Superconducting nanowire single-photon detector with integrated impedance-matching taper

Superconducting nanowire single-photon detectors (SNSPDs) are the leading single-photon detection technology at infrared wavelengths.^1,2 With exceptional performance,^3–7 they have played essential roles in various applications, especially quantum information science^8,9 and deep-space optical communication.¹⁰ 

A common problem with SNSPDs is their low output voltage and signal-to-noise ratio (SNR), which has been a limiting factor in detector timing jitter.¹¹ A simple lumped-circuit model dictates that the output voltage from the nanowire cannot exceed I_B × Z_load, where I_B is the bias current and Z_load is the load impedance.¹² I_B is usually limited by the nanowire's switching current in the μA range. It can be increased by connecting multiple wires in parallel and utilizing the cascade switchings among them.^13,14 Z_load is set by the input impedance of the coaxial cable and r.f. electronics, which is conventionally 50 Ω. To improve readout SNR, significant progress has been made in developing cryogenic amplifiers with low noise, dissipation, and cost, e.g., using silicon germanium and gallium arsenide transistors.^15–18 Digital readout circuits built directly from superconducting electronics, such as nanocryotrons¹⁹ and single flux quantum (SFQ) circuits,^20,21 have also been demonstrated. These integrated superconducting circuits have low noise and are scalable but usually require additional biasing and suffer from leakage current and crosstalk.

An alternative approach to increase the output signal is to increase Z_load. Compared to a standard 50 Ω load, a high-impedance load is often more desirable—it not only increases the detector output but also enables direct mapping of hotspot resistance and photon number/energy resolution.^22–24 However, high-impedance loading is difficult to achieve in practice. The lack of high-impedance coaxial cables makes it necessary to place the high-impedance amplifiers close to the detectors (at the low-temperature stage), which imposes a more stringent power budget. More importantly, even if a high-impedance amplifier is available,¹⁷ loading a standard SNSPD directly with high impedance can lead to latching.¹² 

In this work, without the need of high-impedance cryogenic amplifiers or any active circuit elements, we break the I_B × 50 Ω limit by using an integrated superconducting transmission line taper. The taper gradually transforms its characteristic impedance from kΩ to 50 Ω, which effectively loads the SNSPD with a kΩ impedance without latching. We designed the taper to be a co-planar waveguide (CPW) and fabricated it from the same superconducting thin film as the SNSPD. Using a taper with a starting width of 500 nm and a nominal passband from 200 MHz (the taper is a high-pass filter), we experimentally observed 3.6× higher output voltage and no added noise compared to the non-tapered reference device. This voltage gain is equivalent to an 11 dB passive, dissipation-free cryogenic amplifier. The large inductance of the taper reduces the detector's maximum counting rate from 40.3 MHz to 9.1 MHz (estimated from reset time) but does not slow down its fast rising edge, resulting in an increased slew rate and reduced timing jitter (from 48.9 ps to 23.8 ps). The integrated impedance taper demonstrated here is useful for interfacing high-impedance nanowire-based devices to conventional low-impedance components, such as memory and electrical or optical modulators.

Figure 1(a) shows a circuit model of a conventional SNSPD readout circuit, where the detector is modeled as a kinetic inductor L_K in series with a time-dependent variable resistor R_N. When an incident photon triggers the detector, R_N switches from 0 to ≈kΩ within ≈100 s of ps and diverts the bias current to the load. The evolution of R_N is determined by the non-linear electrothermal feedback in the detector.^12,25 The currents from the bias source (I_B), in the nanowire (I_D), and to the load (I_L) simply follow Kirchhoff's law I_L = I_B − I_D. The maximum I_L is therefore limited to I_B, corresponding to the case where R_N pushes all the current out of the nanowire (I_D = 0). The output voltage on the load thus cannot exceed I_B × 50 Ω. In practice, due to the electro-thermal feedback,¹² I_D usually has some remainder, which depends on the bias current, kinetic inductance, and thermal constants of the materials.

