# A superconducting-nanowire single-photon camera with 400,000 pixels

B. G. Oripov1,2, D. S. Rampini1,2, J. Allmaras3,
M. D. Shaw3, S. W. Nam1, B. Korzh3, A. N. McCaughan1

(1National Institute of Standards and Technology, Boulder, Colorado 80305, USA
2Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
3Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove
Drive, Pasadena, California 91109, USA )

For the last 50 years, superconducting detectors have offered exceptional
sensitivity and speed for detecting faint electromagnetic signals in a wide
range of applications. These detectors operate at very low temperatures and
generate a minimum of excess noise, making them ideal for testing the non-
local nature of reality [1, 2], investigating dark matter [3, 4], mapping the
early universe [5, 6, 7], and performing quantum computation [8, 9, 10] and
communication [11, 12, 13, 14]. Despite their appealing properties, however,
there are currently no large-scale superconducting cameras – even the largest
demonstrations have never exceeded 20 thousand pixels [15]. This is especially
true for one of the most promising detector technologies, the superconducting
nanowire single-photon detector (SNSPD) [16, 17, 18]. These detectors have
been demonstrated with system detection efficiencies of $98.0\%$ [19],
sub-3-ps timing jitter [20], sensitivity from the ultraviolet (250 nm) [21] to
the mid-infrared ($>$10 µm) [22], and dark count rates below $6.2\times
10^{-6}$ counts per second (cps) [3], but despite more than two decades of
development they have never achieved an array size larger than a kilopixel
[23, 24]. Here, we report on the implementation and characterization of a
400,000 pixel SNSPD camera, a factor of 400 improvement over the previous
state-of-the-art. The array spanned an area $4\times 2.5$ mm with a $5\times
5$ µm resolution, reached unity quantum efficiency at wavelengths of
$370\text{\,}\mathrm{n}\mathrm{m}$ and $635\text{\,}\mathrm{n}\mathrm{m}$,
counted at a rate of $1.1\times 10^{5}$ cps, and had a dark count rate of
$1.0\times 10^{-4}$ cps per detector (corresponding to
$0.13\text{\,}\mathrm{c}\mathrm{p}\mathrm{s}$ over the whole array). The
imaging area contains no ancillary circuitry and the architecture is scalable
well beyond the current demonstration, paving the way for large-format
superconducting cameras with 100% fill factors and near-unity detection
efficiencies across a vast range of the electromagnetic spectrum.

Most superconducting sensors [25], such as microwave kinetic-inductance
detectors (MKIDs) or hot-electron bolometers, produce continuously-valued
outputs that lend themselves well to efficient readout schemes such as
frequency multiplexing [26]. Superconducting nanowire single-photon detectors,
however, are notoriously difficult to multiplex since they produce discrete
pulses that are both low-amplitude and broadband. These pulses are typically
read out individually using one microwave readout cable per detector, unlike
CCD-type sensors which accumulate charge at each pixel and can be serially
interrogated with a single readout line. This per-pulse readout process be
advantageous when photon-counting as it means there is no read noise, but
severely limits the number of detectors that can be read out due to cryogenic
thermal load limitations on the readout wiring.

To date, there have been many attempts to devise readout architectures that
minimize the number of readout lines running from room temperature electronics
to the detector chip. For example, one of the largest architectures to date
used a time-of-flight measurement to measure photon position along the length
of the detector and required only two readout lines [27]. Unfortunately, since
the entire imager was made from a single long nanowire, this architecture is
susceptible to fabrication yield issues, as a single discontinuity can
compromise the entire imager. Additionally, the large inductance of the long
nanowire will inevitably lead to very long reset times and limit the maximum
count rate.

In row-column readout architectures, SNSPDs are arranged on an $N\times N$
grid [28], enabling readout of $N^{2}$ pixels using $2N$ readout lines. The
detection event is defined as correlated voltage pulses appearing on both row
and column lines within a predefined time window. The row-column readout
architecture was used to create the largest SNSPD array to date, a 1,024-pixel
imager, but due to diminishing signal-to-noise (SNR) ratio with increasing
pixel count, this approach cannot scale to much larger sizes [29]. The thermal
row-column scheme overcomes the SNR issue by keeping the row and column pixels
electrically isolated and uses the local heat generated during the SNSPD
detection process to generate correlated events on row and column channels
[30].

