1. INTRODUCTION

Single-photon counting detectors (SPDs) represent the ultimate sensitivity in photodetector technology at a given wavelength. They have become central to multiple fields of science from quantum information processing and quantum communications to fundamental physics [1–3]. The detection energy threshold of a detector governs the maximum wavelength of an absorbed photon that will result in a detection being registered. Lowering this energy threshold to count longer wavelength photons has been proposed as a potential benefit to multiple applications such as quantum sensing [4], light detection and ranging (LIDAR) [5], quantum communications [6], physical chemistry [7], and astrophysics [8]. In particular, the fields of infrared astronomy and dark-matter (DM) detection are driven by the ability to perform low-noise single-photon counting at the longest possible wavelength. However, even at the shorter end of the mid-infrared spectral region (2–10 µm), there is a shortage of photon counting SPD options, with HgCdTe avalanche photodiodes that operate in single-photon counting mode [9] and superconducting nanowire single-photon detectors (SNSPDs [10–12]) the only real technologies available. Looking to longer wavelengths, to the farther end of the mid-infrared (10–25 µm) and into the far-infrared (above 25 µm), there exists no demonstrated technology for single-photon counting. In this work we are primarily concerned with photon counting detector development in this 10–30 µm spectral region, which will be referred to hereafter as the mid-infrared.

Detectors capable of single-photon detection at wavelengths at this longer end of the mid-infrared spectrum, if available, have potential to become revolutionary for a variety of applications, including astronomy, DM searches, and physical chemistry. In exoplanet spectroscopy [13], transiting exoplanets can be detected with far better contrast in the mid-infrared than in the visible [14], and their atmospheric composition can be deduced [15]. Working at these longer wavelengths also allows less stringent requirements on the optics and control of a characterization system [16]. Proposals for characterization of exoplanets in the mid-infrared have recently been studied, and concluded that a detector with a high signal-to-noise ratio and a long wavelength cutoff of at least 18.5 µm would be optimal [17], with some suggesting 25 µm as an even better choice [18]. Photon counting detectors are desirable for this application, because their digital-like signals eliminate several sources of instability in analog detectors, which can make it difficult to detect the small changes in the host star’s spectrum over the time of a transit [8]. Time-resolved detection could prove fruitful for these large interferometric schemes as errors caused by spacecraft drift could be effectively gated out. In addition to the above, a wide variety of atoms, ions, and molecules present in astronomical objects have emissions in this spectral range [19,20]. Beyond astronomy applications, direct DM detection experiments would benefit from the sensitive single-photon time-resolved detection that photon-counting detectors operating in this spectral range could offer [21]. Recent experimental searches for DM candidates such as axions and dark photons like the BREAD [22] and LAMPOST [23] experiments would benefit from detectors such as SNSPDs. Lowering the detection energy threshold of these detectors while maintaining low dark count rates has been shown to be a promising path forward towards probing new parameter space for DM candidates [24]. Lastly, in physical chemistry, low-noise-equivalent-power single-photon detectors operating at mid-infrared wavelengths would allow probing of the whole range of vibrational frequencies found in the molecular finger print region with single-photon sensitivity [25].

To date, however, even non-photon counting photodetectors in the 10–30 µm wavelength range have proved difficult to attain. Blocked impurity band (BIB) detector arrays are common in astronomy applications and have been utilized out to 28 µm with Si:As [26] and demonstrated out to 38 µm with Si:Sb [27]. They are, however, susceptible to a variety of issues—such as reset anomalies, last-frame effects, droop, and drift—that lead to instability in the count rate [28,29] and are inherently limited by readout noise. HgCdTe photovoltaic detectors have been demonstrated at 15 µm [30] and have been proposed out to 20 µm and beyond. However, as the Hg content of such detectors increases to lower the bandgap, they become increasingly soft and prone to defects [31]. III-V material type-II superlattice detectors could provide a pathway to a more robust detector but thus far have not been realized [32]. Alternative superconducting detector options such as kinetic inductance detectors (KIDs) are also under development to operate in the mid-infrared [33] but are yet to be experimentally demonstrated at these wavelengths [34] and are currently limited by two-level system noise [35]. Transition edge sensors (TESs) are sensitive in the mid-infrared but have not been demonstrated in photon counting mode and require complex SQUID-based readout [36]. It is worth noting that due to all of the above technologies not yet being true single-photon counting detectors at mid-infrared wavelengths, they cannot reach the fundamental noise-equivalent-power limits and are unsuitable for experiments such as DM searches, where single-photon counting is required.

