At the core of an ideal single-photon detector is an active material that absorbs and converts every incident photon to a discriminable signal. A large active material favours efficient absorption, but often at the expense of conversion efficiency, noise, speed and timing accuracy. In this work, short (8.5 μm long) and narrow (8 × 35 nm2) U-shaped NbTiN nanowires atop silicon-on-insulator waveguides are embedded in asymmetric nanobeam cavities that render them as near-perfect absorbers despite their small volume. At 2.05 K, when biased at 0.9 of the critical current, the resulting superconducting single-photon detectors achieve a near-unity on-chip quantum efficiency for ∼1,545 nm photons, an intrinsic dark count rate <0.1 Hz, a reset time of ∼7 ns, and a timing jitter of ∼55 ps full-width at half-maximum. Such ultracompact, high-performance detectors are essential for progress in integrated quantum optics.
Over the past decade, photonic quantum information processing1,2 has shown considerable promise for quantum computing3,4,5, communication6 and metrology7,8,9. Most of the impressive proof-of-principle demonstrations have relied on bulk optics2 that is inherently non scalable10. Independent progress on conventional integrated photonic circuitry11,12,13,14 suggests that integrated quantum photonic circuits10 may offer a scalable solution. A variety of pertinent host material systems15,16,17,18,19,20,21 are being studied, but the unparalleled recent progress in classical silicon-based photonic circuits12,22,23,24 makes silicon particularly attractive. Phase modulators and a wide assortment of ultracompact (tunable) passive components have been demonstrated in the silicon-on-insulator (SOI) platform25. Already some of these have been integrated26,27 with on-chip entangled and heralded photon sources28,29,30,31,32,33,34, single-photon detectors35, and used to demonstrate quantum interference and manipulation36,37.
All the optical components on a SOI platform—including the detectors—should operate at telecommunications compatible infrared wavelengths. Superconducting nanowire single-photon detectors (SNSPD)38,39 represent the most promising stand-alone infrared photon counting technology, and so it is not surprising that nanowires placed on top of optical waveguides have figured prominently in recent demonstrations of integrated single-photon detectors35,40,41,42,43,44. In the travelling wave (TW) configuration employed in these detectors, photons propagating down micron-wide waveguides are evanescently absorbed by a critically biased superconducting nanowire over a distance of tens of microns, and then an easily detectable normal-state transition in the nanowire occurs39. Various of TW SNSPDs have achieved high quantum efficiencies (up to 91% ref. 35), or low noise (down to <0.01 Hz45), or fast recovery time (<10 ns35), or accurate timing response (<20 ps of jitter35), but no single integrated detector in a fixed operation condition performs well in all of these critical categories. If truly scalable quantum information on-a-chip is to become practical, then detectors that excel in all of these individual performance metrics are needed.
The evanescent absorption in the TW geometry intrinsically puts a minimum on the coupling length of an efficient detector, and correspondingly, the length of the nanowire (typically between 40 and 400 μm35,41,42 depending on the nanowire layout and the host material system). A higher packing density of lower noise46, faster47,48 and more accurate detectors49 should be possible if the nanowire length could be further reduced. The obvious challenge is the apparent trade-off with absorption efficiency50 (shorter wires offer less absorbing volume).
This paper describes a successful strategy for circumventing this trade-off, by embedding a short (8.5 μm) ultranarrow (8 × 35 nm2) superconducting nanowire within a high-quality factor microcavity specifically designed to turn the overall detector into a near-perfect absorber of coherent radiation51,52,53. Implemented on a SOI platform, the detector’s ultrasmall footprint (0.5 × 7.0 μm2)—smaller than any reported to date—also incorporates a built-in optical filter. It absorbs and detects nearly all of the ∼1,545 nm light in the waveguide, exhibits a sub-Hz intrinsic dark count rate, has a fast recovery time of ∼7 ns, and shows a small timing jitter of ∼55 ps full-width at half-maximum (FWHM). The latter timing quantities are consistent with limitations imposed by the readout electronics, which have not been optimized. This ultracompact integrated detector therefore achieves a comprehensive set of metrics that are all either close to ideal or comparable to the best of class that have been reported using various implementations of infrared single-photon detectors.