More recently, the thermally-coupled imager (TCI) architecture used a
combination of thermal coupling to a superconducting bus and time-multiplexing
along the readout bus, to achieve kilopixel imaging capability [24]. This
scheme used an asymmetric thermal coupling process to transmit pulses on a row
or column detector to a readout bus, significantly reducing inter-detector
crosstalk and enabling much greater scalability. The SNSPD array demonstrated
in this work combines a thermal row-column sensor element with TCI readout in
order to achieve its large degree of multiplexing. Additionally, the
perpendicular orientation of the two nanowire layers enables polarization-
insensitive optical cavity designs.

Figure 1: (a) Imaging with the $800\times 500$ array at 370 nm. Raw time-delay
data from the buses are shown as individual dots in red, and binned 2D
histogram data is shown in black and white. (b) Count rate as a function of
bias current for various wavelengths of light as well as dark counts. (c)
False-color scanning electron micrograph of the lower-right corner of the
array, highlighting the interleaved row and column detectors. (inset, lower
left) Schematic diagram showing detector-to-bus connectivity. (inset, lower
right) Closeup showing 1.1 µm detector width and effective $5\times 5$ µm
pixel size.

The array, shown in Fig. 1, was comprised of 800 row and 500 column detectors
and was operated at a temperature of 0.8 K. The row and column detectors were
made by patterning 1.1-µm-wide wires from two independent 4-nm-thick WSi films
with a Tc of 3.4 K and kinetic inductance of
$250\text{\,}\mathrm{p}\mathrm{H}\mathrm{/}\mathrm{s}\mathrm{q}$. Row and
column detectors were spaced 5 µm apart and arranged in a grid, giving a
resolution of $5\times 5$ µm as shown in Fig. 1c. There were four buses used
for readout, requiring a total of 8 microwave coax lines, and the row and
column detectors were interleaved between them as shown in Fig. 1c. Each row
or column detector was connected to a resistive thermal coupler, which
contained a small heater that is thermally coupled to (but electrically
isolated from) the readout bus by a thin, electrically insulating dielectric
spacer.

The readout buses were made from the same layer of material as the column
detectors and so have the same basic properties. The majority of the bus
length had a width of 8 µm that, in combination with the 50-nm-thick SiO2
dielectric spacer and ground plane, formed a microstrip transmission line with
approximately 50 $\Omega$ impedance. During operation, these sections of the
bus contained a relatively low current density and were thus not directly
photosensitive, allowing the readout bus to avoid generating false counts from
stray photons. Below each heating element, the bus briefly narrowed to a
1.5-µm-wide constriction with high current density, creating a heater-tron
like device [31]. The high current density ensured that every time the heater
was activated during a detection event, it created a corresponding hotspot on
the bus.

Figure 2: (a) Circuit diagram of a bus and one section of 50 detectors with
ancillary readout components. SNSPDs are shown in the gray boxes, and all
other components are placed outside of the imaging area. A photon that arrives
at time $t_{0}$ has its location determined by a time-of-flight readout
process based on the time-of-arrival difference $t_{2}-t_{1}$. (b)
Oscilloscope traces from a photon detection, showing the arrival of positive
(green) and negative (red) pulses at times $t_{1}$ and $t_{2}$ respectively.

Detectors were grouped into sections of 50 rows or 50 columns, and each
section was biased independently. For each section, the bias-current was
resistively distributed among the 50 detectors, sharing a common source and
ground. Fig. 2 shows the circuit diagram for a single section comprising 50
column SNSPDs. When a photon was absorbed by a detector, a hot-spot formed on
the detector with a peak value of a few k$\Omega$. This resistance diverted
the bias current out of the detector and into the heating element of the
thermal coupler. The resulting phonons generated within the thermal coupler
locally destroyed the superconducting state on the readout bus, creating two
opposite-polarity voltage pulses that traveled down the readout bus as shown
at the top and inset of Fig. 2. Owing to the large kinetic inductance of the
bus material, these microwave pulses propagated at 0.36% of $c$ (1.10$\times
10^{6}$ m/s), allowing relatively short lengths of bus (400 µm) to separate
adjacent detectors while maintaining excellent distinguishability.

