[1]Lun-Jun Liu

[1]Department of Physics, California Institute of Technology, 1200 E
California Blvd, Pasadena, 91125, CA, USA

2]Jet Propulsion Laboratory, Pasadena, 91011, CA, USA

3]University of Pennsylvania, Philadelphia, 19104, PA, USA

4]University of Illinois Urbana-Champaign, Urbana, 61801, IL, USA

5]Arizona State University, Tempe, 85287, AZ, USA

6]University of Arizona, Tucson, 85721, AZ, USA

7]ELE Optics, Tucson, 85705, AZ, USA

# Cosmic ray susceptibility of the Terahertz Intensity Mapper detector arrays

<EMAIL_ADDRESS>Reinier M.J. Janssen  Bruce Bumble  Elijah Kane  Logan M.
Foote  Charles M. Bradford  Steven Hailey-Dunsheath  Shubh Agrawal  James E.
Aguirre  Hrushi Athreya  Justin S. Bracks  Brockton S. Brendal  Anthony J.
Corso  Jeffrey P. Filippini  Jianyang Fu  Christopher E. Groppi  Dylan
Joralmon  Ryan P. Keenan  Mikolaj Kowalik  Ian N. Lowe  Alex Manduca  Daniel
P. Marrone  Philip D. Mauskopf  Evan C. Mayer  Rong Nie  Vesal Razavimaleki
Talia Saeid  Isaac Trumper  Joaquin D. Vieira  *  [  [  [  [  [  [

###### Abstract

We report on the effects of cosmic ray interactions with the Kinetic
Inductance Detector (KID) based focal plane array for the Terahertz Intensity
Mapper (TIM). TIM is a NASA-funded balloon-borne experiment designed to probe
the peak of the star formation in the Universe. It employs two spectroscopic
bands, each equipped with a focal plane of four $\sim\,$900-pixel, KID-based
array chips. Measurements of an 864-pixel TIM array shows 791 resonators in a
0.5 GHz bandwidth. We discuss challenges with resonator calibration caused by
this high multiplexing density. We robustly identify the physical positions of
788 (99.6 %) detectors using a custom LED-based identification scheme. Using
this information we show that cosmic ray events occur at a rate of
2.1$\,\mathrm{events/min/cm^{2}}$ in our array. 66 % of the events affect a
single pixel, and another 33 % affect $<\,$5 KIDs per event spread over a
0.66$\,\mathrm{cm^{2}}$ region (2 pixel pitches in radius). We observe a total
cosmic ray dead fraction of 0.0011 %, and predict that the maximum possible
in-flight dead fraction is $\sim\,$0.165 %, which demonstrates our design will
be robust against these high-energy events.

###### keywords:

Astrophysics, Balloon, Terahertz, Spectroscopy, Kinetic Inductance Detectors,
Aluminum

##  1 Introduction

The cosmic star formation rate density (SFRD) peaks at redshift $\sim\,2$
($\sim 10\,$Gyr ago) and then declines significantly ($\sim 10\times$) to the
current Universe [1]. Understanding the mechanism of the drastically declining
cosmic SFRD since $z\sim 2$ is a compelling topic in astrophysics. During this
epoch of cosmic noon, most of the active star-forming regions are heavily
surrounded by dust [2, 3], which is optically thick to the ultraviolet (UV)
radiation emitted by newly formed stars. Measuring far-infrared (FIR) emission
lines is a vital probe of the dust-obscured star-forming regions as (1) dust
absorbs UV radiation and re-emits it at FIR wavelengths and (2) FIR photons do
not suffer from the dust extinction.

