1 Introduction

Superconducting nanowire single-photon detectors (SNSPDs) have been thoroughly researched and developed for years [1]. They exhibit a broadband response from visible to infrared photons. However, for infrared photons, their detection efficiency decreases as a power law because of their vortex-assisted detection mechanism. Theoretical and experimental development has improved research on SNSPDs, particularly in terms of broadband response and detection efficiency. The detection efficiency of SNSPDs in the infrared wavelength can be improved in two ways. The first method is the enhancement of optical coupling or optical absorption efficiency. The second method is the improvement of the intrinsic detection efficiency. In the first method, researchers have succeeded in fabricating high performance devices with an optical cavity [2, 3], optical waveguide, [4], or optical antenna [5]. However, despite the increase in the system efficiency, the working bandwidth remains restricted. Hot-spot model, as one of the detection mechanism mentioned in articles, describes the mechanism of photon detection, which is hot-spot formation and diffusion, phase-slip center (PSC) formation, resistive region formation. The minimum photon energy (ε min) required for the formation of resistive nucleus could be expressed in the following equation [6–9]:

$$\varepsilon_{\hbox{min} } = h\gamma = h\frac{c}{{\lambda_{\text{C}} }} = \frac{3\sqrt \pi }{{4e^{2} \varsigma }} \cdot \frac{{\Delta^{2} w}}{{R_{\text{S}} }}\sqrt {\frac{\tau }{D}} \left( {1 - \frac{{I_{\text{B}} }}{{I_{\text{C}}^{\text{d}} }}} \right)$$
(1)

where ∆ is the superconducting energy gap, w is the width of the nanowire, R S is the square resistance, τ is the time constant of quasi-particle multiplication, D is the quasi-particle diffusion coefficient, ζ is the quasi-particle multiplication efficiency, I B is the bias current, I dC is the depairing critical current, and λ C is the cut-off wavelength. For a wavelength larger than λ C, the detection efficiency of SNSPD exponentially drops with increasing wavelength. Thus, λ C significantly influences the performance of SNSPD at longer wavelengths. Since R S is proportional to the thickness (d), λ C could be inversely proportional to w, d, and ∆. Reducing the size of Nb* nanowires such as width and thickness or choosing a low energy gap material could enhance λ C so that the sensitivity to the infrared photons could be improved. Attempts have been made to extend λ C by adjusting the parameters of nanowires. First, the width of the nanowire is reduced to 30 nm, which extends the single-photon sensitivity of the NbN device to 5 μm [10]. Second, the thickness of the film is reduced, which expands λ C into the red boundary [8]. However, both methods result in a device that is insufficient to transmit a distinct response signal, which complicates the readout circuit. A third method is the fabrication of SNSPD using a material with a relatively lower energy gap [e.g., tantalum nitride (TaN), NbSi, or amorphous tungsten silicide (a-WxSi1−x)], and this method also extends λ C and increases the intrinsic efficiency [11–14]. Niobium is a popular superconducting material used for electronic devices. It has a lower superconducting energy gap, with T C of 9 K, and a lower kinetic inductance than NbN. Nb SNSPD [6, 15] demonstrates an ultrafast response, with a pulse width of 2.5 ns. In this study, we used a special doped niobium (Nb*) material [16] to design and fabricate Nb* SNSPDs. Both Nb* films and nanowires were covered with a protective layer of aluminum nitride (AlN) film, which is commonly used as an insulating or protecting layer in superconducting electronics [17, 18]. Compared with the traditional Nb device, the Nb* device exhibited better electronic characteristics, such as higher T C and J C. Thus, both the width and thickness of the nanowire could be reduced, λ C could be extended, and the single-photon sensitivities at the mid-infrared wavelength could be improved.

2 Fabrication

The special doped niobium target contains a 99.6 % weight ratio of Nb* with a diameter of 4 in. The target also contains 0.2 % aluminum, 0.12 % ferrum, 0.05 % silicon, 0.02 % titanium, and 0.01 % chromium, as shown in [16]. Using an Nb* sputtering target, we devised a method of preparing high performance ultra-thin Nb* films, which were optimized by protective AlN films. First, the Nb* films were deposited on MgO substrates using direct current (DC) magnetron sputtering. Under carefully optimized conditions, the Nb* ultra-thin films were fabricated at a rate of 0.8 nm/s. Under the same vacuum environment, ~1 nm AlN films were deposited on top of the Nb* films through radio-frequency sputtering to prevent the latter from oxidizing. The rate of AlN sputtering was controlled at 0.2 nm/s. The meandering shape of the nanowire was obtained using electron beam lithography. The Nb* nanowires were then etched out using reactive ion etching under a mixed gas environment (40.0 sccm of SF6 and 10.0 sccm of CHF3), which allowed the etching of the Nb* films at a rate of 2.0 nm/s. The nanowires were either 100 or 50 nm wide and covered an area of 10 μm × 10 μm or 10 μm × 20 μm with a filling factor of 50 %.