By measuring the time-difference between the arrival of these pulses at the
ends of the buses, one can compute the location of the detection event and the
corresponding row or column. As shown in Fig. 2a, for a photon arriving at
time $t_{0}$, the emitted positive pulse will arrive at the left readout at
time $t_{1}=t_{0}+\tau_{1}$, and the negative pulse at $t_{2}=t_{0}+\tau_{2}$.
Applying this process to both row and column readout, we were able to
precisely identify the location where each photon was absorbed. Given arrival
times of $t_{1}$ and $t_{2}$ from a column bus and $t_{3}$ and $t_{4}$ from a
row bus, we calculated the differential time-delays as $\Delta
t_{\text{col}}^{\text{}}=t_{1}-t_{2}$, $\Delta
t_{\text{row}}^{\text{}}=t_{3}-t_{4}$. Similarly, the photon time of arrival
can be calculated from $t_{0}=(t_{1}+t_{2}-\tau_{b})/2$ where $\tau_{b}$ is
the time-length of the bus. To ensure that these pulses were generated by the
same single-photon detection event, we imposed the four-fold coincidence
condition that the arrival time of all four pulses were within
$100\text{\,}\mathrm{n}\mathrm{s}$ of each other.

To capture the image shown in Fig. 1a, we patterned a metallic mask on a glass
substrate, placed it directly on top of the array, and flood illuminated the
entire mask. We then recorded the pulse timings coming out of the readout
buses with a timetagger, extracted the four-fold coincidence events, and
computed $\Delta t_{\text{col}}^{\text{}}$ and $\Delta
t_{\text{row}}^{\text{}}$. No further post processing of the pulse data was
performed and no 4-way coincidences were discarded. The raw differential-delay
data shown in red corresponds closely to the black and white binned histogram
image, excepting the regularly-spaced gaps in the differential-delay data that
correspond to extra bus delay between adjacent detector sections.

Fig. 1b shows photon count rate measurements for multiple wavelengths for one
of the sections as a function of bias current. As evident from the figure, our
detectors have large plateau regions for wavelengths $370\text{\,}\mathrm{nm}$
and $635\text{\,}\mathrm{nm}$, indicating unity quantum efficiency over a wide
range of bias current. At 370 nm, the wavelength for which this array was
targeted, a bias current bias of 40 µA yielded unity quantum efficiency and at
this bias current we recorded 5 dark counts over a measurement period of 1,000
s. Since this measurement occurred over a section of 50 detectors, this
corresponded to a dark count rate of $1\pm 0.45\times 10^{-4}$ cps per
detector. In a setup that was better shielded optically, this value would
likely be even lower, as the dark count curve in Fig. 1b suggests that the
source of dark counts at this bias current were likely stray blackbody photons
[32].

Figure 3: (a) Histogram of the pulse differential time-delays $\Delta
t=t_{1}-t_{2}$ from the north bus during flood illumination with a Gaussian
spot. All 400 detectors resolved clearly, with gaps indicating detectors that
were pruned. (a, inset) Zoomed region showing that counts from adjacent
detectors are easily resolvable, and no counts were generated by a pruned
detector. (b) Plot of raw $t_{\text{row}}^{\text{}}$ and
$t_{\text{col}}^{\text{}}$ time-delays when flood illuminated at 370 nm. (c)
Zoomed subsection of the array with $25\times 25$ detectors. (d) Histogram of
time-delays for a $2\times 2$ detector subset with 10 ps bin size showing
clear distinguishability between adjacent detectors.