Motivated by the advantage of FIR wavelengths, we are designing and
constructing the Terahertz Intensity Mapper (TIM), a NASA-funded balloon-borne
spectrometer, to unravel the star formation and galaxy evolution during its
rapid decline ($0.5<z<1.7$) [4]. TIM will measure the emission of the
redshifted 157.7$\,\mathrm{\mu m}$ emission line of singly ionized carbon,
[CII], which is a key tracer of star formation. To perform these spectroscopic
observations, TIM employs two long slit grating spectrometers covering the
240-317 $\mathrm{\mu m}$ and 317-420 $\mathrm{\mu m}$ wavelength bands with
spectral resolution of $R\sim 250$ [5]. Each of TIM’s spectrometers is
equipped with a focal plane architecture containing four quadrant arrays, each
of which contains $\sim\,$900 hex-packed, horn-coupled aluminum kinetic
inductance detectors (KIDs) on a single readout line. A single RFSoC-based
readout system will simultaneously monitor the loading on all pixels in a
single focal plane [6].

Single pixel testing of our KID design has demonstrated a sensitivity that
exceeds TIM’s science requirement based on the predicted loading during
flight. Specifically, (1) the detector’s noise equivalent power (NEP) is
$3.5\times 10^{-18}\mathrm{W/Hz^{1/2}}$, and (2) the detector is photon noise
limited at 100 fW of loading at the in-flight operation temperature of 250 mK
[7]. The detector arrays have been fabricated and tested in a sub-scale focal
plane architecture. They have demonstrated a high fabrication yield, $>\,$95
%, and a negligible susceptibility to magnetic fields of a few $\mathrm{\mu
T}$, which is easily achievable with basic shielding [8, 9].

Further characterization of TIM’s KID-based focal plane array is required to
translate the high fabrication yield into a yield of science-quality
detectors. In this paper we present progress of the focal plane
characterization with an emphasis on the effects of cosmic rays. In Section 2,
we present a brief overview of our experimental setup, including the KID array
layout and our custom KID identification method, through which we identify
$>\,$99 % of the resonator positions. Section 3 shows an improvement in our
noise analysis routine, which accounts for close, but non-collided, resonances
in this densely multiplexed array. Using properly calibrated noise
timestreams, we quantify the effect of cosmic ray hits on the array in Section
4. In Section 5, we summarize our results and discuss future steps in the
characterization of the TIM focal plane arrays.

##  2 Experimental setup

In this paper we present measurements of an 864-pixel array of KIDs for TIM’s
long-wavelength spectrometer. The lumped-element KIDs (LEKIDs), similar to
those in Janssen et al. [7], consist of the same $\sim\,$500$\,\mathrm{\mu m}$
diameter inductive absorber surrounded by 3 choke rings, an interdigitated
capacitor (IDC), and a coplanar capacitor coupling to the microstrip readout
line. All these structures are lithographically patterned in a single layer of
30 nm aluminum (Al) on top of a 6 ” silicon-on-insulator wafer. Centered on
each absorber a 1.3 mm diameter (matching the outer diameter of the largest
choke ring) hole is etched through the 600$\,\mathrm{\mu m}$ carrier wafer to
create a 25$\,\mathrm{\mu m}$ backshort, by depositing 100 nm of Al across the
entire backside.

The total array is a $90.6\times 80.75$ mm die, of which the $36\times 24$
pixel array covers a $85.0\times 48.5$ mm active area in the north-east corner
of the die, as shown in Fig. 1 of Liu et al. [9]. To efficiently pattern the
entire array with stepper lithography, we carry out a unit cell approach [10].
Each unit cell contains 16 $(4\times 4)$ LEKIDs. The resonator frequencies of
these 16 KIDs are designed to be widely separated $(df/f\sim 0.05)$ and define
16 resonator clusters within the $500-1000\,$MHz readout bandwidth. This is
achieved by varying the number of IDC tines between 24 and 68. Stepping
through each of the 54 $(9\times 6)$ unit cells, the 16 resonances in the unit
cell are designed to be shifted by $df/f\sim 7.5\times 10^{-4}$ by reducing
the IDC tine length in steps of $dL=0.9\,\mathrm{\mu m}$. As such, each
consecutive unit cell is shifted incrementally in frequency to fill out the
entire frequency bandwidth of the array.

