1. Introduction

The mid-infrared (MIR) wavelength is essential for various application scenarios, such as molecular spectroscopy [1], biomedical sensing [2], Earth meteorology [3], atmospheric remote-sensing [4], and exoplanet exploration [5]. Conventional MIR photodetectors based on semiconductors such as indium antimonide (InSb), indium antimonide arsenic (InAsSb) and mercury cadmium telluride (MCT) have been well developed and applied in the above scenarios. However, they often have poor sensitivity far from the single-photon level, and the time resolution is usually limited to ∼µs level. These disadvantages limit the application of conventional MIR detecting technology. Recently, there has been an increasing demand for improved MIR detection systems with single-photon sensitivity and picosecond time resolution, particularly in applications such as fast molecular dynamics, environmental monitoring, and atmospheric remote sensing.

Single-photon detectors (SPDs) based on conventional semiconductor technologies, such as Si and InGaAs avalanche photodiodes (APDs) and vacuum photomultipliers (PMTs), have a cutoff wavelength lower than 1.7 µm, which prevents them from being used in MIR applications. One common approach to MIR single-photon detection is to frequency upconvert the MIR photons to shorter wavelengths and detect them with visible or near-infrared SPDs [6,7]. The upconversion MIR detectors have recently been used to implement ultra-sensitive edge enhanced MIR imaging [8] and wide-field MIR imaging based on the aperiodic quasi-phase-matching configuration with an unprecedented field of view up to about 30° [9]. However, this indirect detection method often has a complex setup, suffering from the pump-induced fluorescence noise, and the MIR detection efficiency is limited by the conversion efficiency. Another approach is the direct detection using SPDs fabricated with low energy gap materials. Superconducting nanowire single photon detectors (SNSPDs) fabricated with superconducting films with energy gaps of a few meV are natural broadband SPDs. They have achieved excellent performance in both visible and near-infrared wavelengths with system detection efficiency (SDE) higher than 95% [10–12], timing jitter on the order of a few ps [13], and negligible dark counts as low as 10⁻³ cps [14]. The superior overall performance makes SNSPDs irreplaceable in quantum information fields such as long-haul quantum key distribution [15,16], quantum random number generation [17], and optical quantum computing [18]. MIR SNSPDs have also been explored with different superconducting materials. Amorphous films such as WSi and MoSi are popular choices for preparing MIR SNSPDs, due to their relatively low energy gap (2Δ) which is 1.52 and 2.28 meV, respectively [19]. Recently, Chen et al. [20] achieved saturated intrinsic detection efficiencies from 1.55 to 5.07 µm with a MoSi-based SNSPD. Verma et al. [21] reported WSi-based SNSPDs with a response capacity of up to 9.9-µm wavelength. However, MIR SNSPD fabricated with NbN film, a representative polycrystalline superconducting material, have a modest performance compared with the amorphous-film based devices. Marsili et al. [22] reported the single-photon response of 0.5–5 µm NbN-SNSPDs with an ultra-narrow linewidth (30 nm), the photon response curve was not completely saturated at wavelengths longer than 3 µm. Recently, we reported the potential of γ-Nb₄N₃ thin film in preparing MIR SNSPDs [23]. γ-Nb₄N₃ has a reduced N content and a lower energy gap than the commonly used δ-NbN film, which makes the γ-Nb₄N₃ based device more sensitive to low energy photons.

In this study, we demonstrate a broadband MIR SNSPD based on a 6.5 nm-thick γ-Nb₄N₃ film with a nanowire linewidth of 62 nm. The critical temperature (T_C) of the device was about 3.9 K because the ratio of N to Nb content of the film was decreased to 0.63. A gold mirror was deposited on the substrate before fabricating the nanowire to enhance the photon absorption in the wavelength range of 2.3–5 µm; a compact dual-lens package with a single mode ZBLAN fiber was used for efficient signal coupling and a filter was inserted between the two lenses for the dark count suppression. The Nb₄N₃-based SNSPD exhibits saturated intrinsic detection efficiency (IDE) plateaus at wavelengths up to 4 µm in an absorption cryocooler (0.35 K) and the device detection efficiency (DDE) at 2.95 µm was measured to be 32.5%, with an uncertainty of 12.7%. We also measured the photon response of a device with the nanowire width of 42 nm for the wavelength range of 3–10 µm, with an IDE of 95%, 81%, 40%, and 6% for 4.8, 6, 8, and 10 µm, respectively.