After an initial screening we observed that some detectors were defective,
producing anomalously high dark count rates, overwhelming the bus, and
obfuscating true counts. To resolve this, we applied a measure-and-prune
process to eliminate the faulty detectors. We first determined exactly which
detectors were anomalous by flood illuminating the array and collecting 1D
histograms for each bus. We then identified any row or column detectors that
produced excessive counts and disconnected them by etching through their bias
wiring, effectively turning them off. Within a single iteration of this
pruning process, we were able to effectively remove all of the defective
detectors (58 defective detectors out of 1300), resulting in the smooth
Gaussian-spot shape of the histogram shown in Fig. 3a. Identifying the
offending detectors was straightforward – the full-width half-max of the peaks
was $62\text{\,}\mathrm{p}\mathrm{s}$ and the separation of the peaks had a
median value of $362\text{\,}\mathrm{p}\mathrm{s}$, giving a greater than $6$
FWHM distinguishability between neighboring rows or columns. We further
examined the 2D uniformity of the array by flood illuminating it and examining
the output of the buses. As shown in Fig. 3b, the photon counts are tightly
clustered in $\sim 62$-ps-diameter circles, indicating that the readout
process works to accurately position both the photon row and column
simultaneously.

One potential area for concern was that detected photons may trigger the
detectors but not produce corresponding outputs on the buses, resulting in
lost detection events. We characterized this photon-to-bus conversion
efficiency with test structures, and found the minimum energy required to
create a hotspot on the bus was 8.1$\times 10^{-17}$ J. In the array, the
detection process deposited
$\frac{1}{2}L_{\text{s}}^{\text{}}I_{\text{bias}}^{\text{}}$ = 1.2$\times
10^{-15}$ J of energy on the heater, greatly exceeding the requirements of the
thermal coupler. Correspondingly, during operation we observed large operating
margins for the detectors and buses, indicating good uniformity and
sensitivity of the thermal coupling process. When the detectors were biased
between 30-55 µA, any $I_{\text{bus}}^{\text{}}$ between 15-40 µA produced a
photon-to-bus conversion efficiency of approximately unity. We note that while
the thermal coupling efficiency was high, an area for improvement will be the
increasing the density of the layout for high fill-factors – in the this work,
only 13.7$\%$ of all photons detected resulted in a four-fold coincidence, due
to the relatively large spacing between adjacent detectors.

Figure 4: (a) Count rate versus optical attenuation for a section of detectors
biased at 45 µA per detector. The dashed purple line shows a slope of 1, with
deviations from that line at higher rates indicating blocking loss. (b) System
jitter of a 50-detector section. Detection delay was calculated as the time
elapsed between the optical pulse being generated and detection event
recorded.

We additionally measured the timing performance of the array. Fig. 4a shows
the count rate from one of the 50-detector sections versus optical attenuation
measured at $635\text{\,}\mathrm{nm}$ and with the detectors biased at 45 µA
per detector. We observed that the photon count rate was proportional to the
photon flux, indicating the array was operating in the single-photon regime
[16, 33]. The count rate was limited primarily by the speed of the bus – after
detection, the current in the bus dropped to zero for a period of time
$\tau_{\text{dead}}^{\text{}}$, and any other photon detections during this
time would be lost. For our device this dead time was
$9.16\text{\,}\mathrm{\SIUnitSymbolMicro s}$. Similar to single-pixel SNSPDs,
once count-rates approached $1/\tau_{\text{dead}}^{\text{}}$, photons could
still be lost due to blocking loss as evidenced by the 3 dB compression point
at 1.09$\times 10^{5}$ cps. To increase the maximum readout rate, additional
buses may be added trivially. For a fixed array size, increasing the total
number of buses by a factor of $B$ leads to a $B$-fold increase in the maximum
readout rate per bus and thus a $B^{2}$-fold increase in the maximum readout
rate of the entire array.

Fig. 4b shows the timing jitter of one of the array sections. To obtain this
data a single section was biased and illuminated with a
$1550\text{\,}\mathrm{nm}$ mode-locked laser with
$100\text{\,}\mathrm{f}\mathrm{s}$ optical pulse width. The distribution of
detection delays had the FWHM of $336\text{\,}\mathrm{p}\mathrm{s}$ and
standard deviation of $245.4\text{\,}\mathrm{p}\mathrm{s}$. This relatively
large jitter can be primarily attributed to the longitudinal geometric jitter
of our $5\text{\,}\mathrm{m}\mathrm{m}$ long detectors, and could be
significantly reduced by converting to a differential-style readout [34].