In order for a short nanowire to absorb virtually every photon incident along a waveguide, it is placed within an asymmetric optical microcavity defined by etching a series of holes on either side of the nanowire (see scanning electron microscope images (SEM) in Fig. 1a,b). The cavity containing the weakly absorbing nanowire is designed to function as a coherent perfect absorber51,52,53. Figure 2a shows a model of the cavity. Ideally (ignoring all other losses), the reflectivity of the back mirror (right side) is unity, so all of the light incident from the left must be either absorbed or reflected. At the resonant frequency of the cavity, ωR, a portion of the light incident from the left excites a resonating cavity mode with amplitude A. The normalized power reflected back into the incident waveguide is then , and the power absorbed by the nanowire is 2|A|2/τA, where τr and τA are the time constants associated with the decay of A into the waveguide and the nanowire, respectively54. Power conservation in this idealized scenario requires , which in general determines how much of the incident light reflects, and how much is transferred into the cavity. However, if the left side mirror reflectivity is designed such that τr=τA, then all of the incident light is perfectly transferred to the cavity and absorbed.
In the ideal scenario above, an arbitrarily short nanowire (arbitrarily long τA) can absorb all of the incident radiation as long as the reflectivity of the input mirror can be precisely tuned close to 100% (that is, a very long τr). In practice, there will also be some additional scattering losses associated with the cavity, so its overall quality factor, Q will be given by , where QA=ωRτA/2, and Qr=ωRτr/2. The above analysis indicates that detectors with absorption efficiency ηA∼1, can be achieved using very short and narrow nanowires as long as dielectric reflectors can be designed such that QA=Qr<<Qscatt. The minimum nanowire length (LNW) is dictated by how tightly localized the high Qscatt cavity mode is, and therefore high-index contrast host materials like SOI are ideal. Finally, it is noted that this approach necessarily limits the bandwidth over which the detector absorbs efficiently, to ∼ωR/Q. However, for many quantum information processing applications, optical filters are placed in front of detectors to minimize spurious counts due to stray photons55,56. The near-perfect absorber detector design described here actually integrates the filter and detector into a single, compact unit.
The microcavity SNSPDs are formed by patterning holes in a silicon nanobeam (silicon on SiO2, 190-nm thick, 500-nm wide) to form an asymmetric cavity around a U-shaped nanowire (NbTiN, 8 nm thick, WNW wide) that lies on top of the nanobeam, as illustrated in Fig. 2a. Nanobeam cavities54,57 allow low-loss coupling to waveguides, high Qscatt, low mode volume and an accessible near field that are all useful features for microcavity SNSPDs. The back (perfect) reflector consists of 10 holes, 6 of fixed radius (Rm=100 nm) and 4 with shrinking radii, down to R1=50 nm, towards the input waveguide to impedance match the Bloch mode to the waveguide mode. The front (partial) reflector has Nr holes, all of which are linearly tapered from a maximum hole radius of Rr down to R1=50 nm on both sides. These one-dimensional photonic crystals54 were designed (see simulation Methods) to have a bandgap centered at 1,545 nm. To design the microcavity, Nr=14 and Rr=100 nm are fixed, and the cavity length (Lc) in the absence of the nanowire is adjusted to get a mode at the detector operation wavelength of 1,545 nm with a moderate Q=5.6 × 104. This ensures appropriate design of tapers and consequently a high enough Qscatt >5.6 × 104. When the nanowire is added to the same cavity, the mode profile and wavelength stay almost fixed, but the new Q≃QA(WNW) is substantially reduced, even for the smallest WNW=20 nm (see squares in Fig. 2b). Removing the nanowire and reducing Rr and Nr results in a new set of Q≃Qr(Rr, Nr), with values comparable to QA(WNW) (see circles on Fig. 2b). A nanowire with a certain WNW (for example, vertical dashed line in Fig. 2b) and thus fixed QA (horizontal dashed line) will absorb almost all incident coherent light if Nr and Rr are chosen such that Qr(Rr, Nr)=QA(WNW) (pink arrow in the same figure). Note that in this design algorithm, LNW is fixed by what is required for electrical connection through the back reflector (∼2 × 4 μm); this can in principle be further reduced by employing a better connection topology.
