1. INTRODUCTION

Diverse experiments and applications ranging from fundamental research [1], communications [2,3], metrology [4], remote sensing [5], materials research [6], and astronomy [7,8] rely on single-photon detection. Superconducting nanowire single-photon detectors (SNSPDs) have become a dominant platform for such endeavors, as they boast very high system detection efficiencies (SDEs) [9–11], low timing jitter [12], and very low dark counts [13,14]. These properties have popularized their employment in several recent quantum-optics experiments, including loophole-free tests for local realism [15], quantum teleportation [16] and key distribution [13], characterization of quantum states [17–19], and quantum buffer memories [20,21].

Recent advances in device-fabrication technology [22], in combination with advances in cryogenic cooling have rendered SNSPDs a commercially viable investment for years to come. The record for the highest SDE, however, has remained stagnant to within error at around 93% since the first report in 2013 [9]. The lingering mismatch between theoretical predictions and experimental realizations for SDE has imposed generously loose bounds on often immeasurable channels of loss, including scattering, off-nanowire absorption, and the internal quantum efficiency of the superconducting material system. Here, we focus on improving the SDE by optimizing the device’s vertical optical stack design, as well as the coupling of the guided fiber mode to the active detection area of our device. We achieve a new record SDE of $98.0 \pm 0.5\%$ at a wavelength of 1550 nm, thus tightening the bounds on several loss mechanisms and offering insight into the optical coupling process.

2. DEVICE DESIGN AND FABRICATION

SNSPDs consist of a nanoscale, meandering current path etched into a thin (sub-10 nm) layer of superconducting film. When operated at sub-critical cryogenic temperatures and current biased below the critical current density value, this “nanowire” poses zero resistance. In this setup, the introduction of any thermal energy (say, via absorption of a single incident photon, or kinetic implantation of a massive atom/ion) onto the nanowire creates a local region of normal resistance [23–29], thus momentarily interrupting the current flow and generating a radio-frequency (RF) “detection pulse” in the bias line.

To efficiently couple light onto the nanowire, we mount our devices on a self-aligning fiber-packaging system [30]. We use SMF-28e+ fiber pigtails terminated in standard 2.5 mm ceramic ferrules and AR-coated for 1550 nm light. The SDE for this system is defined as the probability of the device registering a detection given that a photon is launched into the fiber pigtail from outside the cryostat.

SNSPD vertical optical stacks consist of interferometric trapping structures above and below the thin, nanowire layer to facilitate multiple interactions of the photons with the nanowire. The typical constructions use a reflector below the nanowire, which could be a metallic mirror [9,10,22,31] with an electrically isolating dielectric layer in between forming a slab cavity for the photons. If optimizing for SDE, the stack might also consist of layers deposited on top of the nanowire [32–35] effectively forming an AR coating. The optimization is done for normally incident plane waves using rigorous coupled-wave analysis (RCWA) [34,36]. By reformulating the resulting steady-state field distribution in terms of Poynting vectors [37], we can determine the net absorption in each layer. In a generic, three-layer AR-coating optimized stack with a metal mirror reflector (as in [9]), the metallic layer is responsible for the absorption of nearly 3% of the photons at the optimum design wavelength even under ideal, simulated conditions (see Fig. 1). The electromagnetic field penetrates into the metallic layer due to the skin effect, inducing the movement of conduction electrons (the very mechanism of reflection) within a non-zero resistance metallic medium, which functions as a loss channel. This prompted us to use a distributed Bragg reflector (DBR) instead, consisting of alternating layers of high- and low-refractive-index dielectrics [11,38–40]. A 6.5 period (13 layer) DBR, with dielectric layers of optical thicknesses $\lambda /4$ each, suffices for near-unity photon absorption into the nanowire.

 

Fig. 1. (a) SNSPD vertical optical stack with gold mirror. (b) Simulated cumulative absorption versus depth [37] for normally incident plane wave at optimum wavelength.

