin O-ring and potted with Torr Seal to
minimize heat leak during operation.

####  II-B4 Power and Data Acquisition

We use several commercial electronic modules in conjunction with the testing
chamber. A CAEN 1471A high-voltage power supply (HVPS) is used to provide the
–250V reverse bias necessary to fully deplete the detectors, as well as to
monitor the supply current. A 14-bit CAEN N6725 digitizer is used to sample
the voltage waveforms at 250 MS/s from eight Si(Li) strips simultaneously.
Both CAEN modules are mounted into a NIM crate whose onboard cooling fan was
disabled and replaced with an external fan to reduce electromagnetic noise
pickup. The discrete preamplifiers are supplied with $\pm 5\text{\,V}$ and
ground connections via a commercial HY3005F-3 low-voltage DC power supply
(LVPS). The 32 preamplifier signal outputs (one per Si(Li) strip) are
connected to a CXAR-64/MF patch panel, from which up to eight inputs can be
selected and sent to the digitizer (the remaining inputs are terminated by
50$\,\Omega$). The patch panel and digitizer are both controlled by a computer
running custom software. Finally, we use a Tripp-Lite 1-kW power isolation
transformer to provide steady, low-noise AC power and grounding to the NIM
crate, LVPS, and patch panel (the computer and cold chamber receive power
directly from the building mains).

####  II-B5 Radioactive Source

We use a sealed 1-mCi ${}^{109}\text{Cd}$ source to study the energy response
of the GAPS detectors. This isotope has several properties that make it ideal
for GAPS detector testing [35]. First, its ${\sim}$88-keV decay $\gamma$-ray
lies in the energy range of the exotic-atom x-rays that GAPS is designed to
detect. Second, ${}^{109}\text{Cd}$ decays by electron capture to the first
excited state of ${}^{109}\text{Ag}$, and does not produce high-energy
$\alpha$\- or $\beta$-particles that might lead to unwanted detector
backgrounds during testing. (We note that ${}^{109}\text{Cd}$ emits Auger and
conversion electrons with kinetic energies ranging from
${\sim}2.6\text{\,keV}$ to ${\sim}87.9\text{\,keV}$, though these electrons
are easily stopped by the sealed source, aluminum Faraday cages, and FR4 board
above the detectors [36].) Finally, the decays of ${}^{109}\text{Cd}$ also
produce fluorescence x-rays with energies between ${\sim}$22–25 keV, allowing
the study of low-energy detector behavior, though this is outside the scope of
this analysis.

##  III Detector Processing and Testing

###  III-A Detector Pre-selection Model

To enable efficient testing and integration of the GAPS Si(Li) detector
modules, we developed a pre-selection model to group detectors of similar
quality based on their room-temperature leakage current at –250 V bias. The
pre-selection criteria are shown in Table I, and are based on several
requirements. First, the power system developed to supply high voltage to the
flight instrument imposes a current limit of ${\sim}6\,\upmu\text{A}$ per
detector module at –250 V (conservatively, ${\sim}1\,\upmu\text{A}$ per
detector). Second, the ASIC readout developed for GAPS places an upper limit
of 50 nA on each strip’s leakage current, above which the strip cannot be read
out. Initial testing of $\mathcal{O}(20)$ bare (i.e., non-passivated)
detectors showed first that detectors with total room-temperature leakage
current below 300$\,\upmu\text{A}$ remained below the required
$1\,\upmu\text{A}$ at –37$\,{}^{\circ}\text{C}$ (i.e., were functional
detectors); second, that strips with room-temperature leakage current below
12.5$\,\upmu\text{A}$ remained below the required 50 nA at
–37$\,{}^{\circ}\text{C}$ (i.e., were functional strips); and third, that
strips with room-temperature leakage current below $2\,\upmu\text{A}$ had
ASIC-projected energy resolution below 4 keV FWHM at –37$\,{}^{\circ}\text{C}$
(i.e., were suitable for x-ray spectroscopy). We note that all detectors were
assembled into modules and tested at –37$\,{}^{\circ}\text{C}$, even if the
pre-selection criteria indicated they might not be operable.