The fabricated microcavity SNSPDs have nominal parameters; WNW=35 nm, Nr=7, Rr=70 nm, , and LNW=8.5 μm. The distributions of electric field and power loss are as shown in Fig. 2c, for the structure excited with the mode of the strip waveguide at 1,545 nm. The field is tightly localized by the cavity, and the absorption is concentrated over a micron-length portion of the nanowire. At resonance, the calculated absorption peaks at 98.4%, while reflection, transmission and radiated losses are 0.04, 0.3 and 1.1%, respectively (see simulated spectrum shown in Fig. 2d). Analysing the variation of peak absorption with different fabrication imperfections (Supplementary Note 1, Supplementary Table 1) shows the structure is quite robust. Analysis of the radiation losses shows that 1% of the total 1.1% is lost to the substrate. Qscatt could therefore be further increased by undercutting the nanobeam, and the back-transmission could be further reduced by adding more holes. Applying both strategies, the losses would be reduced to ∼0.2% and the absorption could peak close to ∼99.8%. For comparison, the simulated absorption of the same 8.5 μm long nanowire, but without the cavity, is 29%; a 160 μm long nanowire would be needed to obtain 99.8% absorption in the absence of the cavity. The huge reduction of LNW without compromising absorption efficiency (ηA) promises fewer dark counts, and a more compact footprint for an efficient high-speed detector, as demonstrated and discussed below.
Figure 1c is a micrograph showing a portion of one of the fabricated chips. It consists of detectors with input waveguides connected to focusing grating couplers58 (GC) as well as gold electrical connections that are routed to large contact pads (not shown). Also included on the chip are devices with two GCs connected by a waveguide; these were used for alignment and calibration purposes. The chip was installed on, and wire-bonded to, a custom-made printed circuit board that hosts electronic circuits to apply bias, preamplify the detection signal and impedance match the detector to a 50 Ω coaxial cable that runs to room-temperature amplifiers and then to a counter (see schematics in Fig. 1). The board was installed in an optical cryostat (SVT-300, Janis Inc.) where it was submerged in superfluid helium (T=2.05 K). The whole-sample holder is surrounded by a cylindrical brass shield with two holes (S in Fig. 1) of 6 mm diameter coaxial with the two 45° windows (W in Fig. 1), one for the excitation laser light, and the other to image the chip for aligning and calibration. An attenuated and polarization-controlled continuous-wave tunable laser (TLB-6600, New Focus Inc.) was coupled to waveguides by focusing it on the input grating couplers. The setup was calibrated to read the rate of photons incident through the input cryostat window (RPh in Fig. 1) by the power meter D1 (see Supplementary Note 2 and Supplementary Fig. 1 for details).
Efficiency and dark count characterization
To measure the quantum efficiency and noise performance, three different count rates were determined (see Methods): photon count rate (PCR) measured when the input grating couplers were excited by the laser; background (mostly blackbody) count rate (BCR, also called system dark count rate) measured in the same conditions but with the laser off; and dark count rate (DCR, also called intrinsic dark count rate) measured when a cylindrical brass shield (50 μm thick) without any holes surrounded the sample holder. The BCR will exceed the DCR because the large cryostat windows—which were unshielded for PCR and BCR measurements—allow intense black body radiation to enter the cryostat. The quantum efficiency (QE=ηAηD, where ηD is the bias-dependent efficiency of converting absorbed photons to electric pulses) was deduced from the measured rates as (PCR−BCR)/(ηCRPh), where ηC is the efficiency of coupling the incident photons (RPh) into the strip waveguides.
Figure 3a shows the system quantum efficiency, QEηC, for several SNSPDs, all biased at a current equal to ∼0.9 of the experimentally determined critical current (IC). Triangles are for two microcavity SNSPDs, while squares are for a device with the same nanowire layout, but without any cavity holes, effectively a TW structure. In contrast with the TW device that exhibits a broad spectral response, the microcavity devices show a resonant response. Note that the off-resonant QEηC goes to negligibly small values compared with the peak (only 0.3% of the peak QEηC), confirming negligible contribution of non-guided photons to the peak PCR.
