1. Introduction

Recent progress in improving the performance of superconducting nanowire single-photon detectors (SNSPDs or SSPDs [1]) are nothing short of eye-opening. At present, their system detection efficiency (SDE) is reaching unity at a wavelength of 1550 nm with a dark count rate (DCR) lower than 1 kcps [2–4], and a short system timing jitter of 20–40 ps can be obtained [5]. These values are strikingly superior to those obtained with commonly used avalanche photo diodes (APDs) at telecommunication wavelengths [6]. In fact, practical SSPD systems are already employed in a variety of applications such as quantum key distribution, quantum optics experiments, and so on [7–13]. Meanwhile, arranging the independent multipixels into an active area is an attractive configuration because this allows high-speed operation, enlargement of the device area, pseudo photon number resolution, and spatial resolution [14]. The realization of large-format SSPD arrays will have a great impact on various application fields such as fluorescent imaging, laser ranging, high-resolution depth imaging, free space optical communications, and so on.

One of the critical issues to realize large-format SSPD arrays is how to reduce heat flow from room temperature through coaxial cables, the number of which increases as of the number of pixels increases in a conventional readout scheme. Therefore, our primary effort so far has been focused on the development of cryogenic readout electronics using a single flux quantum (SFQ) circuit because the required number of cables can be drastically reduced by implementing SFQ circuits and SSPDs in a cryocooler system. We have confirmed correct SFQ operation with output signals from SSPDs [15], and we have succeeded in implementing a four-pixel SSPD array and SFQ circuit in a Gifford–McMahon (GM) cryocooler system with no serious crosstalk [16]. Meanwhile, scaling the number of SSPD pixels is other critical issue to realize large-format SSPD arrays. Although two, four, and twelve pixel SSPD array has been reported so far [3,14,17,18], significant uniformity of superconducting nanowire characteristics is required for further scaling up the number of pixels. Because our recent development of single-pixel NbTiN SSPDs prepared on a thermally oxidized Si substrate can provide high SDE devices with high yield [4], it is natural to apply this technology to scale up the SSPD arrays. In this work, we report the development of two-dimensionally arranged 64-pixel NbTiN SSPD array and characterization of electrical and optical properties in a GM cryocooler system. We also show the spatial resolution of the 64-pixel SSPD array by irradiating it with incident light from a single-mode optical fiber at different distances between the fiber tip and the active area.

2. Experimental procedure

Figure 1 shows the scanning electron micrograph (SEM) of the 64-pixel NbTiN SSPD device. The NbTiN nanowire pixels were fabricated on a Si substrate with a 250-nm-thick thermally oxidized SiO₂ layer. Although we chose a thermally oxidized substrate that can configure the double-sided cavity structure by placing a λ/4 dielectric cavity and mirror on the nanowire [4], they were not embedded in this device in order to exclude the influence of optical absorbance fluctuations that may be caused by each layer’s thickness variations or by partial imperfections of the cavity structure. The fabrication process of the NbTiN SSPDs was basically the same as described elsewhere [4,19]. The 5-nm-thick NbTiN nanowire was formed to be 100 nm wide and 100 nm spaced meandering lines covering an area of 5 × 5 μm, thus configuring one nanowire pixel. The 8 × 8 nanowire pixels were two-dimensionally arranged with spacing of 3.4 μm, covering an area of 63 × 63 μm. The 200-nm-wide interconnection lines were formed using the same 5-nm-thick NbTiN nanowires in the spaces between the nanowire pixels, in which the width of interconnection lines was two times wider than that of the nanowire pixel in order to prevent a response to single-photon incidence. The interconnection lines were then connected to coplanar waveguide (CPW) lines. Since the dc resistance of long (~2 mm) CPW lines could lead to a disturbance of the correct operation of the SSPD, 100-nm-thick NbN films with a superconducting transition temperature (T_c) of ~15 K were used to assure zero dc resistance.

 

Fig. 1 Scanning electron micrograph of 64-pixel NbTiN SSPD array.

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Figure 2(a) shows a photograph of the chip-mounting block for the 64-pixel SSPD array. As shown in the figure, the 64-pixel SSPD array chip was mounted on the chip-mounting block with a specifically designed printed circuit board (PCB), and each nanowire pixel was wire bonded to a 50 Ω microstrip line on the PCB. Since nine coaxial cables were introduced into our cryostat system, we characterized the electrical and optical properties of the 64 nanowire pixels individually by changing the connections between the nanowire pixels and the coaxial cables per cool-down process. A single-mode optical fiber for a wavelength of 1550 nm was introduced into the cryocooler system, and the end of the fiber was fixed to the rear side of the chip-mounting block after aligning the incident light from the fiber with the device active area, as schematically drawn in Fig. 2(b). We adjusted the distance between the fiber tip and the device active area (L_fiber-sspd) to 3 mm and 470 μm in order to observe the incident photon response at the respective distances. The packaged block was cooled with a 0.1 W GM cryocooler system, which can cool the sample stage to 2.3 K [20].