SNSPDs are currently the gold standard for near-infrared photon counting in terms of system detection efficiency [37–39], timing jitter [40], dark count rate [41,42], and maximum count rate [43]. A characteristic of a high-performance SNSPD is the presence of a saturated plateau in the detection efficiency against bias measurement, indicating that every photon absorbed in the nanowire results in an output pulse being produced when the detector is biased in this saturated regime. When operated in this region, the efficiency is somewhat immune to bias current fluctuations, making SNSPDs highly stable devices [8]. In addition, they exhibit zero readout noise and are truly single-photon sensitive, time-resolved photon counting devices.

SNSPDs have been developed in recent years as a promising technology for the mid-infrared wavelength range as the device properties can be tuned to allow detection of single low-energy photons. Although potential long-wavelength photon detection with SNSPDs has been predicted for many years [44], it still remains an engineering challenge to realize detectors with high detection efficiency due to the required fabrication tolerances and necessary material development. To date, unity internal detection efficiency has been demonstrated out to wavelengths of 10 µm [11] in short nanobridges and 7.4 µm in large-active-area meander structures [45]. Other research groups have also demonstrated sensitivity at mid-infrared wavelengths up to 10 µm with unity internal efficiency at shorter wavelengths [46–48]. SNSPDs with high system detection efficiencies (system detection efficiencies include optical losses) have also been reported at the shorter end of the mid-infrared spectrum [49].

In this work, we fabricate SNSPDs from a low-${T_{\rm c}}$, high-resistivity WSi thin film and demonstrate unity internal detection efficiency at wavelengths up to 29 µm (${E_{{\rm photon}}} = 43\;{\rm meV}$, $\nu = 10.3\;{\rm THz}$), for the first time.

2. MATERIAL ENGINEERING

The detection energy threshold of an SNSPD scales with the characteristic energy, ${E_0} = 4N(0)({k_b}{T_{\rm c}}{)^2}{V_0}$, where $N(0)$ is the density of states per spin at the Fermi level in the normal state, given by $N(0) = (2\rho {e^2}D{)^{- 1}}$, ${k_b}$ is Boltzmann’s constant, ${T_{\rm c}}$ is the critical temperature, ${V_0}$ is the characteristic volume, $D$ is the diffusion coefficient, $\rho$ is the resistivity of the film, and $e$ is the electron charge [50]. By increasing the Si content of the WSi superconducting film we can increase the resistivity of the film (lower the free carrier density), thus reducing the density of states, $N(0)$. In the detection process, this results in the deposited photon energy being divided among a smaller number of quasiparticles within a given volume, increasing the quasiparticle energy, and facilitating the suppression of superconductivity [11]. Increasing the Si content also reduces the ${T_{\rm c}}$ of the material. Additionally, we can utilize thinner films, which both further lowers the ${T_{\rm c}}$ and also the characteristic volume ${V_0}$. This volume factor is a complicated function of several device parameters including bias current, electron–phonon and phonon escape timescales, and wire geometry, but as the film thickness is the same order as the coherence length, the system can be treated as quasi-two-dimensional such that ${V_0}$ scales linearly with thickness. Combining the above approaches, we see we can effectively lower the characteristic energy in a three-fold fashion by minimizing $N(0)$, ${T_{\rm c}}$, and ${V_0}$.