The overall system efficiency numbers reported in Fig. 3a are small mainly due to the low grating coupling efficiency, and waveguide propagation losses. A far more relevant metric for integrated quantum optics applications is QE, the efficiency of detecting waveguided photons that are incident on the partial reflector of the microcavity SNSPDs (or the bare nanowire in the case of the TW devices). Therefore, a measurement of ηC is needed to normalize the QEηC values reported in Fig. 3a to get the QE. As discussed in Methods: (i) ηC(λ) is determined up to a scaling constant, (asymptotic saturated value of ηD at high bias currents), by normalizing to the single-photon count rate from a reference TW SNSPD, (ii) ηC(λ) is fully determined using a detailed analysis of all the losses experienced by photons focused into the cryostat, before reaching the integrated SNSPDs. The final results are: (i) ηC(λ) shown by circles in Fig. 3a (the one s.d. uncertainty is ±8%); and (ii) for the reference TW SNSPD studied in this analysis, to one s.d. of uncertainty.
The on-chip QEs at ∼0.9IC shown in Fig. 3b (with the same symbol conventions of Fig. 3a) were thus obtained by dividing the respective curves in Fig. 3a by ηC. The QEs for the two microcavity SNSPDs peak close to unity (1.02±8% and 0.97±8%). The nominal peak QE for one of the microcavity devices exceeds unity, but values as low as 1.02−0.08=0.94 are also consistent with the one sigma statistical uncertainty associated with the measurements. The peak QEs for the microcavity devices at ∼0.9IC are consistent with ηA close to unity, as expected from simulations and further discussed below. Note that the QE for the device without the cavity stays flat and small, consistent with the broadband nature of both ηA and ηD59, and the relatively low ηA for this particular TW device that consists of a relatively short nanowire.
Shown on the same figure, with filled circles and a dashed line (best Lorentzian fit), is the simulated ηA for the designed microcavity detector. The spectral line shapes of the fabricated microcavity devices are close to the designed line shape, but blue shifted (the resonant wavelengths are 1,541 nm and 1,543 nm compared with target value of 1,545 nm.). This slight discrepancy is most likely due to the uncertainty associated with the physical dimensions of the waveguide used in the simulations, given the high sensitivity of the resonant wavelength on the geometry (for example, a 1 nm change in waveguide width results in a ∼1 nm shift in resonant frequency, as shown in the Supplementary Table 1).
In addition to wavelength, the quantum efficiency of a microcavity SNSPD is a function of bias current. Figure 3c shows the QE versus bias current at a fixed wavelength for the same devices with the same symbols. The bias current of ∼0.9IC used for each device reported in Fig. 3a,b is marked with a large square. The QEs of the two microcavity devices (triangles) measured at the resonant frequencies follow a single sigmoidal line shape (see solid red lines on the triangles). These QEs at ∼0.9IC are both ∼2% smaller than their respective saturation levels at 1.04 and 0.99. This suggests an ηD at ∼0.9IC as high as . As noted above, the calculated peak ηA is at most 0.984, so even for a microcavity SNSPD with an ideal , the highest possible QE at 0.9IC will be QE=ηAηD<∼0.984 × 0.98=∼0.96. This is consistently within the one s.d. uncertainty of the nominal values of the measured QEs.
The QE for an 8.5 μm long nanowire device without a cavity (squares on Fig. 3c) measured at 1,550 nm follows a more complex dependence on bias current, signalling the presence of a material or geometrical constriction in the nanowire (consistent with its smaller IC). Investigating the nanowires of this work under an SEM revealed the presence of an asymmetry in some of the fabricated nanowires: the two parallel branches that make a U-shape have slightly (approximately few nanometer) different widths. Therefore, a double sigmoidal curve (one sigmoid for each branch) possibly explains the response of such devices. The result of this fit is shown by a solid red line on the squares of Fig. 3c. The fitted sigmoid has a saturation at QE=0.27, close to the simulated ηA of 0.29. The electron-beam lithography step was identified as the cause of this width asymmetry, and reducing the pattern writing speed helped mitigate the effect. However, more experimental tuning is still needed to completely resolve the problem.