 

Fig. 2 (a) Photograph of chip-mounting block for 64-pixel SSPD array. (b) Schematic drawing of positional relationship between 64-pixel SSPD array, single-mode optical fiber, and illuminated light from the fiber.

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To measure the SDE, a continuous tunable laser was used as the input photon source. The wavelength of the light source was fixed to 1550 nm and attenuated so that the photon flux at the input connector of the cryostat was 10⁹–10¹¹ photons/s. Although these values are much higher than usually used for SDE measurements (~10⁶ photons/s [19]), the incident photon flux to each pixel was low enough to maintain the linearity of the output counts to photon flux due to the low coupling efficiency to each pixel (P_couple,pixel). We confirmed the linearity of the output counts to the incident photon flux before deciding on the input photon flux. A fiber polarization controller was inserted in front of the cryocooler’s optical input in order to control the polarization properties of the incident photons so as to maximize the SDE. The SDE was determined by the relation SDE = (R_output – R_DCR)/R_input, where R_output is the SSPD output pulse rate, R_DCR the dark count rate, and R_input the input photon flux rate to the system. The SDE of each pixel was measured individually by changing the connection of the readout components at the outer side of the cryocooler system.

3. Results

Figure 3 shows the histograms of the observed T_c [Fig. 3(a)] and the superconducting switching current [I_sw, Fig. 3(b)] for the 64 nanowire pixels. As shown in the figure, both T_c and I_sw of all pixels fell within the small ranges of 7.19–7.23 K and 15.8–17.8 μA, respectively. These results indicate that all pixels were fabricated uniformly without significant defects in terms of their electrical properties. We then characterized the optical responses of all pixels. Figure 4(a) shows the SDE as a function of bias current for the 64 nanowire pixels when L_fiber-sspd is adjusted to 3 mm. Although the absolute value of the SDE was low due to low P_couple,pixel, all pixels showed a response against single-photon irradiation. In addition, bias current dependencies in most of the pixels were well fitted with sigmoid function by least squares method and they are about to reach the plateau at high bias current region. The sigmoid shape for the bias current dependence of the SDE has been shown, and these devices showed near unity SDE at their plateau region in bias current dependency [2,4,21]. Therefore, from empirical point of view, it is valid to assume pulse generation probability after photon absorption (P_pulse) reaches 1.0 at plateau region and hence P_pulse at each bias current can be approximated if the bias current dependency can be well fitted with sigmoid function. Figure 4(b) shows the histogram of approximated maximum pulse generation probability in each pixel (P_pulse,max), the value of which were highest P_pulse obtained in bias current dependency in each pixel. As shown in the figure, 60 of the 64 pixels exceeded 90% of P_pulse,max.

 

Fig. 3 Histogram of (a) T_c and (b) I_sw for the 64 NbTiN nanowire pixels.

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Fig. 4 (a) SDE as a function of bias current for the 64 NbTiN nanowire pixels at L_fiber-sspd of 3 mm. (b) Histogram of P_pulse,max for the 64 NbTiN nanowire pixels.

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The SDE of each nanowire pixel can be expressed as P_couple,pixel × P_abs × P_pulse × (1 − P_loss), where P_abs is the optical absorptance into the nanowire and P_loss is the optical loss of the system. Here, the asymptotic system detection efficiency SDE_asymp, which is the expected plateau value in bias current dependencies [22], should only be proportional to P_couple,pixel if P_abs and P_loss are uniform for all pixels, because P_pulse can be treated as 1.0. As described above, the dielectric cavity and mirror layers on the nanowires were intentionally not included in order to retain the variation of P_abs as small as possible. P_loss must be constant over the 64 pixels because we introduced the incident light through one optical fiber to all pixels. Therefore, the spatial distribution of SDE_asymp can clearly reflect the spatial distribution of the incident photon intensity. Figures 5(a) and 5(b) show the color maps of SDE_asymp over the 64 pixels when L_fiber-sspd is 3 mm and 470 μm, respectively. In the figures, SDE_asymp for each pixel was normalized by the highest value among the 64 pixels. If L_fiber-sspd is 3 mm, the illuminated light from the fiber-end spread and beam waist at the device active area become much larger than the active area of 63 × 63 μm. Since the illuminated light from the single-mode fiber follows the Gaussian beam profile, the active area is exposed to a tiny area of Gaussian beam where the spatial photon flux intensity distribution can be regarded as approximately flat. Although the SDE_asymp varied by factor of ~3.5 across the 64 pixel array in Fig. 5(a), the spatial distribution represent the relatively flat distribution in log-scale as expected. One possible reason of this variation can be supposed due to the misalignment because expanded light spot was too blurred to define the center position of light spot accurately in the alignment process. On the other hand, illuminated light from the fiber-end at L_fiber-sspd of 470 μm does not spread as compared to that at L_fiber-sspd of 3 mm, and the size of the beam waist at the active area is supposed to be smaller than the size of the active area, resulting in spatial variations of the illuminated light power in the device active area according to the Gaussian distribution. The obtained spatial distribution of SDE_asymp in Fig. 5(b) clearly represents the Gaussian beam profile as expected. This distribution could be well fitted to a Gaussian function by the method of least-squares fit, which is shown in Fig. 5(c), and the beam waist (2ω₀) was estimated to be 19.1 μm at L_fiber-sspd of 470 μm, which is relatively smaller than predicted value of 28.1 μm given from fiber NA and working distance.