We deposited 3 nm WSi thin films on Si substrates with 240 nm of thermal oxide via sputtering with a 30:70 W:Si compound target at a power of 130 W and a pressure of 5 mTorr. A 20 nm a-Si cap was added as a passivation layer. The resulting film had sheet resistance, ${R_s} = 1.16\;{\rm k}\Omega$, RRR (${{\rm R}_{300\,{\rm K}}}/{{\rm R}_{20\,{\rm K}}}$) of 0.98, and ${T_{\rm c}} = 1.3\;{\rm K}$. We take $D$ to be $0.53\;{{\rm cm}^2}\,{{\rm s}^{- 1}}$ as in [45] for the same target. This gives us an $N(0)$ of $17.3\;{\rm eV}^{ - 1}\;{{\rm nm}^{- 3}}$ and a $4N(0)({k_b}{T_{\rm c}}{)^2}$ value of $0.81\;{{\unicode{x00B5}\rm eV\, nm}^{- 3}}$. Comparing this to [45] we see that we have reduced the $N(0)$ very slightly and, due to the lowering of the ${T_{\rm c}}$, have substantially lowered the $4N(0)({k_b}{T_{\rm c}}{)^2}$ value. A reduction by a factor of 2.9 is achieved compared to the work in [45] and a factor of 4.9 reduction when compared to [11]. We summarize these data in Table 1. This should result in improved detection of low-energy photons.

Table 1. Summary of Material Parameters in This Work Compared to Previous Demonstrations of Mid-Infrared Photon Detection with SNSPDs

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The film was patterned into nanowires of 80 nm width via electron-beam lithography with ZEP530A resist (1:1 mix with anisole) and developed with ZED N60 developer at 7°C. Nanowires were etched with a fluorine-based reactive-ion etch [45]. The wire width was chosen in order to keep the cross-section of the nanowire small for efficient photon detection, while minimizing constrictions caused by fabrication imperfections, which are more prevalent at narrower wire widths [51]. Narrowing the nanowire further would also reduce the switching current (${{\rm I}_{{\rm sw}}}$), resulting in smaller output pulses that become increasingly difficult to count. Meander structures, where the nanowire was meandered back and forth in order to provide a larger active area, and straight nanobridges of a smaller active area were fabricated. The pitch of the meanders was 240 nm, and they covered an active area of 11 µm by 10 µm. The nanobridges were 20 µm long and included a separate wide meander section to add inductance and prevent latching [52]. Bond pads were patterned via photolithography (LOL1000/UV1100 bi-layer, AZ300 developer) and lift-off with Ti-Au-Ti evaporation.

3. PHOTORESPONSE

The devices were cooled to 250 mK with a $^3{\rm He}$ sorption cryocooler. A pulsed cryogenic blackbody source, operated at 1 Hz with a duty cycle of 37.5% (Axetris EMIRS50; see Supplement 1 for more information), was mounted on the 4 K stage and flood illuminated the device through a filter stack. For each wavelength except 29 µm, a bandpass filter at the wavelength of interest was combined with ZnSe short pass filters to exclude long wavelength photons. For the 29 µm measurements, two 29 µm bandpass filters were combined. The resulting filter stacks were characterized in a Fourier-transform infrared (FTIR) spectrometer to ensure unwanted short wavelength photons were effectively suppressed. We calculated the temperature of the blackbody source by calibrating the temperature versus resistance curve and monitoring the resistance during operation. Figure 1 shows the calculated blackbody emission spectra through the various filter stacks. It is worth noting that we take the center wavelength of each stack as the naming convention, though in reality the full-width half maximum value can span 3–4 µm, particularly with the longer wavelength filter stacks. More details on the blackbody source and characterization of filters are shown in Supplement 1.

 

Fig. 1. Blackbody source emission with various filter stacks for different target wavelengths. The temperature of the source is noted in the legend. The data here have been smoothed with a Savitzky–Golay filter for clarity; see Supplement 1 for the raw data.

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Devices were biased via a cryogenic bias tee and output pulses were read out via a cryogenic amplifier (Cosmic Microwave CITLF1 - 1.5 GHz BW, 45 dB gain, ${\rm NF} \lt {0.06}\;{\rm dB}$ at 12 K) at 4 K and a room temperature low-noise amplifier (Mini-Circuits ZKL-1R5+ -1.5 GHz BW, 40 dB gain, NF 2.8 dB). Pulse traces are shown in Supplement 1.

Photon count rate (PCR) versus bias current curves were taken for the 80 nm nanobridge for wavelengths of 10, 15, 18, and 29 µm and the results are shown in Fig. 2. The blackbody source was pulsed (1 Hz, 37.5% duty cycle) so that the background count rate (BCR) could be measured in the same period as the PCR during the dark portions of the sources cycle. This minimized any temperature variation between measurements, as well as the heat load on the 4 K stage. For a full timing diagram, please see Supplement 1. For each data point the BCR was subtracted from the counts measured to give the PCR. The BCR is also shown in Fig. 2.