For comparison, a TW device with a simulated ηA of 0.90 was also fabricated using a relatively long nanowire (WNW=35 nm) length of 57.2 μm. The QE of this device (diamonds in Fig. 3c) changes considerably more gradually with the bias current than the microcavity structures; such that at ∼0.9IC the QE is 0.89 of its saturated level at ∼0.92. Therefore, compared with the microcavity devices with , the QE of this long nanowire device is reduced both because of the smaller ηA, and the relatively poor saturation behaviour of the ηD(IB).
The above relatively poor performance of the longer nanowire in the TW geometry most probably reflects the inevitable non-uniformities (both in geometry and superconducting material properties) along the nanowire. This can cause non-uniformity in the ηD(IB) values for photons absorbed by different sections of a nanowire carrying a fixed bias current of IB. The difference of the two detector structures is that in a microcavity device optical absorption is highly focused on a very short nanowire length (see power dissipation density plot of Fig. 2c), and therefore the QE(IB) depends on the ηD(IB) of a very short length of the nanowire. In contrast, the optical absorption in a TW device takes place over a much longer nanowire length, and therefore the QE(IB) is smoothed by averaging the ηD(IB) values over a longer length. The present hypothesis suggests another possible advantage of reducing LNW in microcavity detectors: it helps achieve high ηD in addition to high ηA, and therefore a high QE.
Quite apart from being efficient, a good detector must exhibit low noise. Figure 3d shows DCR and BCR measurements for the devices of Fig. 3c with the same symbols. The DCR starts from a plateau-like level at around 0.1 Hz followed by a fast exponential increase as expected for nanowire detectors. The plateau likely originates from black-body radiation that enters the cryostat from the top or even through the thin brass foil; it could be reduced by using better shields45,55. At ∼0.9IC the DCR for the non-cavity 57.2 μm long device is ∼1.1 Hz, whereas the DCR for the microcavity device is ∼0.1 Hz. This confirms another advantage of the microcavity design, in substantially reducing the DCR. Note that a microcavity SNSPD at ∼0.9IC (see vertical dashed line connecting Fig. 3c and Fig. 3d) maintains its high QE (1.02±8%) over a bias current range for which the DCR stays negligibly small (∼0.1 Hz); this represents an almost ideal detector performance. The BCR versus bias current curves show QE-like shapes which further suggests it originates from black-body or stray photons rather than being intrinsic to the detectors, like the DCR. This is in agreement with other studies that show how the BCR can be diminished by using well-shielded fibre-coupled cryostats and utilizing inline cold filters45,55.
Timing performance characterization
Figure 4a shows the electric pulse response of a microcavity SNSPD biased at IB=3.5 μA and excited by a continuous-wave laser. The root-mean-square of the electrical noise is σn=1.4mV, and the slope of the falling edge is K=51 mV ns−1. The pulse has a negative polarity to make it compatible with the counter, and shows an under-damped shape because of the frequency cut-offs of the chain of amplifiers (10 MHz to 1.2 GHz). The shape of the response pulse in this readout configuration can be significantly different from the temporal shape of the nanowire bias current, and therefore this setup does not allow a direct estimation of the reset time from the shape of the electrical response (as is traditionally used for estimating the speed of SNSPDs). Instead, the detector reset time is determined by measuring a time histogram of photon detection events conditioned to a detection event at t=0. As shown in Fig. 4b, the detection is restored in ∼7 ns after an initial detection event.