Table I: Table of criteria and yield rates for x-ray, tracking, and non-usable strips and detectors. The pre-selection criteria are based on RT performance, and all $I_{\text{leak}}$ values are quoted at –250-V bias.  | Strip-Level | Detector-Level
---|---|---
Quality | Pre-selection criteria [RT] | Cold [–37 ∘C] | Yield | Pre-selection criteria [RT] | Cold [–37 ∘C] | Yield
X-ray | $I_{\text{leak}}<2\,\upmu\text{A}$ | ASIC FWHM $<$ 4 keV | 7090 |  $\geq$7 x-ray strips |  $\geq$7 x-ray strips | 776
|  | and $I_{\text{leak}}<50\text{\,nA}$ |  | and $I_{\text{tot}}<300\,\upmu\text{A}$ | and $I_{\text{tot}}<1\,\upmu\text{A}$ |
Tracking | $2\,\upmu\text{A}<I_{\text{leak}}<12.5\,\upmu\text{A}$ | ASIC FWHM $>$ 4 keV | 944 |  $\leq$2 non-usable strips |  $\leq$3 non-usable strips | 235
|  | and $I_{\text{leak}}<50\text{\,nA}$ |  | and $I_{\text{tot}}<300\,\upmu\text{A}$ | and $I_{\text{tot}}<1\,\upmu\text{A}$ |
Non-usable | $I_{\text{leak}}>12.5\,\upmu\text{A}$ | Unstable waveform | 854 | $I_{\text{tot}}>300\,\upmu\text{A}$ |  $\geq$4 non-usable strips | 100
|  | or $I_{\text{leak}}>50\text{\,nA}$ |  |  | or $I_{\text{tot}}>1\,\upmu\text{A}$ |
Total | — | — | 8888 | — | — | 1111

###  III-B Detector Storage and Shipping

Our main goal during detector storage and shipping is to provide as inert an
environment for the detectors as possible. Following passivation at Columbia
University (CU), detectors are returned to their plastic cases and placed into
antistatic bags. Each antistatic bag contains a silica desiccant pack and is
vacuum-sealed before being placed into a freezer maintained at
–20$\,{}^{\circ}\text{C}$ to suppress the rate of lithium drift. When
detectors are selected for testing, they are removed from the freezer and
(still sealed in their antistatic bags) allowed to slowly return to room
temperature in a dry environment before being assembled into modules. Each
module (including FR4 top window, four detectors, and the aluminized
polypropylene bottom window) is placed into an antistatic bag with silica
desiccant and lightly vacuum-sealed, and subsequently placed into another
antistatic bag and lightly vacuum-sealed. The module bags are then enclosed in
custom antistatic foam inserts before being packaged for shipment to the
testing sites (MIT and UHM). At the testing sites, the modules (still in their
antistatic bags) are placed into room-temperature dryboxes maintained at
relative humidity $\lesssim$15%. The modules typically remain at the testing
sites for one to two weeks before being tested and subsequently packaged for
return to CU for long-term storage. We have also tested several detector
modules after nearly two years in storage, both in the room-temperature
dryboxes and in the freezers, and observed no significant change in detector
performance.

###  III-C Module Testing Protocol

When a module is to be tested, we remove it from drybox and affix the aluminum
Z-bars to the four corners of each module to elevate it ${\sim}$2 cm above the
tray. The module is then mounted to the SUN chamber tray with non-conductive
PEEK screws, and the four preamplifier holder boards are mounted and secured
to the top FR4 window. Next, we connect the signal readout and low-voltage DC
power cables to each preamplifier holder board, taking care to ensure that the
readout cables are connected to the high-gain output. Finally, we secure the
aluminum Faraday cage above each detector/holder board with conductive tape,
ensuring that each cage is grounded to the aluminum frame of the module.
Immediately before mounting the door assembly to the SUN chamber, we place a
sealed 1-mCi ${}^{109}\text{Cd}$ source atop the Faraday cages, in the center
of the module, to provide a consistent x-ray flux across the detectors.