 

Fig. 2. Normalized PCR curves for 80 nm wide nanobridge at 250 mK for wavelengths of 10, 15, 18, and 29 µm. The saturated count rates were 6, 12, 7, and 8 kCPS for each wavelength, respectively. BCR is shown in black $\times$’s on the right y-axis. The inset shows an SEM of the device with the active area highlighted in red. The remaining structures visible are for proximity error correction during the electron beam lithography.

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Saturation of the PCR curve as the bias current is increased is observed for all wavelengths in the nanobridge, indicating unity internal detection efficiency (IDE). A slight slope is observed in the longer wavelength measurements, which is likely due to the absorption of longer wavelength photons beyond 29 µm due to imperfect optical filtering, as well as absorption of photons in the tapered region at the ends of the nanobridges.

The 80 nm meanders also exhibited photoresponse at 15, 18, and 29 µm, and the PCR curves are shown in Fig. 3. The meander structure leads to increased chance of constrictions in the bends and along the length of the nanowire during fabrication and results in a reduced ability to saturate. The 15, 18, and 29 µm curves, however, show an inflection point and plateau region, although the PCR continues to climb slightly after the plateau is reached. This is likely predominantly due to local regions of increased ${{\rm I}_{{\rm sw}}}$ [53] caused by constrictions and current crowding in the bends, with a contribution from long wavelength photons due to imperfect filtering also likely.

 

Fig. 3. Normalized PCR curves for 80 nm wide $10 \times 11\;{\unicode{x00B5}{\rm m}}$ meander at 250 mK for wavelengths of 15, 18, and 29 µm. The saturated count rates were 23, 35, and 34 kCPS for each wavelength, respectively. BCR is shown in black $\times$’s on the right y-axis. The inset shows an SEM of the device with the active area highlighted in red. The remaining structures visible are for proximity error correction during the electron beam lithography.

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4. DARK COUNTS

The dark counts of a detector can be broadly split into the intrinsic detector dark count rate (DCR) and the background count rate (BCR). The DCR is the counts that would be registered by the device in the absence of photon absorption, and the BCR includes the counts registered due to external radiation coupling into the experimental environment. The BCR is a function of the optical coupling scheme used to direct signals to the detector, so it is highly dependent on the optical design of the detector system. It is useful to characterize both the BCR and the DCR. In initial testing, the samples were mounted onto a copper sample plate with no shielding from higher temperature stages and components. This resulted in a BCR on the order of ${10^2}$ counts per second (cps) for the nanobridge and ${10^3}$ cps for the meander, when biased on the saturated plateau (see Supplement 1 for data).

In order to lower the BCR, a new detector mounting package was designed and manufactured. The detector is housed in a gold-plated, oxygen-free high-conductivity (OFHC) copper box with a ${{1/2}^{{\prime \prime}}}$ aperture. The filter stack was then mounted directly onto the aperture. Care was taken that no dielectric materials were included inside the package due to transmission in the mid-infrared and the likelihood of Cherenkov-radiation induced dark counts [54]. The resulting BCR of the nanobridge and meander in the new package with the 18 µm filter stack in place is shown in Fig. 2 and Fig. 3, respectively. The BCR was integrated for 10 s per bias point. A reduction of the BCR to sub-10 cps was achieved on the saturated plateau for both detector geometries. More information on the packaging is available in Supplement 1.