 

Fig. 5 The color maps of SDE_asymp over 64 pixels when L_fiber-sspd is (a) 3 mm and (b) 470 μm. (c) Fitting data of Gaussian function from the results at L_fiber-sspd of 470 μm by means of the method of least squares.

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Although SDE_asymp was verified to be a good reference for determining the photon flux intensity distribution, a sigmoid function fitting process from the bias current dependency is necessary in order to derive the values, which are unfavorable for realizing a real-time signal processing unit such as an SFQ circuit. For simultaneous 64-pixel operation with real-time signal processing, bias currents supplied to each pixel should be the same in order to employ a simple biasing scheme such as that reported in [23]. Therefore, we next verified whether the actual SDE values at a constant bias current well represent the spatial photon flux intensity distribution. Figures 6(a)–6(d) show color maps of the SDE distributions (left) and histograms of P_pulse (right) at L_fiber-sspd of 470 μm at constant bias currents of 15.0, 15.5, 16.0, and 16.5 μA, respectively. The mean values μ and μ', and standard deviations σ and σ' are shown in each histogram; those were taken with excluding (μ, σ) and including (μ', σ') the pixels that could not operate due to locking into a resistive state (the diagonal-lined pixels and bars in the figures). As the bias current increased, the μ increased and the σ decreased, enabling to represent the spatial distribution of the photon flux intensity more precisely. However, the number of disabled pixels (N_disabled) increased with increasing bias current, resulting in lower μ' and larger σ', as shown in the figures. On the other hand, N_disabled was zero at the lowest bias current of 15.0 μA. Although the μ was lower and σ was larger than those at higher bias currents, the SDE variations still represented the photon flux intensity properly. The value of 2ω₀ estimated from Gaussian function fitting was 18.5 μm, which is almost same as that obtained from SDE_asymp.

 

Fig. 6 The color maps of the SDE and histograms of P_pulse at L_fiber-sspd at 470 μm at constant bias currents (I_b) of (a) 15.0, (b) 15.5, (c) 16.0, and (d) 16.5 μA, respectively. The diagonal-lined pixels and bars in the figures indicate the nanowire pixels that could not operate due to locking into a resistive state. The mean values μ and μ', and standard deviations σ and σ' are shown in each histogram; those are taken by excluding (μ, σ) and including (μ', σ') disabled pixels, respectively.

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4. Conclusion

We characterized the electrical and optical properties of a 64-pixel NbTiN SSPD array prepared on a thermally oxidized Si substrate. Our two-dimensionally arranged 64-pixel SSPD array exhibited uniform superconductivity in all pixels and pulse generation higher than 90% in 60 of the 64 pixels. We verified that the spatial distribution of SDE_asymp in the 64-pixel SSPD array reasonably represents that of the photon flux intensity by irradiating the light from the fiber tip with different distances to the device active area. In addition, even at a constant bias current of 15.0 μA, we obtained similar SDE distributions as compared to SDE_asymp distributions with no disabled pixels. These results indicate that two dimensionally arranged SSPD array could work in imaging application if the free space coupling between the spatially distributed photon image and the sensitive area of SSPD array can be realized. Our next study will be a simultaneous operation of all of 64 nanowire pixels with an SFQ signal processing circuit for real-time spatially resolved photon detection. To accomplish this, the 64-pixel NbTiN SSPD array verified in this work already has favorable features. For example, a bias current of 15.0 μA is available to operate the SFQ circuit [24], and adequate image acquisition of the photon intensity distribution at a constant bias current makes it possible to apply the parallel biasing scheme with few feed lines [23]. Of course, although further improvement of bias current dependencies in the SDE such as those achieved by WSi-SSPDs at a low operation temperature of ~300 mK is more favorable for retaining the variations of P_pulse even at low bias current regions [2], the results of this work provide insights into realizing large-format position-sensitive SSPD arrays even at operating temperatures of 2–3 K.