In this work, we demonstrated the largest superconducting photon-counting
camera to date by a factor of 20, using an efficient, time-resolved
architecture that is both scalable and tolerant of fabrication defects. The
architecture allows for the imaging area to contain only detectors, allowing
future arrays to reach 100% fill factors with high system detection
effiencies. While the work here demonstrated classical imaging at the single-
photon level, we expect future large-format implementations to greatly enable
applications in quantum imaging[35] such as sub-Rayleigh super-resolution
imaging[36] or sub-shot-noise imaging[37]. These applications typically
require the detection of quantum correlations in both time and space, and
depend heavily on high efficiencies and low background noise.

## Methods

The chip was fabricated with 6 layers: two WSi detectors layers, two Nb wiring
layers, a resistor layer, and a dielectric spacer layer. First, we sputtered a
thin ($4\text{\,}\mathrm{nm}$) WSi film on a $75\text{\,}\mathrm{m}\mathrm{m}$
Si wafer with $150\text{\,}\mathrm{nm}$ of thermal oxide. The film was in-situ
capped with $2\text{\,}\mathrm{nm}$ of aSi to avoid oxidation. Then column
detectors, series inductors and the readout bus were patterned using SPR660
and optical lithography with an i-line ($365\text{\,}\mathrm{nm}$) stepper.
Finally these patterns were etched with an inductively-coupled plasma (ICP)
etcher using an AR:SF6 etch. Next, a liftoff pattern was created using optical
lithography and $90\text{\,}\mathrm{nm}$ thick Nb wires with
$10\text{\,}\mathrm{nm}$ of PdAu capping were sputtered to create a low
inductance bottom Nb wiring layer.

At this point, it is important to planarize the surface before depositing row
detectors. In our tests, it was observed that if this planarization step is
skipped, the topography of the column detectors results in a step-like edges
on the row detectors which reduces the critical current of row detectors,
degrading their performance. The planarization can be achieved by using a
dilute divinylsiloxane-benzocyclobutene (DVS-BCB) polymer. This BCB polymer
was applied to the wafer, and spun dry at
$4000\text{\,}\mathrm{r}\mathrm{p}\mathrm{m}$. The wafer was later baked at
$250\text{\,}\mathrm{C}$ in a nitrogen furnace for 60 min, to cure the BCB.
Later, $25\text{\,}\mathrm{nm}$ of SiO2 was sputtered on the wafer with
$4\text{\,}\mathrm{nm}$ of amorphous silicon sputtered in-situ as a capping
layer. Finally, the wafer was patterned and etched with a CHF3 and O2
chemistry to create vias through the dielectric layer. The PdAu deposited on
the bottom Nb wiring layer acts as a non-oxidizing etch stop, allowing us to
overetch and create $1\times 1$ µm vias.

Next, $4\text{\,}\mathrm{nm}$ of WSi film was sputtered again, patterned and
etched to produce row detectors and the heaters on the thermal coupler. Later,
$30\text{\,}\mathrm{nm}$ of PdAu was sputtered with a liftoff process to
create all of the resistors needed for the device operation (see Fig. 2).
Finally, 200 nm of Nb was sputtered and patterned with a liftoff process to
create the top Nb wiring layer and the GND plane for readout buses.
$2\text{\,}\mathrm{nm}$ of Ti was used as an adhesion layer for the Nb and
PdAu layers.

After this we performed the final etch to disconnect the ground from the
readout bus, which was intentionally left connected to the ground plane.
Skipping this step usually causes antenna-like RF-pickup, leading to damage of
the readout bus in our devices. To improve the yield and reproducibility of
lithographically defined patterns, the detectors were designed as images
containing 10 detectors, and the stepper was used to repeat this pattern
forming the full array. The readout circuits and readout bus were designed to
connect to 50 detectors each. The overall pattern was generated by rotating
the wafer inside the stepper and repeating these images, hence both column and
row detectors and their readout circuitry are produced with the same reticles.