It is also useful to quantify the intrinsic DCR, that is, the DCR in a completely sealed environment, in order to put a lower limit on the achievable BCR. For completely light-tight experiments such as DM detection, the intrinsic DCR sets a limit on the noise floor of the experiment [23]. To do this, the meander device was mounted in a similar package with no aperture. To quantify the intrinsic DCR, a counts versus bias current curve was taken with a 60 s integration time per bias point. The resulting data are shown in Fig. 4 alongside the data from a previous BCR measurement with the 18 µm optical filter stack in place. The intrinsic DCR is measured to be below 0.1 cps just before the exponential increase as the current approaches ${{\rm I}_{{\rm sw}}}$. An upper limit was calculated for the bias points where no counts were registered in the integration period using the modified Wald Barker method [55] using a 68% confidence interval. To further bound this value we used an oscilloscope (LeCroy, 6 GHz BW) to perform a long integration DCR measurement over a timescale of 2 h. The oscilloscope was used to digitize the output pulses so they could be manually examined to ensure that actual detector clicks and not spurious noise were triggering the counter. A bias point of 0.22 µA (0.73 on normalized Fig. 4) was selected as this was on the saturated plateau for all wavelengths but before the exponential onset of dark counts, i.e., a suitable operating bias point for this detector. Over the 2 h integration time, 130 events were recorded, nine of which were determined to be caused by noise/spurious signals on the readout lines. This gives a DCR of $1.6 \times {10^{- 2}}\;{\rm cps}$, consistent with the data obtained in the 60 s integration measurement.

 

Fig. 4. DCR comparison between the detector package with a filtered aperture and the closed box intrinsic DCR. Bias is normalized to the ${{\rm I}_{{\rm sw}}}$ to account for slight DC offset between cooldowns. The upper bound for the DCR where no counts were observed in the integration period is shown in the red shaded region.

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5. DISCUSSION

The presence of a saturated plateau region in the PCR curve of an SNSPD indicates unity IDE—that is, every photon absorbed by the nanowire results in an output pulse being produced. The nanobridges exhibited unity IDE for all wavelengths tested, while the meanders showed an inflection point and flattening of the PCR curve, indicating close-to unity IDE, but did not show a fully saturated plateau. This was likely due to photon absorption events in the bends and fabrication imperfections along the length of the nanowire. Meander bends and fabrication imperfections can cause constrictions, resulting in local regions of increased current crowding. This leads to a suppression of the switching current at certain points in the wire, and hence a spatial variation to the bias point at which unity IDE is achieved. The presence of saturated IDE in our devices is also indicative of single-photon detection at these wavelengths. The multi-photon regime in SNSPDs is based on the absorption of two (or more) photons in a local region where the combined deposited energy is sufficient to break superconductivity. As the bias current is increased, the threshold for breaking superconductivity decreases, meaning the absorbed photons can be spaced further apart both spatially and temporally while still providing enough localized energy to cause a detection event [56]. This manifests itself as increasing two-photon sensitivity as bias current is increased, and the lack of a saturated plateau. This argument is true when the nanowire area is much larger than the hotspot area, which is the case in our detectors, and when the count rates are far from saturating the detector, which was controlled in our measurements to kCPS.

The total detection efficiency depends on both the IDE and the optical coupling efficiency, so the next step in the development of these detectors is to increase the absorption of incident radiation by the nanowire. SNSPDs are usually fabricated in an optical cavity [57] to enhance their absorption efficiency, but this proves difficult in this wavelength range due to the unavailability of suitable dielectrics and thickness requirements for efficient coupling. Antenna coupling [58] and microlenses [59] could provide possible pathways to increasing the absorption efficiency at these long wavelengths. Optimizing the transmission of optical filter stacks or cryogenic gratings for efficient throughput of photons will also be necessary for high-efficiency systems.

In the mid-infrared, photodetectors are typically characterized by their noise-equivalent power (NEP). The NEP for a single-photon detector is calculated by [60]

 

Fig. 5. Calculation of noise-equivalent power for our detector at 15, 18, and 29 µm wavelength, given the measured DCR and internal detection efficiency saturation, for a range of optical coupling efficiencies. The dashed lines show the best reported NEPs for other mid-infrared detectors. KID: [62] (test wavelength unspecified, 25–200 µm band design); HgCdTe: [63] (test wavelength unspecified, cutoff wavelength 16–17 µm); Si:As BIB: [64] (assumed ${25} \times {25}\;{\unicode{x00B5}{\rm m}}$ pixel size, taking the lowest reported NEP at a wavelength of 23 µm); Si:Sb: [64] (assumed ${18} \times {18}\;{\unicode{x00B5}{\rm m}}$ pixel size, taking the lowest reported NEP at a wavelength of 31 µm).