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The SNSPDs presented here were all fabricated on a single 76.2 mm diameter silicon wafer. To begin, we deposited 13 alternating layers of silicon dioxide (${{\rm SiO}_2}$) and amorphous silicon ($\alpha {\rm Si}$)—starting with ${{\rm SiO}_2}$—onto the wafer using plasma-enhanced chemical vapor deposition (PECVD). The refractive indices of these two dielectrics at 1550 nm were measured to be 1.453 (${{\rm SiO}_2}$) and 2.735 ($\alpha {\rm Si}$). For a DBR with the reflection band centered at 1550 nm, the layers deposited had thicknesses of $266.75 \pm 0.84$ nm (${{\rm SiO}_2}$) and $141.70 \pm 0.27$ nm ($\alpha {\rm Si}$). We then deposited gold terminals and assorted alignment marks using a photolithographic lift-off process. The terminals are composed of a three-layer stack of titanium (Ti, 2 nm), gold (Au, 50 nm), and titanium (Ti, 2 nm) deposited in an electron-beam evaporative sputtering tool. Following this, we use magnetron sputtering to co-sputter a 4.1 nm thick, 75:25 ratio molybdenum silicide (MoSi) layer capped with a 2 nm sputtering of $\alpha {\rm Si}$ to prevent oxidation. The refractive index of the MoSi layer was estimated to be $(n,\kappa) = (5.817,6.033)$ at 1550 nm (see Supplement 1, Section 2). This forms our superconducting layer and has been measured to have a critical temperature of ${T_c} \gt 5\,\,{\rm K}$ [41,42]. Coarse features are then etched into this layer using photolithography and an ${{\rm SF}_6}$ reactive-ion etch (RIE) recipe. The nanowire meander patterns generated using phidl [43] are then written onto the active area using a PMMA resist layer and an electron-beam lithography tool. The electron-beam resist pattern is then transferred onto the superconducting layer using a second RIE step with the same ${{\rm SF}_6}$-based recipe.

 

Fig. 2. (a) DBR-based vertical optical stack with the MoSi nanowire layer labeled. (b) Top view of optical-microscope image of the device chip. (c) SEM of a small region of the nanowire meandering at the edge of the active area, showing 180° hairpin bends. The darker regions are MoSi.

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Fig. 3. System detection efficiency (SDE) versus applied voltage bias at the optimized input polarization for three different active area diameters. The pulses are read out of the nanowires directly using $50\,\Omega$ coaxial SMA lines (without extra series resistors). The inset is a zoomed-in view of the marked region. Error bars not shown for discernibility.

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We patterned the nanowire meanders to cover circular active areas of diameters 20 µm, 35 µm, and 50 µm across different devices. The nanowires had widths of 80 nm and a fill factor of 0.57 (gap distance of 60 nm) [see Fig. 2(c)]. Atop the nanowire, we then deposited a three-layer AR coating of $\alpha {\rm Si}$ (50 nm), ${{\rm SiO}_2}$ (248.7 nm), and $\alpha {\rm Si}$ (68 nm) using the PECVD tool [Fig. 2(a)]. The final deposition step was for a pair of Ti (2 nm) and Au (100 nm) fiber spacers on either side of the active area [see Fig. 2(b)]. The AR coating on the device chip was then selectively etched off of certain regions to expose the Au terminals. All the dielectric layers were etched away to expose the substrate on the outside of the Au terminal polygons [gray region in Fig. 2(b)], and a deep-RIE process was used to etch through the Si wafer substrate and release the detector dies in a keyhole pattern [30], ready for mounting and wirebonding.

 

Fig. 4. (a) Pulse shapes for SNSPDs of the three active area diameters. (b) The same over a longer time scale. (c) Pulse shapes for a 50 µm diameter SNSPD with and without ${R_s} = 450\,\Omega$ resistor in series with the $50\,\Omega$ coaxial readout lines. The shaded regions mark the variance.

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3. MEASUREMENT SETUP AND RESULTS

The devices were then mounted into the self-aligning fiber packaged mounts [30] and cooled inside a sorption-based cryostat to 720–780 mK. The bare ends of the fiber pigtails were accessible via a vacuum feedthrough and could be spliced to a photon source. The input state of light for SDE measurements is derived from a highly attenuated continuous-wave laser. The attenuated laser output passed through a polarization controller and was fed into a ${1 \times 2}$ optical switch, which can route light either to a monitoring power meter or the device under test. The full measurement setup and calibration method is detailed in Supplement 1, Section 1, and is nearly identical to those in [9,30,38].