Figure 1(b) shows a simplified circuit diagram for the tapered readout. The taper is inserted between the SNSPD and the load, with a low impedance of Z_L = 50 Ω on the load end and a high impedance of Z_H on the detector end. In our implementation, the taper consists of a continuous nanowire transmission line without any dissipative elements. The taper is high-pass—it works as a transformer at high frequency but acts as an inductor at low frequency. When an incident photon triggers the SNSPD, R_N switches on and pushes the current away from the nanowire. Instead of diverting the current directly to the 50 Ω load as in the conventional readout, the SNSPD injects current to the taper at Z_H. As the electrical pulse travels towards the low impedance end, its current amplitude increases while the voltage amplitude drops, with a ratio that satisfies the change of impedance [Fig. 1(c)]. Assuming an ideal broadband transformer with perfect impedance matching and power transmission, the current leaving the low-impedance end (to the load) ΔI_DL is related to the current injected to the high-impedance end ΔI_DH by $ΔIDL2ZL=ΔIDH2ZH$⁠. In our transmission line taper, this relation is valid only at high frequency (passband of the taper), which dominates the rising edge of the detector pulse. In the extreme case where the SNSPD pushes all the bias current out, i.e., ΔI_DH = I_B, the current diverted to the load can be as large as $IL=ΔIDL=IBZHZL$⁠, corresponding to an output voltage of $VLtaper=IB×50 ΩZHZL$ and an effective voltage gain of $ZHZL$ with respect to the conventional readout. In practice, when terminated with the high-impedance taper, the SNSPD latches, leaving the residual current at the hotspot current I_ss, and then resets through reflection from the taper. As we will show later, the actual voltage gain is always less than $ZHZL$ due to the electro-thermal feedback and the limited taper bandwidth.

Figure 1(d) shows an optical micrograph of a fabricated SNSPD with a meandered transmission-line taper. The bright area is NbN, and the violet area is the substrate, where the NbN was etched away. The NbN was sputtered at room temperature on a silicon substrate with a 300 nm thick thermal oxide layer.²⁶ The film had a critical temperature of 8.1 K and a room-temperature sheet resistance of 342 Ω/sq. The sheet inductance was estimated to be 80 pH/sq by fitting the falling edge of the output pulse from a reference detector. The nanowire fabrication process is described in Refs. 4 and 27. The taper was made from a CPW with a fixed gap size of 3 μm and a varying center conductor width from 135 μm (50 Ω) to 500 nm (1.7 kΩ; see Fig. S1). Transmission lines made from thin-film superconductors operate in the kinetic-inductive limit and have been studied previously.^28,29 The taper's left/wide end was wire bonded to an external circuit board, and the right/narrow end was connected to the SNSPD through a 1 μm-long hyperbolic taper. The short hyperbolic taper is not for r.f. impedance matching, but to allow width transition without causing d.c. current crowding. The SNSPD was 100 nm wide, densely packed with a 50% fill factor and spanned a rectangular area of 11 μm × 10 μm [see Fig. 1(e)]. A 200 nm gap surrounded the detector region to reduce the proximity effect in fabrication. On the same chip, we also fabricated non-tapered detectors as references.

The taper was designed to be a 5672-section cascaded transformer with a lower cut-off frequency of 200 MHz and a total electrical length of 851 mm, following the Klopfenstein taper profile.³⁰ The physical length was 77.9 mm due to the slow phase velocity of the superconducting transmission line, and the total inductance was 1.410 μH (see Fig. S2 for the simulated S parameters). This length was chosen so that the maximum reflection in the passband (≥200 MHz) would not exceed −20 dB. The total electrical length is calculated as l_e = Ac/2πf_co, where f_co is the nominal cut-off frequency and c is the speed of light in vacuum. A is a factor that determines the maximum reflection in the passband and is calculated as $cosh(A)=ρ0/ρpb$⁠, where ρ₀ is the initial reflection coefficient (i.e., without taper) and ρ_pb is the maximum passband reflection coefficient (taken to be 0.1 here). For design convenience, we followed Klopfenstein's original approach and took ρ₀ = 0.5ln(Z_H/Z_L) instead of (Z_H − Z_L)/(Z_H + Z_L).³⁰ 