With the module now sealed in the SUN chamber, we cool it to
–37$\,{}^{\circ}\text{C}$ over approximately 30 minutes. We also supply dry
nitrogen gas at a rate of a few liters per minute to further suppress any
residual humidity within the chamber. When the chamber temperature readout
indicates the set temperature has been reached, we begin to bias the detectors
at a rate of 3 V/s until –250 V is reached. We find that an additional
${\sim}$15 minutes are required for the high-voltage current to decrease to
its equilibrium value (typically below 100 nA for high-quality detectors). The
data-acquisition software is described in the next section; here, we note that
three minutes is sufficient to acquire several thousand events per strip for a
single detector. During acquisition, we turn off the chamber interior fan,
heating, and cooling systems to suppress noise (i.e., only the temperature
readout remains active). Following the three-minute period, these systems are
turned back on and the chamber is allowed to re-cool for at least ten minutes.

Once x-ray events have been acquired for all detectors, we ramp the detector
bias down to zero at a rate of 3 V/s and allow the chamber to return to room
temperature over approximately 30 minutes. The nitrogen gas flushing is
particularly important for humidity suppression during the warm-up, as the
liquid nitrogen valve is closed. Once the chamber has returned to room
temperature, we remove the door assembly and disconnect the module’s
mechanical and electrical connections. The module is then returned to the
drybox for short-term storage.

###  III-D Data Acquisition and Processing

For each Si(Li) detector strip, we must acquire and fit x-ray energy spectra
using at least ten peaking times $\tau_{\text{p}}$, ranging from
0.5–30$\,\upmu\text{s}$, to fully sample the noise model described in Sec.
II-D. (The pulse peaking time $\tau_{\text{p}}$ is the time required for the
shaped pulse to reach its maximum [37].) With more than 1000 detectors to
test, any method involving the acquisition of spectra at individual peaking
times would require an impractical amount of time.

To increase the module testing speed, we implement custom software to read
each strip’s voltage waveforms directly from the N6725 digitizer for later
offline processing. To fully sample the preamplifier signal, which has a decay
time constant $\tau_{\text{d}}\sim 50\,\upmu\text{s}$, we record 160
$\upmu\text{s}$ per waveform, of which $4\,\upmu\text{s}$ is pre-trigger to
establish a baseline. Each waveform is sampled at a rate of 250 MS/s, and the
dynamic range of the digitizer is set to 0.5V peak-to-peak with 80% DC offset.
We acquire waveforms from eight strips (i.e., one detector) simultaneously for
three minutes, producing several thousand events per strip depending on
proximity to the x-ray source. The waveforms for each detector are saved in a
root file for offline analysis.

To construct x-ray spectra for each strip, we first shape the waveforms with
fourth-order Gaussian filters [38] implemented in software, as shown in Fig.
3. We use a set of peaking times $\tau_{\text{p}}$ ranging from
0.5–30$\,\upmu\text{s}$, allowing us to sample the three terms in the noise
model described in Sec. IV. The amplitude of the shaped pulse is proportional
to the x-ray energy deposition. For each detector strip, we generate one
spectrum per $\tau_{\text{p}}$ value. We fit the x-ray spectra with two
Gaussian functions representing the ${}^{109}\text{Cd}$ full-absorption peak
and Compton shoulder, with both Gaussians’ peak location, width (FWHM), and
amplitude allowed to vary. Finally, we convert these spectra to energy by
normalizing the best-fit peak centroid to the known ${\sim}$88-keV full-
absorption peak from ${}^{109}\text{Cd}$. Previous testing with the 59.5-keV
and 88-keV $\gamma$-rays from ${}^{241}\text{Am}$ and ${}^{109}\text{Cd}$,
respectively, has demonstrated the linearity of the GAPS Si(Li) energy
response in the range ${\lesssim}100$ keV relevant for this work [27].

Crucially, a single three-minute data acquisition per detector is sufficient
to construct a noise model for all eight strips. Including re-cooling after
each detector is tested, this method allows us to acquire a full set of data
for each module in less than one hour; thus, our throughput is mainly limited
by the ${\sim}$two hours required to cool the chamber, warm it back up to room
temperature, and mount/unmount the detector module from the chamber.

(a)  (b)  (c)

Figure 3: The data-analysis workflow for strip A of GAPS Si(Li) detector 1054
tested at –37 ${}^{\circ}\text{C}$. Top: a single baseline-subtracted waveform
and the corresponding $\tau_{\text{p}}=4\,\upmu$s Gaussian-shaped pulse.
Middle: the corresponding ${}^{109}\text{Cd}$ x-ray energy spectrum, binned to
0.2 keV/bin for presentation. Bottom: the best-fit x-ray noise model from Eq.
(1) as a function of $\tau_{\text{p}}$. FWHM uncertainties are comparable to
the size of the data points.