2. Device design and fabrication

The thin films used in our experiment were deposited by reactive DC magnetron sputtering in a cluster deposition system, with a background pressure of approximately 10⁻⁵ Pa. All substrates were cleaned using an Ar ion beam in a cleaning chamber before film deposition. The Ar/N₂ flow ratio and deposition currents were set to 30:2 and 1.75 A, respectively. The NbN_X (the ratio of N to Nb content in NbN materials is defined as X) with stoichiometry X = 0.63 was obtained with a T_C value of 9.1 K(with 100-nm thickness), which were slightly lower than those in our previous study (0.77 and 10.4 K) [23]. The phase of the film (100-nm thick) was confirmed by X-ray diffraction (XRD) (see Supplement 1).

The schematic of our proposed SNSPD is shown in Fig. 1(a). A metallic mirror was first deposited on the Si substrate by electron beam evaporation and ion beam etching, comprising a 100-nm Au with a 10-nm Ti adhesion layer below and above the mirror. A quarter-wave spacer layer comprising about 550-nm SiO₂ was then deposited by magnetron sputtering to form an optical cavity, which was expected to enhance the nanowire absorption when the SNSPD was illuminated from the substrate top. The 6.5-nm Nb₄N₃ thin film was deposited above SiO₂ and patterned into a nanowire by electron-beam lithography and etched via reactive-ion etching (RIE). Finally, a 50-Ω matched coplanar waveguide was formed using ultraviolet lithography and etched via RIE. As shown in the scanning electron microscopy (SEM) image in Fig. 1(b), the nanowire covers a 15-µm-diameter circular area and has a linewidth and pitch of 62 and 120 nm, respectively. An analysis of the SEM images using ProSEM revealed that the average line edge roughness ($\overline {LER} $) was about 4.5 nm. The T_C value of the device was measured to be 3.9 K, which was marginally lower than that of the thin film (4.1 K).

 

Fig. 1. (a) Schematic of the device (not to scale). (b) SEM image of the SNSPD (top view), indicating the active area with a diameter of 15 µm; the nanowire has a width of 62 nm (zoom in at the lower left), which was slightly wider than the designed value of 60 nm. (c) Simulated optical absorption of the device as a function of wavelengths. Inset shows the refractive index and extinction coefficient of 30-nm Nb₄N₃ film with different wavelengths.

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The refractive index of Nb₄N₃ was measured using a spectroscopic ellipsometer (IR-VASE Mark II, J.A. Woollam) on a 30-nm-thick Nb₄N₃ film, as shown in the inset of Fig. 1(c). An electromagnetic simulation was performed using Comsol Multiphysics [24], considering the incidence of a plane wave on the detector. When the electric field of the incident light wave is parallel to the nanowire (TE waves), the simulated absorptance (η_abs) of the device exceeds 80% in the wavelength range of 2.3–5 µm, indicating potential high SDEs over this wavelength range, as shown in Fig. 1(c).

3. Device performance measurements

First, we studied the device response to different wavelengths. Figure 2 shows the setup used for the measurements. The MIR laser was generated by a tunable optical parametric oscillator (OPO) system (OPO-TB-α, HC Photonics), which can output signal waves from 1.5 to 1.9 µm and idle waves from 2.5 to 3.3 µm. The 4-µm light was generated by an incoherent light (Silicon Nitride source, Zolix) coupled to a monochromator. The reflective neutral density filters (NDFs) in the system were used to attenuate the light sources. The MIR light source was attenuated with several NDFs and then coupled into the single-mode fluoride fiber (ZBLAN, FiberLabs) with a core diameter of 9 µm and transmission range of 0.6–4.0 µm for the following propagation into a refrigeration system. To ensure efficient optical coupling, two infrared aspheric lenses with an antireflection coating range of 1.8–3 µm were installed in front of the SNSPD (see the bottom of Fig. 2), one of which was used to collimate the diverging beam launched from the fiber and the other was used to focus the collimated beam onto the device. A filter was implanted between them to eliminate the noise photons. The output port of the ZBLAN fiber was fixed in the object plane of the lenses, whereas the sensitive area of the detector was fixed in the image plane. The lenses and device were mounted in a custom copper package with an FC/PC adapter to connect an FC/PC-terminated ZBLAN fiber. The coupling loss of this dual-lens package module at the wavelength range of 1.8–3 µm was measured to be about 0.6 dB using MIR power meters (S148C for 1.2–2.5 µm and S180C for 2.9–5.5 µm, Thorlabs), i.e., a coupling efficiency (η_coup) of about 87% was obtained. Then, the packaged module was mounted on the cold head of an adsorption cryocooler, which was set to a working temperature of 0.35 K. The signal generated by the SNSPD was amplified using a homemade cryogenic low-noise amplifier (Cryo-LNA) mounted on the 40 K stage, with a gain of 38 dB at the range of 9 kHz–1 GHz, and noise temperature of less than 15 K [25]. The amplified pulse signals (details can be found in Supplement 1) were either read by an oscilloscope or counted by a photon counter.