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Due to the low ${{\rm I}_{{\rm sw}}}$ of these devices, a natural result of the low ${{T}_{\rm c}}$ and nanowire geometry, pulse heights after amplification were in the 10 s of mV scale. While large enough to be satisfactorily counted, a larger signal-to-noise ratio (SNR) would be beneficial to separate the true detector clicks from spurious noise. Impedance matching tapers on the nanowire ends [65] and a superconducting nanowire avalanche photodetector (SNAP) [66] architecture would be readily applicable techniques here to increase the output pulse height and improve the SNR. This would allow a higher triggering threshold, which would further reduce the DCR, as shown earlier where the oscilloscope was used to veto noise counts.

The temperature dependence of the detectors was characterized by taking a different 80 nm wide nanobridge device from the wafer and cooling to 100 mK in an adiabatic demagnetization refrigerator (ADR). By ramping the magnetic field, the temperature could be tuned to observe the behavior of the detector. A PCR curve for an illumination wavelength of 10 µm was taken for different temperatures, and a summary of the results is shown in Table 2. The current where the detector began to detect photons (turn-on current) was 0.12 µA for this device. The current where saturated behavior began was 0.235 µA, and the plateau length was calculated by subtracting this from the ${{\rm I}_{{\rm sw}}}$ for each temperature. The detector showed no degradation in performance between 100 and 306 mK. At 481 mK, the ${{\rm I}_{{\rm sw}}}$ was slightly reduced but saturated performance was still observed with a long plateau indicating that 15, 18, and 29 µm plateaus would likely still be achievable. At 780 mK, the detector performance had degraded beyond use with no plateau observed. From this is it reasonable to conservatively conclude, given the ${T_{\rm c}}$ of the device was 1.3 K, that these detectors will exhibit saturated performance in the mid-infrared at a fraction of ${{T}_{\rm c}}$ of around 0.4 and lower. Performance at higher temperatures may be feasible at a reduced internal detection efficiency. With this knowledge, it is likely that we can tune the stoichiometry of the WSi film by further increasing the Si content, which would result in films with even lower ${T_{\rm c}}$, and still operate them without requiring the use of a dilution refrigerator. As outlined in Section 2, the characteristic energy, ${E_0}$, scales with $T_{\rm c}^2$, although at longer wavelengths, factors such as latency and diffusion may cause deviations, which would weaken this scaling to be closer to ${T_{\rm c}}$. Amplification of pulses, however, becomes more challenging as ${{\rm I}_{{\rm sw}}}$ decreases as $T_{\rm c}^{3/2}$ (assuming fixed ratio of ${{\rm I}_{{\rm sw}}}/{{\rm I}_{{\rm dep}}}$), but we expect an increase in SNR of three to five times is possible through the SNAP architecture and impedance matching taper techniques explained above. By simple scaling arguments for the depairing current and assuming a fixed nanowire geometry, this suggests we could achieve the same readout SNR with a ${T_{\rm c}}$ reduced to 0.4 of the current ${T_{\rm c}}$. An optimistic scaling of detection energy as $T_{\rm c}^2$ leads to a sensitivity improvement by a factor of six over the current demonstration, but even a more conservative scaling by ${T_{\rm c}}$ is still more than a factor of two improvement. As the photon energy is reduced, there are additional theoretical concerns that have not been considered in detail, such as the impact of lattice heat capacity of amorphous metals at low temperatures, and the threshold at which the escape of a single acoustic phonon during downconversion can remove a sizable fraction of the photon energy and prevent photon detection. More theory effort and a better quantitative model of the SNSPD detection mechanism are needed in order to make more definitive statements about the long wavelength limit of these devices.

Table 2. Temperature Dependence on the ${{\rm I}_{{\rm sw}}}$ and Plateau Presence for an 80 nm Wide Nanobridge at 10 µm Wavelength Illumination

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In conclusion, we have demonstrated that SNSPDs can offer low-noise single-photon counting operation in the mid-infrared. By demonstrating saturated internal detection efficiency at wavelengths as long as 29 µm, while maintaining DCR as low as $1 \times {10^{- 2}}\;{\rm cps}$, we have shown that they are capable of achieving excellent detection metrics in this wavelength range. Investigation of the temperature dependence suggests the techniques utilized in this work are readily extendable to even longer wavelengths. This work promises a new class of single-photon detectors for the mid-infrared spectral range with the inherent low timing jitter, high stability, low noise, and potential for high count rates that SNSPDs can provide.