3 Results

Nb has a relatively strong affinity to oxygen. An AlN layer with thickness of 1 nm could effectively resist oxidation in the surrounding atmosphere. Before preparing Nb* SNSPDs, we tested T C and J C of Nb* films and bridges with or without AlN layer in liquid Helium. The results indicated Nb* films have a higher T C and J C than pure Nb films, and J C could be improved more significantly by depositing an AlN layer on top. T C of 8 and 7.8 K could be obtained by 10 nm thick Nb* film with or without AlN layer, respectively, while it is ~5 K for pure Nb films [19]. J C could been obtained higher than 107 A/cm2 for 8 nm thick Nb* film with AlN layer, but for pure Nb films, it is as low as 106 A/cm2 [19, 20]. The precise data could be referred by Jia [16].

We fabricated Nb* SNSPDs with different geometries to investigate the relationship between the geometric dimensions and the characteristics of the device, such as λ C, response bandwidth, and temperature. Table 1 shows the electrical parameters of five Nb* SNSPDs with different geometric dimensions. The film thickness of the devices varied from 4.5 to 7 nm, with a corresponding T C ranging from 4.67 to 6 K. For the fabricated nanowires, J C was larger than 7 × 1010 A/m2 at 2.3 K. Both T C and J C were higher than those in traditional Nb nanowires. As shown in Table 1, the Nb* SNSPDs had a lower L K than that of traditional NbN SNSPDs. Sample 243# presented L K of 56.18 nH. We anticipated an ultrafast photon response from Nb* devices with low L K.

Table 1 Electrical parameters of five devices
Full size table

Five Nb* devices were coupled with single-mode fibers and mounted on a GM cryocooler. A biased DC current was supplied through a bias-T (mini-circuits 4R2GW+). The output signal of the device was amplified by a room temperature amplifier with a voltage gain of 20 dB. These Nb* devices were all biased at 0.5 I C. After illumination with an attenuated 404 nm pulsed laser, the output responses were obtained. The normalized results are shown in Fig. 1. We found that the fall time increased with increasing L K of devices. The shortest full width at half magnitude of pulse was ~2 ns for sample 243#, as shown in the inset of Fig. 1. By reducing the area of the nanowire or the filling factor, L K could be further decreased, and a faster response could be obtained.

Fig. 1
figure 1

Normalized output voltage versus time for the five tested devices. Inset Ultrafast response was shown by sample 243#, whose full width at half magnitude was ~2 ns

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3.1 Cut-off wavelength

The dependence of geometric dimensions to λ C of Nb* SNSPDs was measured. A monochromator was used as a light source to excite the photons from 330 to 2,500 nm. The photon response spectrum of sample 571# with different bias currents is shown in Fig. 2. For photons of 415 nm, the count rate (CR) reached saturation at a bias level of 0.85 I C, as seen in the inset of Fig. 2. At this time, the detection mode was dominated by a hot-spot model. For a longer wavelength, CR decreased as a power law, and the detection mode entered a vortex-assisted regime.

Fig. 2
figure 2

Spectrum characteristics of sample 571#. CR was saturated at 415 nm and exponentially declined with the wavelength beyond λ C. Sample 571# was sensitive to 2,010 nm single photons. Inset CR as a function of I B for the single photons of 415 nm. CR was saturated at a bias current around 0.85 I C

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As Fig. 2 shows, CR slowly decreased by about one order of magnitude in the range of 1,064–1,650 nm. However, this decrease was possibly two or three orders of magnitude for traditional NbN devices. This phenomenon was possibly caused by the lower energy gap of Nb and the extended λ C of the device. The hot-spot and vortex-assisted regions could easily be distinguished in Fig. 2 through the saturated CR and drop in CR curves. Based on the boundary between both regions, we defined λ C at different bias currents, namely 488 nm for 0.85 I C, 501 nm for 0.88 I C, and 515 nm for 0.91 I C.

λ C of the devices could also be calculated by Eq. (1), where τ th is the electron thermalized time, which is an important value that determines both the time needed for the hot-spot to grow and the maximum size of the hot-spot. τ th is ~63 ps for traditional Nb films. Another parameter is D, the electron diffusivity, which can be calculated by 4k B T C/πeB 0, where B 0 is the second critical magnetic field for Nb films and k B is the Boltzmann constant. R S, the square resistance of Nb* films, increased with a reduction in nanowire thickness, as shown in Table 1. And the nanowire width also had a key function in extending λ C as discussed above. At last, I dC , the depairing current, is expressed as follows:

$$I_{\text{C}}^{\text{d}} = \frac{{4\sqrt \pi (e^{\gamma } )^{2} }}{21\zeta (3)\sqrt 3 }\frac{{w(\varDelta (0))^{2} }}{{eR_{\text{S}} \sqrt {D\hbar k_{\text{B}} T_{\text{C}} } }}\left[ {1 - \left( {{\raise0.7ex\hbox{$T$} \!\mathord{\left/ {\vphantom {T {T_{\text{C}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${T_{\text{C}} }$}}} \right)^{2} } \right]^{{{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-0pt} 2}}}$$
(2)

where ∆(0) is the superconducting energy gap at T = 0 K, which can be calculated by T C of each device; ζ(3) is the zeta-function = 1.202; γ is the Euler’s constant, which equals 0.577; and D is the electron diffusivity mentioned above. The I dC values for the five devices were also calculated, and the results are shown in Table 1.