A schematic of the cryogenic electronic circuit can be seen in Fig. 1. An inductor, L=100 nH, is externally placed in series with the nanowire and the two are looking at an impedance of R=100 Ω. This roughly makes an electric time-constant of L/R∼1 ns. A reset time on the order of 5L/R∼5 ns, compatible with the measured value, should therefore be expected. Note a small IB keeps QE(IB) away from saturation (Fig. 3c), and therefore an easy comparison of the detector reset time and the electrical time constant is possible60. The external inductor was used in the measurement set-up to (i) avoid after pulses by allowing a smooth over-damped return of the bias current to the nanowire61, and (ii) ensure the stability and low noise performance of the microwave amplifier (LNA in Fig. 1) by keeping the impedance seen at its input port closer to the standard value of 50 Ω. However, this inductor can in principle be replaced with a more sophisticated readout circuit to further reduce the reset time to its intrinsic limit, which is known to scale with the nanowire length47,48,62.
One estimation of the electronic timing jitter in this setup at IB=3.5 μA is, from Fig. 4a, 2.355σn/K=65 ps FWHM. The total timing jitter was directly measured by inserting a microwave intensity modulator (APE of JDSU Inc.) fed by a picosecond pulse generator (Model 4016 of Picosecond Pulse Labs) between the tunable laser and the polarizer of Fig. 1. The resulting pulsed laser can source fast optical pulses at the peak detection wavelength of any microcavity detector on the chip. A wideband optical/electrical oscilloscope (DCA86100A of Agilent Technologies with Hewlett Packard 83485a plug-in module) synchronized to the electronic trigger output of the pulse generator was used to measure the profile of the optical pulse. The result is a 46 ps FWHM optical pulse (see solid cyan line in Fig. 4c) with a timing jitter better than a few picoseconds. With these optical pulses applied to a microcavity SNSPD, a total timing jitter measurement obtained using the same oscilloscope resulted in the blue histogram shown in Fig. 4c, with a ∼90 ps FWHM. Subtracting the additional jitter due to the finite width of the optical pulses from the measured total jitter yields FWHM as the measured jitter of the detector at IB=3.5 μA. This is close to the above 65 ps estimation of the electronic noise jitter. Convolving the profile of the optical pulse with a 65 ps FWHM Gaussian distribution results in the dashed red line of Fig. 4c which well describes the overall shape of the measured total jitter. Increasing the IB from 3.5 μA to 5.0 μA increased the slope of the falling edge to K=63mV ns−1, and reduced the total measured jitter to ∼72 ps FWHM. This gives a detector jitter of FWHM at IB=5.0 μA which is again close to the value of the electronic timing jitter of 2.355σn/K=53 ps FWHM. All these experiments and observations suggest a read-out noise limited performance of the timing jitter for the microcavity SNSPDs, consistent with reports on conventional SNSPDs with comparable bias currents60.
The energy stored in a microcavity cavity decays with a time constant τe=Q/ωR. This gives τe=0.23ps for the microcavity SNSPD designs reported here. Provided τe is much smaller than the minimum reported timing jitter for nanowire detectors (>∼15 ps), this cavity decay time constant should not have any adverse effect on the timing jitter of microcavity SNSPDs.
The demonstrated impact of cavity-based near-perfect absorption on the performance of a single-photon detector paves the way for integrating hundreds of ultrahigh performance detectors on a chip. The silicon host material facilitates high-performance microcavity SNSPDs because of its high index contrast, while also offering the potential of integrating on-chip electronic circuits with the detectors to further boost the performance, and to handle the complexity of scaling up the read-out circuits. This latter point is especially interesting in light of studies that show the compatibility of CMOS transistors with the cryogenic environment63,64. The speed performance of microcavity SNSPDs combined with their built-in filtered QE, and advanced fibre to waveguide-coupling methods65, will also make these detectors ideal for implementing fast quantum communication systems.
Frequency domain finite element solvers (COMSOL, Inc.) are used for numerical simulations. The index of refraction for silicon is set to 3.45 (measured close to 1,550 nm at cryogenic temperatures66), and the environment is assumed to be superfluid helium (n=1.03). The index of refraction for NbTiN is set to 4.17+i5.62 (ref. 67). Eigenmode analysis is used for all Q factor simulations, while the simulated spectra are obtained by using available numeric port boundary conditions.