The detectors were operated at 1.3 K in a closed-cycle cryostat. Both the bias circuit and the readout electronics were at room temperature. The output signal of the detectors was amplified using a 2.5 GHz, 25 dB gain low-noise amplifier (RF BAY LNA-2500), and a 3 dB attenuator was inserted before the amplifier to reduce reflection and prevent latching. The output pulses from the amplifier were then acquired using a 6 GHz real-time oscilloscope (Lecroy 760Zi). In fact, the output of the tapered SNSPD is large enough to operate without amplifiers. However, adding a room-temperature amplifier increases the SNR and reduces the timing jitter. The detector chip was flood illuminated using attenuated sub-ps pulsed lasers at 1550 nm (FPL-02CCF) through an optical fiber (SMF-28e). The laser pulses were split into two arms, one to a variable attenuator then to the cryostat and the other to a fast photodiode (Thorlabs DET08CFC) as timing references. Since the distance between the non-tapered detector and the tapered detector (≈5 mm) was much less than the distance between the detector chip and the fiber tip (≈10 cm), we expect the difference in photon arrival time to be <1 ps. Both the tapered and non-tapered detectors had a switching current of 30 μA and were biased at 27.5 μA throughout the measurement.

Figure 2(a) shows the measured pulse shapes from the reference and tapered detectors. The amplifier gain was removed to better compare with simulations. To avoid phase distortion in reconstructing the unamplified pulses, we used a weighted gain, $G¯=∫dfPSD(f)G(f)/∫dfPSD(f)$⁠, where PSD(f) is the power spectral density of the pulse, and G(f) is the measured system gain spectrum (see Figs. S3 and S4). $G¯$ was calculated to be 20.5 dB. As shown in Fig. 2(a), we observed a voltage gain of 3.6 and a delay of 2.8 ns from the tapered device compared to the reference device (by aligning the electrical pulses to the optical references). This voltage enhancement is equivalent to a passive, excessive-noise-free 11 dB amplifier.

We simulated the tapered detector using a SPICE model that incorporates both the hotspot dynamics in the SNSPD and the distributed nature of the transmission line taper.^31,32 The simulation was implemented in LTspice, a free electrical circuit modeling software. The SPICE model for SNSPD was developed by Berggren et al.³¹ based on the phenomenological hotspot velocity model by Kerman et al.¹² The taper was simulated as cascaded lossless transmission lines (down-sampled to 300 sections),³² and each section was implemented using the Lossy Transmission Line Model (LTRA) in LTspice with different length, inductance, and capacitance settings.

Figure 2(b) plots the simulated load voltages, showing a voltage gain of 3.5 and a delay of 2.8 ns, as compared to the measured gain of 3.6 and delay of 2.8 ns. The subsequent peaks in the output voltage are spaced by ≈4.2 ns, which should correspond to the round trip time in the taper. The single-trip delay of the taper calculated from the reflection peaks (2.1 ns) is shorter than the delay between the tapered detector and the reference detector (2.82 ns) because the hotspot grows for a longer period of time and to a larger resistance in the tapered detector, as can be seen in the simulated currents.

Figure 2(c) shows the simulated currents. For the tapered detector, the current in the nanowire (I_DH) first drops at a similar rate as the non-tapered case (I_D) and then enters a intermediate plateau due to latching.¹² Similar current plateau and latching behaviors are often observed when loading an SNSPD with a kΩ resistor. However, at ≈4.6 ns, I_DL drops again and kicks the detector out of the latching state. The drop in current is from the reflection in the transmission line taper. Alternatively, it can be interpreted as the distributed capacitors in the transmission line drawing current from the SNSPD. After a few oscillations (high frequency), the current in the detector recovers with a τ = L/R exponential time constant (low frequency). Here, L is the total inductance of the SNSPD and the taper (at low frequency, the taper behaves as an inductor), and R is 50 Ω. The simulated currents at the high- and low-impedance ends of the taper roughly follow our intuitive understanding of how a transformer works. I_DH drops from the original bias current 27.5 μA to ≈4.6 μA at the plateau (ΔI_DH = −22.9 μA), while I_DL drops from 27.5 μA to −54.7 μA (ΔI_DL = −81.5 μA), giving ΔI_DL/Δ_DH ≈ 3.6. This is 39% less than the theoretical limit for a matched source and ideal transformer (⁠$1.7 kΩ/50 Ω=5.8$⁠), due to the complex electrothermal feedback and finite taper bandwidth. In this particular detector and taper design, the maximum counting rate (estimated as 1/3τ) decreases from 40.3 MHz (L = 414 nH) for the non-tapered detector to 9.1 MHz (L = 1.824 μH) for the tapered detector. We would like to point out that the added inductance and consequently the slower maximum counting rate are currently the major drawbacks of the tapered readout and may limit its usage for certain applications, such as high-data-rate communication. A study of the trade-off between the gain factor and taper inductance based on current CPW design can be found in Fig. S8 in the supplementary material. To reduce the taper inductance, one may use microstrip or CPWs with smaller gaps or with additional top/bottom ground. With larger distributed capacitances, these transmission lines will have shorter effective wavelengths, and the tapers will thus have smaller inductances.