##  IV Analysis and Results

There were three primary goals of the Si(Li) detector testing effort. First,
we sought to demonstrate that the detectors’ noise characteristics were
consistent with the noise model described in Eq. (1). Second, we used the
measured x-ray energy resolution to sort the detectors’ quality and inform
their placement within the payload. Finally, we used the extracted noise-model
parameters to model the detectors’ expected performance in the flight
instrument.

###  IV-A Noise Model

For each strip, we fit the full-width-at-half-maximum (FWHM) energy resolution
at each peaking time $\tau_{\text{p}}$ to the following noise model
appropriate for the discrete preamplifiers [27]:

$\displaystyle{}\text{ENC}^{2}$
$\displaystyle=\left(2qI_{\text{leak}}+\frac{4kT}{R_{p}}\right)F_{i}\tau_{\text{p}}$
(1)
$\displaystyle\;\;\;\;+4kTC_{\text{tot}}^{2}\left(R_{s}+\frac{\Gamma}{g_{m}}\right)\frac{F_{\nu}}{\tau_{\text{p}}}+2\pi
A_{f}C_{\text{tot}}^{2}F_{\nu f}$

Here, ENC is the equivalent noise charge, related to the detector FWHM energy
resolution via

$\text{FWHM}\simeq 2.35\epsilon\frac{\text{ENC}}{q},$ (2)

where ${\epsilon\approx 3.6\text{\,eV}}$ is the ionization energy per
electron-hole pair in silicon [39] and $q$ is the elementary charge. The noise
model for each strip contains three free parameters: the strip leakage current
$I_{\text{leak}}$, the coefficient of $1/f$ noise $A_{f}$, and the series
resistance $R_{s}$ arising mainly from the pressure-mounted pogo-pin readout
(though as described below, we are principally interested in $I_{\text{leak}}$
and $A_{f}$). The other terms are as follows: $C_{\text{tot}}$ is the total
capacitance to be defined shortly, $k$ is the Boltzmann constant, $T$ is the
absolute temperature, $\Gamma=1$ is calculated from the geometry of the
preamplifier JFET, $g_{m}=0.1\text{\,mS}$ is the room-temperature
transconductance of the input FET, and $R_{p}=100\text{\,M}\Omega$ is the
parallel resistance in the preamplifier. (We note that any deviation from the
assumed value $\Gamma=1$ adopted in Ref. [27] and in this work would lead to a
small variance in the best-fit value of $R_{s}$; however, $R_{s}$ is not used
in the ASIC noise projection.) The form factors $F_{i}=0.45$, $F_{\nu}=1.02$,
and $F_{\nu f}=0.52$ are appropriate for the fourth-order Gaussian shaper. The
total input capacitance is given by
$C_{\text{tot}}=C_{\text{strip}}+C_{\text{FET}}+C_{\text{int}}+C_{\text{stray}}$,
including contributions from the Si(Li) strip ($C_{\text{strip}}\approx
37\text{--39\,pF}$ at –250 V), the preamplifier FET ($C_{\text{FET}}\approx
10\text{\,pF}$), and any inter-electrode ($C_{\text{int}}$) and stray
($C_{\text{stray}}$) capacitance. Previous work [27] has shown that
$C_{\text{int}}+C_{\text{stray}}\approx 20\text{\,pF}$, so we fix
$C_{\text{tot}}=70\text{\,pF}$ during our noise-model fits to lift the
degeneracy between $C_{\text{tot}}$, $A_{f}$, and $R_{s}$. Lastly, we note
that the minimum achievable resolution for strips with negligible
$I_{\text{leak}}$, $A_{f}$, and $R_{s}$ is ${\sim}$2 keV FWHM, owing to
thermal noise in the 100-M$\Omega$ resistor and the transconductance of the
FET.