We measure the performance of this array in a pulse-tube pre-cooled triple-
stage He sorption cooler at a stage temperature of 250 mK. The array is
located inside a sub-scale focal plane architecture similar to those designed
for flight [8]. Following pioneering work done by NIST [11], we use a
cryogenic LED array mounted directly on top of our horn array to identify the
spatial location for each of the resonance features in the readout
transmission. Motivated by the concept of the unit cell design, we implement a
custom designed LED mapping scheme. The key feature of this mapping method is
that one single LED illuminates one unit cell (of 16 KIDs). These 16
resonators have widely separated frequencies so they remain in their designed
frequency order, allowing unambiguous identification. By sequentially applying
a bias to every single LED we can then provide unambiguous identification of
all KIDs in the full array. Liu et al. [12] will provide a detailed
description regarding the implementation of this custom LED KID identification
mapper and its potential application to ultra-large KID arrays and small pixel
pitch sizes (especially for those smaller than the LED size). Using our LED
KID mapper, we robustly identify the physical location of 788 out of 791
resonators, resulting in a $>\,$99.6 % identification yield. It is worth
noting that 7 of these resonances were only observed because of the LED
illumination, as they were fully merged with the resonance feature of other
detectors. Figure 1 shows the spatial map of identified resonators, plotted in
blue, cyan, and grey symbols, while the black crosses are those not moved by
the LED’s illumination and labeled as “not yielding.”

Figure 1: Spatial map of TIM’s 864-pixel array, with the array chip facing up.
Dots and diamonds represent pixels that respond to the LED’s illumination,
wherein blue dots represent widely-separated, well-calibrated pixels, cyan
dots have a nearby resonance feature and are properly calibrated thanks to our
improved calibration scheme, and grey diamonds indicate poorly calibrated
resonances, predominantly due to collisions in frequency space. Black crosses
indicate resonators that did not yield.

##  3 Frequency and noise calibration in densely multiplexed KID arrays

Near neighbors and especially the collisions in the frequency space have
always been regarded as a dominant source of contamination in the frequency
and noise calibration process and decrease of the number of science-usable
detectors. An example of their impacts on the conventional ROACH2 calibration
process is demonstrated in Figure 2, using an example of Resonator A with a
resonant frequency ($f_{res,A}$) = 791.084 MHz. In Panel A, Resonator A has a
neighbor in the frequency scan range, Resonator B, with $f_{res,B}=791.212$
MHz, and they both maintain their complete resonance features. This
calibration routine is likely to be confused by the 2 partially overlapping IQ
loops and the phase noise data from 2 separated resonators, so therefore this
routine poorly fits the IQ loop (Panel B) and incorrectly convert the phase
noise to $df/f$ noise (Panel D) given the unreasonable fit (Panel D). The high
multiplexing density makes this a pronounced effect, which will also affect
any future arrays pushing to higher multiplexing densities [13].

Figure 2: An example showing how a resonator can be properly calibrated using
our improved calibration scheme. In this example, Resonator A with
$f_{res,A}=791.084$ MHz has a neighbor, Resonator B, at $f_{res,B}=791.212$
MHz. In Panel A, our improved method isolates Resonator A from Resonator B,
and so Resonator A is properly fitted in green cross marks. Panel B
demonstrates the successful fit in IQ space, enabled by our improved
calibration method, while the original method tries to fit the 2 IQ loops
hence failed. Panel C shows that the improved calibration routine enables the
good fit of the frequency vs. phase diagram, whereas Panel D indicates the
poor fit from the original calibration method, because it tries to fit the
data from 2 near but isolated resonators.