 

Fig. 2. Schematic of a system for characterizing SNSPDs. NDF: neutral density filters; Coup1, Coup2: couplers; L1, L2: Lenses; Cryo-LNA: cryogenic low-noise amplifier.

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Then we measured the photon count rate (PCR) at different wavelengths of the device. PCR is the difference between the total pulse count rate, which was measured with the light coupled to the fiber, and the system dark count rate (DCR), which was measured with the fiber-end optically shielded at room temperature. The switching current (I_sw) was measured to be about 3.7 µA when the SNSPD was shielded at 0.35 K, and the DCR was recorded as shown in Fig. 3 (black squares), which was considered to be the intrinsic DCR (IDCR). With the dual-lens coupling package connected to ZBLAN fiber, the DCR was as high as 3 Mcps (Fig. 3 (green circles)), which was dominated by the black-body radiation from the environment, which propagates through the fiber. Severe compression of I_sw was also observed due to this excessive DCR [26], which will degrade the device performance. Thus, we inserted a bandpass filter (Edmund Optics) between the two lenses to suppress DCR, which was centered at 2.95 µm with a transmittance of 65%, a bandwidth of 110 nm, and optical density ≥ 3 (commercial specifications). The experimentally measured loss of this filter was about 2.6 dB at room temperature. The DCR was suppressed by three orders of magnitude with this filter, and the compression of I_sw was avoided, as shown in Fig. 3 (blue stars). For applications at specific MIR wavelengths, one can choose proper filters because the SNSPD has a broadband absorption design for 2.3–5 µm.

 

Fig. 3. DCR versus bias current, while the device was shielded at 0.35 K, and without/with filter in a coupling package.

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As shown in Fig. 4(a), the device exhibits saturation plateaus for wavelengths up to 4 µm. A distortion of the 1.55-µm data can be observed, which is mainly due to the readout circuit. When the bias current is below 0.9 µA, the signal-to-noise ratio of the output signal using one cryogenic LNA is not enough for discriminating. The sigmoidal bias current dependence of PCR is empirically known, and the photon response curves were fitted with an empirical logistic function [27] to deduce the level of IDE (η_int, the probability that the absorbed photon triggers the output voltage pulse). In the saturation region (Fig. 4(a)), the detection efficiency did not increase with bias current. Hence, we can assume a 100% IDE, i.e., η_int = 1 in the band of 1.55–4 µm. The SDE is determined by SDE=η_abs×η_coup×η_int. We can infer from the simulation results of η_abs, the measured η_coup, and η_int that the device has a SDE of about 70% in MIR wavelengths when bandpass filter insertion loss is not considered.

 

Fig. 4. (a) Normalized PCR at various wavelengths as functions of the bias current (indicated by different colored symbols); (b) DDE as a function of the bias current at 2.95-µm wavelength.

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To clarify the device performance, we measured the DDE at 2.95 µm. Owing to the limited power range of the S180C power meter (Thorlabs), it was difficult to directly measure the 2.95-µm laser power attenuated to a single-photon level. Thus, five NDFs were inserted in the optical path and calibrated separately. The actual incident laser intensity was obtained by first measuring the initial laser power and then subtracting the total attenuation of all NDFs and other losses in the setup (details can be found in Supplement 1). The DDE of the SNSPD at 2.95 µm was measured to be 32.5%, as shown in Fig. 4(b), while the SDE was 15.3% when the losses of the dual-lens coupler and filter were taken into account. The total error of the DDE was mostly attributed to the uncertainty of the incident laser power, which was determined by the calibration on the power meter (error_powermeter), stability of the laser (error_laser), and relative uncertainty of the NDFs (error_NDFs). We also roughly assessed the DDE uncertainty, which was calculated as $\textrm{Total error} = \sqrt {error_{\textrm{power meter}}^2 + \mathop \sum \nolimits_{i = 1}^5 error_{\textrm{Ai}}^2 + error_{\textrm{laser}}^2} = 12.7\%$ (details can be found in Supplement 1). The measured DDE is lower than the simulated value and a few points may contribute to the loss. First, the components in the coupling package were mechanically fixed for component interchangeability, and mechanical vibration of the cryogenic system and/or mechanical deformation of the package may cause the focus of the signal deviate from the device active area in three-dimensional space. Second, the losses of the coupler as well as the filter were calibrated at room temperature, which may also increase at cryogenic temperature. Better package designs and more accurate parameter measurements are necessary to improve the system performance of MIR SNSPDs.