The GAPS flight instrument will use a custom ASIC rather than discrete
preamplifiers to read out the Si(Li) detectors. As fabrication and testing of
the ASIC was ongoing during the Si(Li) detector testing campaign, it was
necessary to develop a noise model to predict the detector resolution expected
with the flight ASIC readout. The ASIC noise model is [32]

$\displaystyle\text{ENC}^{2}$
$\displaystyle=2q(I_{\text{leak}}+I_{k})F_{i}\tau_{\text{p}}+4kTR_{\text{eq}}C_{\text{eq}}^{2}\frac{F_{\nu}}{\tau_{\text{p}}}$
(3) $\displaystyle\;\;\;+2\pi A_{f}C_{\text{eq}}^{2}F_{\nu f},$

where $A_{f}$ is either $0.87\times 10^{-13}\,\text{V}^{2}$ (derived from
simulations) or the fitted value from the discrete preamplifier testing,
whichever is greater; $I_{\text{leak}}$ is the strip leakage current;
$I_{k}\approx 2.5\text{\,nA}$ is the effective current in the analog channel;
${C_{\text{eq}}=C_{\text{strip}}+C_{\text{amp}}}$ is the equivalent parallel
capacitance of the strip (${C_{\text{strip}}\approx 37\text{\,pF}}$) and
amplifier input ($C_{\text{amp}}\approx 5\text{\,pF}$); $R_{\text{eq}}\approx
40\,\Omega$ is the equivalent resistance of the wirebond and input PCB trace
(taking the place of $R_{s}$); and $F_{i}=0.64$, $F_{\nu}=0.85$, and ${F_{\nu
f}=0.54}$ are the form factors of the unipolar semi-Gaussian
$\text{(RC)--(CR)}^{2}$ shaper. With these parameters, the ASIC readout
generally achieves the best energy resolution for $\tau_{\text{p}}\sim
1\,\upmu\text{s}$, somewhat lower than the ${\sim}4\,\upmu\text{s}$ achieved
with the discrete preamplifiers. To minimize the contributions from leakage
current at longer peaking times, the ASIC operates in the range
0.25–1.8$\,\upmu\text{s}$. Tests are ongoing to validate this noise model
using the final flight components (ASIC, front-end board, etc), so this work
will use a conservative value $C_{\text{eq}}=70\text{\,pF}$ to account for any
un-modeled stray capacitance.

###  IV-B Detector Quality

We categorize the quality of each Si(Li) strip and detector into three broad
groups based on their projected ASIC resolution, as shown in Table I. The
flight ASIC readout and high-voltage power system place limits on the allowed
leakage current of 50 nA/strip and 1 $\upmu$A/detector, respectively, which we
take as criteria for non-usable strips and detectors at
–37$\,{}^{\circ}\text{C}$. Also included in these categories are strips which
do not produce stable voltage waveforms during testing and detectors with
$\geq$4 non-usable strips. As shown in Table I, the yield rate of non-usable
strips and detectors is ${\sim}$10%, though this is likely an overestimate, as
more mundane issues (e.g., loose cable connections) can mimic the appearance
of non-functional strips.

For the functional strips and detectors, the key performance metric is the
ASIC-projected x-ray energy resolution. To distinguish between the x-rays from
antiprotonic and antideuteronic exotic atoms, we require the projected ASIC
energy resolution determined using Eq. (4) to be $\leq$4 keV FWHM at
-37$\,{}^{\circ}\text{C}$. Strips which meet this criterion are designated
x-ray-quality strips, and detectors with $\geq$7 x-ray strips are designated
x-ray-quality detectors. Strips whose projected ASIC resolution is $>$4 keV
FWHM are designated tracking-quality strips, as they are still able to provide
position and energy-deposition information for charged particles.

In Fig. 5 we show the distribution of strip x-ray energy resolutions obtained
with discrete preamplifiers at ${\tau_{\text{p}}=4\,\upmu\text{s}}$, separated
into x-ray and tracking-quality detectors. (As shown in Fig. 4, strips with
typical values of $I_{\text{leak}}$ and $A_{f}$ coupled to discrete
preamplifiers attain their optimal energy resolution near this value of
$\tau_{\text{p}}$.) We note several features of the distributions. First, the
most-probable value for the energy resolution of x-ray-quality strips is
${\sim}$3 keV FWHM, but there is a tail extending out to ${\sim}$8 keV, with
some strips exceeding 10 keV. The distribution of strip resolution for the
tracking-quality detectors peaks at ${\sim}$4 keV FWHM and has a longer tail,
though a significant number of strips on tracking-quality detectors have FWHM
$<4$ keV. This reflects our observation that many detectors have ${\sim}$6–7
x-ray-quality strips and ${\sim}$1–2 tracking-quality strips, indicating that
poorly-performing (or even non-functional) strips do not necessarily affect
their neighbors within a detector.