The devices were fabricated on NbTiN-coated (8 nm thick—STAR Cryoelectronics Inc.) SOI wafers with a silicon device layer thickness of 200 nm and a buried oxide thickness of 1,220 nm. The superconducting thin film has a critical temperature TC=7.16 K, and critical current density JC(T=0)=7.57 × 106A cm−2 (see Supplementary Note 3 and Supplementary Fig. 2 for details). Positive electron-beam (e-beam) resist (ZEP520A from ZEON Corp.) was spin-coated at 1,800 r.p.m. and hot-plate backed at 180 °C for 3 min to make a 600 nm thick film. Contact pads and the first set of alignments marks were defined in a 25 KeV e-beam lithography machine (dose 110 μC cm−2) and developed in o-xylene at 20 °C for 60 s followed by a 30 s soak in isopropyl alcohol (IPA) and a deionized water rinse. The chip was rinsed in 140:1 BHF:H2O for 60 s to wet-etch ∼1 nm of NbTiN surface oxides, and was immediately transferred to an e-beam evaporator chamber to deposit an 8 nm/90 nm titanium-gold bilayer, followed by lift-off in sonicated chlorobenzene. The chip was coated again by 600 nm thick ZEP520A, after which the photonic structures and a second set of alignments marks were e-beam written using the original gold alignment marks at 140 μC cm−2. The sample was then developed in cold o-xylene (4 °C—to improve contrast68). Reactive ion etching (RIE) in 15:2 CF4:O2 30 s and 15:1 CF4:O2 ∼300 s was used to vertically etch through the entire thickness of unprotected NbTiN and silicon to yield the NbTiN-coated photonic structures. Spin-coating of 1:1 Anosole:ZEP520A at 2,800 r.p.m. and the same baking conditions were used to coat 180 nm of resist on flat areas and 110 nm on waveguides that are surrounded by relatively deep trenches. The second set of alignment marks were uncovered by e-beam lithography and development to allow sharp imaging of the marks for the last lithography step. The nanowires were written using these uncovered marks at 78 mC cm−2 for which ZEP520A acts as a negative resist69. All of the resist except the area exposed by the high-dose e-beam was removed by 5 min exposure to ultraviolet radiation (λ=320 nm, ∼3 W cm−2) and a 1 min rinse in chlorobenzene. A final RIE in 15:2 CF4:O2 for ∼40 s was used to etch the unprotected NbTiN and 10 nm of silicon. SEM images of several samples indicates this process yields better than ±20 nm alignment of the nanowires with the nanobeam cavities. Four of the reported results in Fig. 3 were obtained from a larger set of 10 devices on a chip, six of which did not work because the measured IC was too small.
It is relatively difficult to directly measure ηC—the coupling efficiency between the photons incident on the cryostat windows at room temperature and the strip waveguide—as there is no direct means of accessing the strip waveguide inside the cryostat. The Supplementary Information (referenced below) provides a detailed explanation of how ηC was laboriously determined by quantifying losses associated with all of the elements between the laser source and the detectors. Another relatively simple method for accurately determining ηC is described here. It makes use of several reference structures to calibrate the microcavity devices to within a scaling constant.
The first set of test devices are laid out as two grating couplers connected with a long waveguide (Fig. 1c) that has a U-shaped nanowire on top (the same nanowire geometry as the TW SNSPD devices presented, but without contacts). Seven of these devices with nanowire lengths (LNW) from 0 to 60 μm were made and their transmission (T) measured (see Supplementary Note 4 and Supplementary Fig. 3 for full details). A linear fit to log(T/T(LNW=0)) versus LNW yields ηA versus LNW for devices without cavities. At LNW=57.2 μm the measured ηA=0.928, and the best linear fit gives 0.917, both in good agreement with the designed ηA of 0.90. The results also indicate that the ηA is almost wavelength independent within the relatively narrow spectrum of interest.