We obtained the optimized fit value ζ = 0.75 in Eq. (1) from the measured λ C of sample 571#. Then, the estimated values of λ C for all five devices at I B = 0.99 I C were calculated as 83, 282, 537, 605, and 558 nm, respectively. The Nb* SNSPD with nanowire thickness and width of 4.5 and 50 nm, respectively, exhibited λ C of 605 nm (sample 448#), which was very close to that of traditional NbN devices [8]. The expansion of λ C should have a positive effect on the performance of the device at infrared wavelength.

3.2 Response bandwidth

The Nb* SNSPD could work in the mid-infrared wavelength because of the extension of its λ C. Three types of continuous wave laser diodes (1,310, 1,550, and 2,010 nm) were used to test the single-photon sensitivity of sample 571# at 2.3 K. This device was 4.5 nm thick and 50 nm wide, with a total length of 2 mm and λ C of 558 nm. We attenuated the photons from 103 to 10−2 photon/pulse and obtained the CR at each photon density, as shown in Fig. 3. CR exhibited a linear relationship with the average number of photons per pulse (μ). The linear fit gave a slope of 1.01302 for 1,310 nm photons, 1.00342 for 1,550 nm photons, and 1.04587 for 2,010 nm photons, which reveal the single-photon sensitivity at mid-infrared wavelength.

Fig. 3
figure 3

Linear relationship between CR and photon per pulse. The device was biased at 0.98 I C. The linear fit gave a slope of ~1 for 1,310, 1,550, and 2,010 nm single photons

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The relationship among the CR, dark CR (DCR), and I B of sample 571# for different wavelengths at the operating temperature of 2.3 K was shown in Fig. 4. CR increased with increasing bias current. With an increase in wavelength, CR slowly declined. The ultra-low DCR was observed in the tests and is represented by the black dot in Fig. 4. The device did not exhibit any DCR until I B = 0.98 I C (16 μA), which indicates that the device could work at a state very close to I C. The maximum DCR was only 300 Hz. The typical values of the system detection efficiency at different wavelengths were estimated at DCR = 1. These values were 26.3 % for 404 nm, 4.38 × 10−2 % for 1,310 nm, 1.015 × 10−2 % for 1,550 nm, and 3.27 × 10−3 % for 2,010 nm.

Fig. 4
figure 4

CR versus I B with 1,064 to 2,010 nm single-photon incidents at 2.3 K. Single-photon sensitivity of 2,010 nm is shown in the graph. Black dots represent DCRs (right axes)

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3.3 Temperature dependence

We mounted the Nb* SNSPD (sample 571#) on a He3 cryocooler illuminated with 1,521 nm single photons. Figure 5 shows the temperature dependence of the Nb* SNSPD. As the temperature dropped, I C and CR continued to increase. I C increased from 13.24 μA at 2.260 K to 19.1 μA at 0.315 K. Below 1.372 K, I c was almost saturated, as shown in the inset of Fig. 5. Correspondingly, CR increased by a factor of 10 in the range of 2.260 to 1.372 K. However, when the temperature further decreased to 0.315 K, the CR slowly increased and reached a saturated state. For better detection efficiency and lower DCR, working at a temperature much lower than T C/2 was necessary for a traditional SNSPD. Compared with T C of sample 571# (4.67 K), the Nb* devices suffered from relatively high working temperatures (T C/2) in the GM cryocooler (2.3 K). Thus, its performance could not be fully demonstrated. The performance of the Nb* SNSPD in the GM cryocooler could be improved by further optimizing the Nb* films, i.e., improving T C of films.

Fig. 5
figure 5

CR as a function of both bias current and working temperature. CR increased by more than 10 times from 2.260 to 0.315 K and was saturated from 1.372 to 0.315 K. Inset I C as a function of working temperature. I C increased with decreasing temperature. Five independent working temperatures were used

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4 Conclusion

We successfully fabricated high quality ultra-thin Nb* films covered with a protective AlN layer. Nb* SNSPDs with different structures were fabricated to explore their λ C, response bandwidth, and temperature dependence. λ C of Nb* SNSPDs increased from 83 to 605 nm with a reduction in nanowire geometries. The device with a width of 50 nm and a thickness of 4.5 nm obtained single-photon responses from 404 to 2,010 nm. We obtained a system detection efficiency of 26.3 % for 404 nm, 4.38 × 10−2 % for 1,310 nm, 1.015 × 10−2 % for 1,550 nm, and 3.27 × 10−3 % for 2,010 nm. Furthermore, the performance of the Nb* SNSPDs was enhanced by a factor of 10 at 0.3 K rather than at 2.3 K. We need to further optimize the sputtering technology to improve T C of Nb* SNSPDs, which resulting in their enhanced performance in the GM cryocooler. By optimizing the absorption efficiency of Nb* SNSPDs, that is, by integrating an optical cavity [2], a better performance could be achieved at mid-infrared wavelengths.