Finally, we examine for the first time the yield of x-ray, tracking, and non-
usable detectors across the entire fabrication timescale (Jan. 2019 to Apr.
2020). As described in [26, 28], the fabrication was divided into 16
sequential batches, each lasting approximately one month. The results are
shown in Fig. 6. We note that batches 1 and 2 have a noticeably higher rate of
tracking and non-usable detectors than the following batches. Following batch
2, the lithium-drifting procedure was modified to terminate either at
${\sim}6200$ minutes or when the drift current began to increase exponentially
above ${\sim}$15–25 mA, whichever occurred first. This allowed us to better
control the depth of the drifted region, and hence the detector leakage
current and capacitance [26, 28]. These results further demonstrate that
large-area Si(Li) detectors with good x-ray resolution can be mass-produced.

Figure 4: Heatmap showing Si(Li) strip energy resolution obtained with the
discrete preamplifiers as a function of $\tau_{\text{p}}$. The data have been
interpolated with a polynomial for presentation purposes only, and the solid
and dashed black lines indicate representative noise models for x-ray and
tracking strips, respectively. Figure 5: Histogram of Si(Li) strip x-ray
energy resolutions measured with discrete preamplifiers at 4$\,\upmu\text{s}$
and –37$\,{}^{\circ}\text{C}$ for x-ray detectors (solid blue) and tracking
detectors (dashed red). Figure 6: Stacked bar chart showing the number of
x-ray (green, top), tracking (hatched yellow, middle), and non-usable (red,
bottom) detectors from each production batch. The approximate production date
ranges of each batch are also shown. The decrease in the number of detectors
produced in batches 1, 2, 4, and 7 corresponds to Japanese public holidays
during those months [28].

###  IV-C Detector Noise Parameters

As described in Sec. II-E, the strip leakage current $I_{\text{leak}}$ and
$1/f$ coefficient $A_{f}$ are the main drivers of the x-ray energy resolution
at the $\mathcal{O}(\upmu\text{s})$ shaping timescales of interest for GAPS.
Figure 7 shows the distributions of $I_{\text{leak}}$ and $A_{f}$ for the
x-ray and tracking-quality detectors. We note several features. First, the
most-probable values of strip $I_{\text{leak}}$ for x-ray and tracking-quality
detectors are ${\sim}$2 nA and ${\sim}$4 nA, respectively, with the tracking-
quality detectors having a significantly longer tail. We also note that
${\sim}120$ strips (i.e., less than 1.5% of the total) have best-fit values of
$I_{\text{leak}}$ and/or $A_{f}$ that are consistent with zero or even
slightly negative. This occurs most often when the other noise parameters are
small (e.g., $I_{\text{leak}}\lesssim 0.5\text{\,nA}$ or ${A_{f}\lesssim
0.2\times 10^{-13}\text{\,V}^{2}}$), since the internal preamplifier
components dominate the fit for these especially low-noise strips.
Furthermore, these low-noise strips are also sensitive to deviations in
$C_{\text{tot}}$ away from the assumed 70 pF value, though as discussed in
Sec. IV-A we needed to freeze $C_{\text{tot}}$ to break the degeneracy with
$A_{f}$. When calculating the projected ASIC energy resolution using Eq. (3),
we do not allow $I_{\text{leak}}$ or $A_{f}$ to go below zero.

Finally, we investigate the scaling of the predicted ASIC x-ray energy
resolution with temperature, as we expect there to be range of temperatures at
different locations in the payload and at different times during flight. The
two detector parameters to which the ASIC resolution is most sensitive are
$A_{f}$ and $I_{\text{leak}}$. Assuming the leakage current is dominated by
the bulk silicon (rather than, e.g., surface effects), we expect
$I_{\text{leak}}$ to scale with absolute temperature $T$ as [40]