In order to further explore the potential of γ-Nb₄N₃ for the fabrication of MIR SNSPDs, we reduced the device geometry and measured its photon response at 3-10 µm. We thinned the film thickness to 5 nm and reduced the linewidth to 42 nm with a $\overline {LER} $ of 6.2 nm, as shown in Fig. 5(a). The film was deposited on a double-sided thermally oxidized Si substrate and then patterned into a nanowire structure. To measure the device photon response in the wavelength range of 3–10 µm (the MIR signal was supplied by the Silicon Nitride source as shown in Fig. 2), the ZBLAN fiber was replaced with a selenide (As-Se) chalcogenide fiber (IRFlex), and the corresponding bandpass filter with the dual-lens coupling package was changed in each wavelength measurement. A second-stage room temperature low-noise amplifier was added to the readout system to improve the signal-to-noise ratio of the output pulse [25]. The details of the output signal can be found in Supplement 1. As shown in Fig. 5(b), the 42-nm wide device shows improved photon responsivity at the measured wavelengths when compared with the 62-nm wide device, with a near-unity IDE (95%) at 4.8 µm; but we do not observe a saturation trend in the wavelength range of 6–10 µm. The IDE only reached 81%, 40%, and 6% for 6, 8, and 10 µm, respectively. In our experiment, the device yield dropped significantly when the linewidth was below 60 nm. Owing to fabrication imperfection, the edge roughness and inhomogeneity of nanowires started to play a major role when the linewidth was lower than 80 nm [21,28], thereby degrading device performance. According to the rough calculation in our previous study [23], the cutoff wavelength of the polycrystalline NbN-based device will be expanded to 10 µm when the device T_C value is lowered to 3.5 K. However, our device did not exhibit a sufficiently long saturation region to match our calculated result, which is mainly attributed to the imperfect fabrication. Although narrower nanowires have longer cutoff wavelengths, the device cannot have a unity IDE due to the inevitable defects in the fabrication process, which greatly degrade the actual detection efficiency of the devices. Therefore, there should be a balance in design between the device cutoff wavelength and the fabrication capability.

 

Fig. 5. (a) SEM image of the SNSPD (top view), indicating the active area with 10 × 10 µm²; the nanowire has a 42-nm width (zoom in at the lower right). (b) Normalized PCRs at various wavelengths (3–10 µm) as functions of the bias current.

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4. Conclusions and discussions

In conclusion, we fabricated broadband Nb₄N₃-based SNSPD with a saturated IDE at MIR wavelengths up to 4 µm. The film stoichiometry was reduced to 0.63, and the device linewidth was set to 62 nm to improve the energy sensitivity. A metallic mirror was deposited under the SNSPD to enhance photon absorption, and a dual-lens with filter package was designed for ZBLAN fiber coupling in a cryocooler with an insertion loss of 3.2 dB. We also accurately assessed the DDE at 2.95 µm, which was 32.5%, with an uncertainty of 12.7%. The photon response of a 42-nm linewidth device was also successfully measured up to 10 µm, though we did not see a saturated IDE at wavelengths of 6–10 µm. Improving the uniformity of the ultra-narrow nanowires and optimizing the turnaround of the nanowires, which will help for the improvement of the cut-off wavelength of the device.

According to previous studies [23,29,30], the T_C value of a polycrystalline superconductor strongly depends on the film stoichiometry. With reduced N content in NbN film, a lower T_C value with a corresponding lower energy gap was obtained, improving the energy sensitivity. The energy gap (2Δ) of our film in this experiment is currently reduced to 1.25 meV, according to the relation $2\Delta = 3.53\;{\kappa _B}{T_C}$ (${\kappa _B}$ denotes the Boltzmann constant). Further reduction of N content in the film to broaden the response spectrum to longer wavelengths, although effective, will increase the burden on cryogenics and signal readout. Another effective approach is to further reduce the device geometry, which will be a challenge for the fabrication process.

The diffusion-based hotspot model [31,32] indicates that reducing the free carrier density (increasing the resistivity) of the superconducting film is also an effective means to improve the device energy sensitivity. The film resistivity was mainly determined by material stoichiometry, and the NbN film resistivity decreased with N content. As we reduced the N content in the film to improve the energy sensitivity, the resistivity (ρ₁₅) of our γ-Nb₄N₃ film was measured to be 274 µΩ*cm, which was almost half of the normally used δ-NbN (490 µΩ*cm). Recently, an alternative method to tune the physical properties of superconducting polycrystalline NbN film by defect engineering through He ion irradiation was reported [33,34]. Irradiation-induced vacancies in NbN films increased the disorder in the NbN crystal lattice, thereby decreasing the superconducting energy gap and free carrier density but increasing resistivity. This study provides a promising approach for further expanding the cutoff wavelength of MIR SNSPDs based on polycrystalline superconducting films. The abovementioned methods, including thin film stoichiometry tuning, geometrical parameter optimization, and He ion irradiation technique, could be applied in future work to obtain high-performance NbN-based SNSPDs at 5-10 µm wavelengths.