The key solution to the proper calibration of the resonator frequency is to
reduce the calibration frequency range centered around the nominal resonator
frequency in post-processing. This ensures that the nominal resonator is
properly isolated from its near neighbors without compromising the measured
frequency range required for lower-Q resonators within the array. In order for
the proper fit to the data, in IQ space it is necessary to maintain an
uncontaminated IQ loop within a phase range from $-\pi/2$ to $+\pi/2$; this
phase range can be translated to the $|S_{21}|$ along the readout transmission
in frequency domain — the proper fit of a resonator feature requires at least
an isolated full width at half minimum of the resonator dip. As a first
demonstration, we implement an improved calibration routine that features a
collision threshold in the frequency domain, $\Delta
f/f=(f_{i+1}-f_{i})/f_{i}=7\times 10^{-5}$ ($\Delta f\sim 50\,$kHz in the
middle of the readout bandwidth), which matches well to the typical $Q\sim
2\times 10^{4}$. With this threshold, every pair of 2 near resonator neighbors
with spacing below this threshold will be labeled as “collision,” and above
will be labeled as 2 isolated resonators. This improved calibration method is
now able to (1) flag collisions, (2) properly separate near neighbor
resonances, (3) reject drifted noise streaming data, and (4) implement robust
interpolation for the conversion from phase noise data to $df/f$ noise.

Figure 3 demonstrates the success on the recovering a large number of
resonators enabled by properly isolating neighbor resonators in our improved
calibration scheme. Figure 3 (left) indicates that the recovered Resonator A’s
fractional frequency noise power spectral density ($S_{xx}$) is at a (white
noise) level in line with others in the array — In Figure 3 (right), the
recovered 381 resonators follow a comparable distribution to the 248 widely
separated resonators when studying their $S_{xx}$ at $1\,$Hz (the modulation
frequency given TIM’s fiducial scan strategy). It is noteworthy that among all
properly calibrated KIDs, the average of $S_{xx}$ at $1\,$Hz is at a white
noise level $\approx 6.3\times 10^{-17}\,\mathrm{Hz^{-1}}$, comparable to our
single pixel measurement (see Fig. 4 of Janssen et al. [7]). This result
clearly indicates that our properly calibrated KIDs indeed reach science
quality. Figure 1 illustrates the boosted yield of proper-calibration, enabled
by our improved calibration routine–the number of properly calibrated KIDs
increases from 248 to 629, a great improvement of $\sim\,$150 %. Panel C of
Figure 2 describes the proper calibration enabled by our improved calibration
routine, in contrast with the original poor calibration. Our improved
calibration scheme is capable of isolating Resonator A from its near neighbor,
Resonator B, and then properly fits both the IQ data and the phase-to-
frequency conversion. As a result, we are able to recover the true $S_{xx}$ of
Resonator A and all properly isolated resonators.

Figure 3: Left: $S_{xx}$ of Resonator A extracted with the improved
calibration routine. The grey curve shows the raw $S_{xx}$, while the green
curve represents the binned $S_{xx}$ in the frequency range of interest.
Right: The stacked distribution of $S_{xx}$ at $1\,$Hz, wherein the blue bars
indicate the histogram of widely separated resonators, and the cyan bars shows
the histogram of resonators recovered by our improved calibration scheme.

##  4 Impact of cosmic rays on the KID array

KIDs will experience data loss when high-energy cosmic rays hit the focal
plane array chip [14]. These high-energy particles hit the detector wafer and
deposit energy in the substrate during TIM’s balloon flight, creating athermal
phonons which break Cooper pairs and generate extra quasi-particles in the KID
absorbers that cause the large frequency excursion and produce spurious
signals. The key to mitigation is to absorb and thermalize these hot phonons
before they reach the absorbers. Techniques to achieve this have been
demonstrated [14], and have informed our design. We present our measurements,
the inferred rates, and how our design mitigates the impact of cosmic rays.

We take time ordered noise streaming data and search for cosmic ray events.
Using our ROACH2 data acquisition system, we simultaneously stream the noise
data of all identified KIDs with sampling rate $f_{sampling}=488\,$Hz for 5
minutes. The excursion rises within a single time interval followed by a quick
decay with a time constant of $\sim\,$100 microseconds [7]. We set a $5\sigma$
threshold to filter out cosmic ray event candidates, because (1) the typical
non-affected resonator’s $df/f$ noise falls in the $5\sigma$ range of a
Gaussian distribution and (2) simulations show that the residuals of cosmic
rays at levels of $<\,$5$\sigma$ in the data do not affect the RMS noise [15].