$I_{\text{leak}}(T)\propto T^{2}\exp\left[-\frac{E_{\text{gap}}}{2kT}\right],$
(4)

where $E_{\text{gap}}\sim 1.14\text{\,eV}$ is the silicon band-gap energy near
$\text{--40}\,^{\circ}\text{C}$ [41]. Thus, we expect the leakage current to
decrease by a factor ${\sim}$2 when the temperature is reduced by
$6\,^{\circ}\text{C}$ near the GAPS operating temperature of
–40$\,{}^{\circ}\text{C}$. (We did not have an a priori expectation for the
temperature dependence of $A_{f}$.) In Fig. 8 we show the evolution of
$I_{\text{leak}}$ and $A_{f}$ between $\text{--37}\,^{\circ}\text{C}$ and
–43$\,{}^{\circ}\text{C}$ for a sample of 37 detectors. (Due to time
constraints, we were unable to test all GAPS detectors at both temperatures.)
We note that $I_{\text{leak}}$ generally scales as expected for values above
${\sim}$5 nA, though this correlation weakens for smaller leakage currents,
which we attribute to two sources. First, for low values of $I_{\text{leak}}$,
surface (rather than bulk) currents which do not scale with Eq. (4) may become
a significant contribution to the total current. Second, as discussed
previously, the noise model of Eq. (1) sometimes has difficulty fitting strips
with low values of $I_{\text{leak}}$, $A_{f}$, and $R_{s}$. We observe no
significant temperature scaling of $A_{f}$.

To determine the effect of Si(Li) temperature on the predicted ASIC energy
resolution, we feed the $I_{\text{leak}}$ and $A_{f}$ values extracted at
–37$\,{}^{\circ}\text{C}$ and –43$\,{}^{\circ}\text{C}$ into Eq. (3), and
compare with the resolutions expected from $I_{\text{leak}}$ scaling as Eq.
(4), assuming constant $A_{f}$. We find that the difference in predicted FWHM
is ${\lesssim}$0.1 keV. Thus, we conclude that measurement of the operating
temperature (faciliated by a sensor integrated into each FEB), combined with
the laboratory testing results at $\text{--37}\,^{\circ}\text{C}$, will allow
an adequate prediction of the x-ray energy resolution in flight. Further
testing with the full GAPS instrument before flight should help to further
confirm this.

(a)  (b)

Figure 7: Histograms showing fitted $I_{\text{leak}}$ (top) and $A_{f}$
(bottom) for Si(Li) strips on x-ray detectors (solid blue) and tracking
detectors (dashed red). Values of $I_{\text{leak}}$ and $A_{f}$ less than zero
are placed in the leftmost bin. There are ${\sim}$30 strips with fit
$I_{\text{leak}}>50\text{\,nA}$ and ${\sim}20$ strips with
$A_{f}>10^{-12}\text{\,V}^{2}$, though since the discrete preamplifiers are
expected to saturate near 50 nA, those results should be taken with care.

(a)  (b)

Figure 8: Scatter plots showing the temperature dependence of fit
$I_{\text{leak}}$ (top) and fit $A_{f}$ (bottom) for Si(Li) strips between
–37$\,{}^{\text{o}}$C and –43$\,{}^{\text{o}}$C. The red line on the
$I_{\text{leak}}$ plot indicates the expected scaling from Eq. (4). The dashed
line on the $A_{f}$ plot indicates $A_{f}$ constant with temperature.

##  V Conclusion

The tests described in this work demonstrate that large-area x-ray and
charged-particle Si(Li) detectors can be mass-produced and operated above
cryogenic temperatures. In particular, we demonstrate that low-noise detector
testing systems can be developed in a cost-effective manner using commercial
electronics. We find that more than 90% of the detectors produced for GAPS are
operable within the payload, with ${\sim}80\%$ of strips projected to be
suitable for both x-ray spectroscopy and charged-particle tracking.

With the testing of Si(Li) detectors complete, the assembly of the flight GAPS
instrument began in early 2022, and is expected to conclude in mid-2023. Work
is ongoing to validate the performance of the full instrument, including the
noise contribution of the flight ASIC readout and the combined tracking
performance of the Si(Li) tracker and time-of-flight system. The first
Antarctic flight of GAPS is currently planned for late 2024.

## Acknowledgments

We thank SUMCO Corporation and Shimadzu Corporation for their cooperation in
detector development. We also thank all of the members of the GAPS
collaboration for their tireless work and for their comments on this
manuscript.

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