The SNSPDs are quasi-current-biased using a bias tee, a $100\,\,{\rm k}\Omega$ series resistor, and a voltage source (see Supplement 1, Section 1). The RF-only port of the bias tee is connected to two room-temperature RF amplifiers. The output pulses are then either recorded on a sampling oscilloscope or conditioned into square pulses and sent to a pulse counter. The polarization optimization algorithm tries to vary all the settings on the polarization controller to either minimize or maximize the count rate (CR) from the SNSPD. As such, the reported maximum-polarization SDE value is at worst a conservative lower bound, and the reported minimum-polarization SDE value is an upper bound for the exact corresponding values. We do not attempt to correct for any fiber-splicing losses. A bad fiber splice to a detector pigtail will decrease the estimated SDE.

Figure 3 shows the bias voltage versus SDE plots for SNSPDs of three different active area diameters at the CR-maximized input polarizations. These devices are being read straight from the nanowires through $50\,\Omega$ impedance coaxial lines. The plots indicate a significant gain in SDE in the 35 µm diameter device over the 20 µm one, which is an effect of Gaussian-beam expansion of the fiber-exit mode now interferometrically trapped within a DBR-based vertical optical stack. The beam exiting an SMF-28e+ fiber has a mode-field diameter of under 10 µm, implying a Rayleigh range of 50 µm. Given how thin the nanowire layer is required to be, the photon in the optical mode is expected to pass through it ${\cal O}{(10^2})$ times before the probability of absorption approaches unity (see Supplement 1, Section 2). This, convolved with the larger effective round-trip length in the DBR-based optical stack [Fig. 2(a)], would favor larger active area nanowire devices for SDE.

The SDE curve, however, latches earlier for the larger SNSPD, and refuses to fully saturate. The problem is exacerbated for the 50 µm diameter SNSPDs. This is an effect of the increased RF pulse width in the larger devices (see Fig. 4) owing to larger kinetic inductances, resulting in a slight nonlinearity in sensitivity to successive events. The curves in Fig. 3 were all plotted at average CRs of ${10^5}$ counts per second within the expected saturation regions. Under no-light conditions, the dark-count profiles for all three device sizes extended to similar latching bias voltages of $0.49 - 0.52\;{\rm V} $.

 

Fig. 5. System detection efficiency (SDE) versus applied voltage bias at the count-rate maximized (max_pol) and minimized (min_pol) input polarizations for four 50 µm diameter devices (labeled A, B, C, and D) from the same wafer, with pulses read out with $450\,\Omega$ resistor in series with the $50\,\Omega$ coaxial lines.

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The exponential-recovery temporal widths of the RF pulses, which indicate detection events [Fig. 4(a)], are directly proportional to the ratio of the inductance of the SNSPDs to the impedance of the coaxial electrical lines, whereas the rise times are inversely related to the hotspot resistance. Over a longer timescale [see Fig. 4(b)], however, the pulses show a slow ringing effect, which is a reflection from the readout electronics due to impedance mismatch [24,44]. To reveal the true saturating SDE of our large-area SNSPDs, we needed to eliminate the undershoot/ringing in the RF pulses by modifying the readout electronics [45,46]. We achieved this by adding ${R_S} = 450\,\Omega$ thin-film resistors in series with the coaxial lines close to the SNSPD inside the cryostat, thus changing the recovery time constant at the expense of pulse height [see Fig. 4(c)].

With the speed-up series resistors in place, all the 50 µm wide circular active area SNSPDs now showed saturation in their bias voltage versus SDE curves. Figure 5 plots these for four different SNSPDs from the same wafer. The devices are color coded and labeled A, B, C, and D in the legend. Both CR-maximized and CR-minimized polarization optimizations are shown. The SDE saturates at a value of $98.0 \pm 0.5\%$, thus breaching the previous record [9].

4. CONCLUSION

We have demonstrated fiber-coupled SNSPDs with SDEs exceeding 98%, which to our knowledge is the highest value published thus far at near-infrared wavelengths. We relied on a DBR-based optical stack design, a well-established fiber-coupling mounting method, and a large active area to capture all of the diverging optical mode that exits the front face of the coupling fiber. We employed a series resistor to mitigate the impedance mismatch issues that plague the output RF pulse shapes for large-area devices. This proved to be a necessary electronic compensation for measuring the true SDE of the device.

The new SDE record restricts the theoretical loss of photons through mechanisms such as scattering, dielectric absorption, and stack fabrication errors with stricter upper bounds. The capability will further the use of fiber-coupled SNSPDs in increasingly elaborate quantum-optics setups and experiments that involve detection of rare events, such as multi-device coincident detections.