Next, the QEηC=(PCR−BCR)/RPh at 1,550 nm for the 57.2-μm long TW SNSPD versus bias current is measured (scaled version of diamonds in Fig. 3c). Using the best sigmoidal fit to the measured points, the maximum saturated QEηC and QEηC at 0.9IC were determined and divided to yield , where is the saturated ηD of the 57.2 μm device at 1,550 nm. Measuring QEηC versus wavelength at 0.9IC, equating it to ηAηD(λ,0.9IC)ηC=0.917ηD(λ,0.9IC)ηC, and multiplying both sides by the constant ηDsat/ηD(1,550 nm,0.9IC)=0.89−1, yields . Given the very small range of wavelengths relevant to the data of Fig. 3, and the results of other studies on SNSPDs that use ultranarrow nanowires59, ηD(λ, 0.9IC)/ηD(1,550 nm, 0.9IC)≃1 is expected. Therefore, the present analysis yields which accurately describes the total profile of ηC(λ) within the scaling constant, .
The nice feature of the above procedure is that it almost completely describes ηC(λ) without need for detailed analysis of the elements that contribute to ηC(λ) (for example losses of cryostat windows, grating couplers, waveguides and so on). However, the value of , which is essential in determining of the absolute value of on-chip QEs, cannot be directly measured using this calibration method. For this reason, a detailed approach that gives ηC(λ) and its uncertainty by determining the efficiency of each contributing element is reported in the Supplementary Note 5 and Supplementary Figs 4–11. The final result in Supplementary Fig. 11 shows ηC(λ) (red and dashed lines). As can be seen, the detailed approach gives ηC with ±8% of uncertainty (corresponding to one s.d.) relative to the mean value for wavelengths close to 1,550 nm. This uncertainty is dominantly determined by the sample to sample variation of the efficiency of the grating couplers (Supplementary Fig. 8).
The independently determined as described above is also shown in Supplementary Fig. 11 (blue dots). Note that follows the same spectral shape as ηC(λ). This validates the assumption that ηD(λ,0.9IC) is independent of wavelength over the small range of relevant wavelengths. That is ηD(λ, 0.9IC)/ηD(1,550 nm, 0.9IC)≃1, as otherwise, would have had a different spectral shape. Also note that almost perfectly overlaps the nominal result for the measured ηC, especially for wavelengths close to 1,545 nm (that is, the important wavelength of the peak QE for microcavity SNSPDs in which ηC is determined with its minimum variation of ±8%). This coincidence of the directly measured ηC, and the obtained using the calibration technique described above, implies that ( to one s.d. of uncertainty). The close to unity is in agreement with other studies on SNSPDs that exhibit a saturated QE(IB) response60,70.
Finally, the above results provide two essentially identical sets of data that could be used for normalizing the QEηC to QE: one is the mean ηC(λ)±8%, and the other is with . As the data for is less noisy (smoother and less Fabry–Perot like shapes) than that associated with the other more involved determination of ηC (compare the two on Supplementary Fig. 11), the later set (shown by blue circles in Fig. 3a) is used as the mean ηC throughout the paper. The consistency of measurement and simulation results (for example, high-quality fit of the resonant response to a single Lorentzian line shape in Fig. 3b, the almost flat response of the TW SNSPD in the same figure, and the saturated levels of Fig. 3c at levels expected from simulations) further confirms the validity of this ηC.
Measuring count rates
The count rates (CR) are by definition the number of counts registered by a counter per unit time during which the detector and all the readout electronics are active. Because the counter used in the set-up (PicoHarp 300, PicoQuant Inc.), has a dead time (TDT) of 87 ns, in all of the CR measurements reported here, the effect of TDT was included by defining CR=CRm/(1−CRmTDT), where CRm is simply the number of counts divided by counting time. The linearity of CR with RPh confirms that the measured CRs are neither affected by TDT or by detector nonlinearities.
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We gratefully acknowledge financial support from the Canadian Institute of Advanced Research, and the Natural Sciences and Engineering Research Council, including the Silicon Electronic-Photonic Integrated Circuits (Si-EPIC) CREATE Program.
The authors declare no competing financial interests.
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Akhlaghi, M., Schelew, E. & Young, J. Waveguide integrated superconducting single-photon detectors implemented as near-perfect absorbers of coherent radiation. Nat Commun 6, 8233 (2015). https://doi.org/10.1038/ncomms9233
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