These $>\,$5$\sigma$ events allow for the calculation of the cosmic ray event
rate over the entire effective area of the array chip, event rate per pixel,
and the data loss fraction. We identify a total of 434 unique events (that is,
events impacting multiple KIDs treated as a single event) measured by the
629-KID array in the full observation time. The area occupied by the KIDs is
approximately 41.23 cm2, and we thus have a lower limit111Larger fluxes could
be possible if the effective area impacted by a single cosmic ray even is
smaller than a pixel. to the energetic particle flux on the chip of
$2.1\,\mathrm{events/min/cm^{2}}$. This estimate is consistent with
literature, where Karatsu et al. [14] reported
$\sim\,$2.5$\,\mathrm{events/min/cm^{2}}$, and Wilen et al. [16] reported a
combined total rate of gamma and muon particles of
$\sim\,$1.9$\,\mathrm{events/min/cm^{2}}$ which was also scaled by McEwen et
al. [17].

We define the total data loss fraction due to cosmic ray hits as
$f_{loss}=\sum\limits_{N}\sum\limits_{i}(E_{N,i}/f_{sampling})/N_{tot}\,t_{tot}$,
where $N_{tot}=629$, $E_{N,i}=0$ except when detector $N$ is impacted by a
cosmic ray in time sample $i$, then $E_{N,i}=1$, and $t_{tot}$ represents the
5-minute noise timestream. The $f_{loss}$ obtained in this experiment is a
neglible 0.0011 %.

We attribute this low $f_{loss}$ to a number of features of our architecture:
(1) Most importantly, the thick (100 nm) Al deposited on the backside of the
wafer and backshorts has a lower transition temperature (thus lower
superconducting gap energy) compared to the 30 nm Al of the absorber. As
athermal phonons interact with this layer, they are down-converted, at least
partially, to gap-edge excitations which are then unable to break pairs in the
higher-critical-temperature KID absorbers. (2) The bulk of the cosmic ray
phonons are generated in the carrier wafer, and do not have a direct path to
the absorber because of the 25$\,\mu$m thick, 1.3 mm diameter backshort, which
provides a geometric constriction to phonons on their path from the bulk
silicon to the absorber. (3) Finally, the constriction is further enhanced by
the fact that the outer 0.5 mm annulus of the backshort has the thick 100 nm
backshort Al on the back and 30 nm Al optical choke rings on the front. They
both absorb and thermalize high energy phonons before they can reach the
500$\,\mu$m diameter absorber in the center of the backshort “membrane.” The
first 2 features are similar to those implemented previously (e.g., Karatsu et
al. [14]), and the third improvement may further reduce $f_{loss}$ compared to
other literature values222This may explain our measured $f_{loss}$
$\sim\,$4$\times$ lower than the minimum value reported by Karatsu et al.
[14], though note that the sensitivity of the TIM devices at 250 mK is an
order of magnitude lower, which complicates the attribution..

Figure 4: The spatial map of events occurring on individual pixels across the
entire TIM focal plane array with the color bar showing the number of cosmic
ray events per pixel per 5-minute noise timestream. An animated movie of an
example event is shown in the online supplementary material.