The chip was fabricated as a $1000\times 1000$ array, and during testing we
identified a uniform section of 800 column detectors and 500 row detectors,
which we designated as the active detection area. This demonstrates the
flexibility of the architecture, since the unbiased sections of the array do
not waste any bandwidth on the readout buses. The same technique can be
straightforwardly applied to allow selection of an active area on-the-fly.

### Circuit parameter values

In this implementation, the values for the circuit elements were optimized
using test structures as well as SPICE simulations. The section biasing
resistor $R_{\text{bias}}^{\text{}}$ was 1000 $\Omega$, the detector biasing
resistor Rs was 80 $\Omega$, the shunting resistor $R_{\text{sh}}^{\text{}}$
was 16 $\Omega$, the thermal coupler series resistor $R_{\text{tc}}^{\text{}}$
was 16 $\Omega$, the series inductor $L_{\text{s}}^{\text{}}$ was
$1.25\text{\,}\mu\mathrm{H}$, and the inductance of the SNSPD
$L_{\text{snspd}}^{\text{}}$ was $1.14\text{\,}\mu\mathrm{H}$. The biasing
resistor Rs needed to be sufficiently large to ensure that current was
distributed uniformly to each detector – if made too small, parasitic
resistances in the wiring or vias can cause uneven distribution. However,
larger values also contribute to the static power consumption of the array and
so its value cannot be too large. $R_{\text{sh}}^{\text{}}$ was chosen to be
relatively small, as it allows the current to be shunted to ground after a
detector clicked. By choosing an appropriately small value, the detectors are
sufficiently shunted such that latching is impossible, simplifying the
operation of the array. Additionally, a small value of
$R_{\text{sh}}^{\text{}}$ guarantees that voltages generated during the
detection process are shunted before they reach the communal bias line,
minimizing crosstalk between neighboring detectors in a section.

A large value of $L_{\text{s}}^{\text{}}$ serves to both minimize crosstalk
voltages on the bias line during detection, and acts as an energy reservoir
with which to power the heating element on the thermal coupler. Too-large
values, however, result in wasted space on the chip as well as generate excess
heating of the bus that can negatively affect reset times. While smaller
$L_{\text{snspd}}^{\text{}}$ values would be preferred to minimize geometric
jitter and reset time in the detectors, for this design we required least
$5\text{\,}\mathrm{m}\mathrm{m}$-long detectors to span the imaging area.

##  1 Data availability

Unprocessed time tags and data used to produce images and graphs shown in Fig.
1,Fig. 3, and Fig. 4 are available from the corresponding author on reasonable
request.

##  2 Code availability

Code used to process the time tags and produce images shown in Fig. 1 and Fig.
4 is available from the corresponding author on reasonable request.

##  3 Acknowledgements

The U.S. Government is authorized to reproduce and distribute reprints for
governmental purposes notwithstanding any copyright annotation thereon. Part
of this research was performed at the Jet Propulsion Laboratory, California
Institute of Technology, under contract with NASA (Contract No.
80NM0018D0004). A.N.M. was supported in part by NASA APRA via Grant No.
NNH17ZDA001N. Support for this work was provided in part by the DARPA DSO
Invisible Headlights program. Certain equipment, instruments, software, or
materials, commercial or non-commercial, are identified in this paper in order
to specify the experimental procedure adequately. Such identification is not
intended to imply recommendation or endorsement of any product or service by
NIST, nor is it intended to imply that the materials or equipment identified
are necessarily the best available for the purpose. This research was funded
by NIST (https://ror.org/05xpvk416), University of Colorado Boulder
(https://ror.org/02ttsq026), and the Jet Propulsion Laboratory
(https://ror.org/027k65916).

##  4 Author contributions

ANM, BK, and BGO conceptualized these experiments. Fabrication of devices was
done by BGO. Measurements were performed by BGO, DSR and ANM. Analysis and
interpretation of the data was done by BGO, SWN, MDS, BK, and JA. ANM directed
and supervised this work. BGO and ANM prepared the manuscript with input from
all co-authors.

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