The impedance taper amplifies the output pulse without sacrificing the fast rising edge, resulting in a faster slew rate. Figure 3(a) compares the averaged rising edges of the detector pulses from the reference and tapered detectors (with the amplifier gain). The sampling rate was 40 GS/s. As shown in Fig. 3(b), the maximum slew rates (dV/dt) were 39 μV/ps for the reference detector, but 143 μV/ps (3.7 times faster) for the tapered detector.

The slew rate directly impacts the electrical noise contribution to the timing jitter, usually referred to as noise jitter, σ_noise.^11,33 We sampled the background electrical noise on the oscilloscope for both detectors by measuring the voltage at 400 ps before the rising edge of the pulses. The noise followed a Gaussian distribution and had standard deviations of 559 μV and 547 μV for the reference and tapered detector, respectively (see Fig. S5). Taking their respective fastest slew rates, we calculated that the reference detector would have a standard deviation σ_noise of 14.3 ps and the tapered detector would have a σ_noise value of 3.8 ps.

We measured the jitter of the detectors following the procedure described in Ref. 34. The discrimination levels for time tagging were set to voltages with the fastest slew rates. Figure 3(c) shows the instrument response function (IRF) of the reference and tapered detectors at an illumination wavelength of 1550 nm. With the impedance taper, the full-width half-maximum (FWHM) jitter reduced from 48.9 ps to 23.8 ps. We fitted the IRF using an exponentially modified Gaussian distribution⁴ and found σ = 16.8 ps and 1/λ = 17.4 ps for the reference detector and σ = 6.5 ps and 1/λ = 13.6 ps for the tapered detector. Here, σ is the standard deviation of the normal distribution and λ is the exponential decay rate. The detectors showed similar jitter reduction at 1064 nm, where both detectors operated on the saturation plateau (see Fig. S6). The FWHM jitter reduced from 47.0 ps (σ = 16.4 ps, 1/λ = 15.9 ps) to 22.4 ps (σ = 6.2 ps, 1/λ = 12.5 ps). We observed a leading edge tail in IRF for the tapered detector. It is likely due to the counting events from the taper or the transition region between the taper and the detector. This effect could be reduced if the optical mode is focused in the center of the detector active area, through self-aligned fiber coupling or focusing lenses.^35,36

As a final remark, we have treated the SNSPD as a lumped element in this paper because the nanowire was closely meandered and had a dispersion similar to an ideal inductor at the frequency of interest.³⁷ Despite this choice, multi-photon absorption would generate a different hotspot resistance compared to the single-photon events.^22,38 The impedance taper provides an effective kΩ load and may thus allow direct discrimination of hotspot resistance and hence photon numbers. In another scheme, where the nanowire is sparse or designed to a transmission line,³² the taper provides impedance-matched readout and has been used to resolve the photon location and photon numbers.^27,39 We expect the integrated taper to become a widely used tool for matching high-impedance nanowire-based devices to low-impedance systems.

See supplementary material for more information on the taper design, device measurement, and discussion on trade-off between the gain factor and taper inductance.

Part of this work was performed at the Jet Propulsion Laboratory, California Institute of Technology, under Contract with the National Aeronautics and Space Administration. Support for this work was provided in part by the JPL Strategic University Research Partnerships program, DARPA Defense Sciences Office through the DETECT program, and National Science Foundation under Contract Nos. ECCS-1509486 (MIT) and ECCS-1509253 (UNF). D.Z. is supported by the National Science Scholarship from A*STAR, Singapore.