Combining the noise data and the spatial map of our KID array, we are able to
further characterize the distribution of cosmic ray events in the array.
Figure 4 reports the number of cosmic ray events occurring per pixel in a
5-minute noise timestream given the individual pixel’s physical location. It
can be seen that the cosmic ray hits are randomly distributed across the
entire wafer. The attached online supplementary shows an animation of an
example cosmic ray event using snapshots of 4 consecutive frames. Figure 5
studies how localized these cosmic ray events are: Panel A indicates that
$>\,$66 % of the events affect 1 single pixel, with another $33\%$ affecting 5
or fewer. Panel B indicates that the cosmic ray events are highly localized,
as $>\,$60 % of the secondary noise spikes are constrained to the nearest or
next-nearest neighbors of the primary pixel that first experiences the energy
deposit from certain cosmic ray event. This implies a typical spread over a
0.66$\,\mathrm{cm^{2}}$ region (2 pixel pitches in radius). These results show
that the cosmic ray events are highly confined, explaining in part our low
$f_{loss}$.

Figure 5: Panel A: The distribution of the number of affected pixels of the
cosmic ray event. Panel B: The distribution of distances between companion
pixels and the primary pixel of time frames affected by the cosmic ray event.

The ground-based characterization enables the prediction of TIM KID arrays’
cosmic ray susceptibility at float. Literature have reported that (1) the muon
flux at float is $\sim 2-3\,\mathrm{/sec/cm^{2}}$ [18], and (2) the flux of
energetic particles measured by Planck space observatory is
5$\,\mathrm{/sec/cm^{2}}$; therefore, we upscale the lab-based cosmic ray
event rate by $\sim 75-150$$\times$ as an estimation of the averaged cosmic
ray flux in TIM’s balloon flight. This leads to our predictions on the in-
flight $f_{loss}$, where (1) $f_{loss,avg}\approx f_{loss,lab}\times
75=0.083\,$%, and (2) $f_{loss,max}\approx f_{loss,lab}\times 150=0.165\,$%.
Even the upper range of this estimate is very favorable for a spaceflight
detector array – our architecture offers improvements relative to some of the
previous KIDs flown, e.g., total $f_{loss}\approx 3\,$% from the OLIMPO
balloon mission’s in-flight measurements with their KID arrays [19, 20].

##  5 Summary and prospects

We present the characterization of TIM’s 864-pixel KID array in an effort to
maximize the science-quality yield and investigate the cosmic ray
susceptibility. We have mapped 788 of the 791 yielded KIDs to their physical
location. We have also improved our frequency and noise calibration method and
then applied it to these identified resonators, obtaining 629 non-collided,
properly calibrated resonators, a $\sim\,$150 % improvement from the original
calibration method.

We further demonstrate that these recovered resonators show an averaged white
noise level of $S_{xx}$ in line with widely separated ones and comparable to
our single-pixel measurement, which clearly indicates their high science
quality. We have characterized the susceptibility of KIDs to cosmic ray
events. We confirm that the cosmic ray event flux in our experiment is
comparable to that reported by others, and we show that our array architecture
offers excellent suppression of the impact of these events on the KIDs. Events
are highly localized and result in a negligible data loss fraction in the lab,
and expected losses of much less than 1% in the stratospheric balloon float or
spaceflight environment. We attribute this excellent performance to a phonon
thermalization layer on the back of our array and the geometry of our choke
rings and the backshort.

To further increase the number of science usable detectors, we are planning to
rearrange collided resonators’ $f_{res}$ by trimming the capacitors folllowing
the techniques demonstrated by NIST [21] as well as the SuperSpec team [22].
We will also combine the spatial and frequency information associated with
every single pixel to analyze the noise correlation coefficient between the
pixels in the array. Based on the nature of these correlations, we will apply
suitable mitigation strategies. Ultimately, we aim to turn all yielding KIDs
into properly separated and science-usable detectors.

Supplementary information

In the online supplementary material, we show an animation of an example
cosmic ray event that records the entire series of the interaction between
this particular cosmic ray hit and the behavior of surrounding affected
pixels, from the generation of the highly perturbed $df/f$ noise to the decay
back to equilibrium.

Acknowledgments

TIM is supported by NASA under grant 80NSSC19K1242, issued through the Science
Mission Directorate. Part of this research was carried out at the Jet
Propulsion Laboratory, California Institute of Technology, under a contract
with the National Aeronautics and Space Administration (80NM0018D0004).

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