Integrated-photonic characterization of single-photon detectors for use in neuromorphic synapses
Sonia M. Buckley, Alexander N. Tait, Jeffrey Chiles, Adam N. McCaughan, Saeed Khan, Richard P. Mirin, Sae Woo Nam, Jeffrey M. Shainline
IIntegrated-photonic characterization of single-photon detectors for use inneuromorphic synapses
Sonia M. Buckley, ∗ Alexander N. Tait, Jeffrey Chiles, Adam N. McCaughan,Saeed Khan, Richard P. Mirin, Sae Woo Nam, and Jeffrey M. Shainline
National Institute of Standards and Technology, 325 Broadway, Boulder CO 80305 (Dated: June 16, 2020)We show several techniques for using integrated-photonic waveguide structures to simultaneouslycharacterize multiple waveguide-integrated superconducting-nanowire detectors with a single fiberinput. The first set of structures allows direct comparison of detector performance of waveguide-integrated detectors with various widths and lengths. The second type of demonstrated integrated-photonic structure allows us to achieve detection with a high dynamic range. This device allows asmall number of detectors to count photons across many orders of magnitude in count rate. However,we find a stray light floor of -30 dB limits the dynamic range to three orders of magnitude. To assessthe utility of the detectors for use in synapses in spiking neural systems, we measured the responsewith average incident photon numbers ranging from less than 10 − to greater than 10. The detectorresponse is identical across this entire range, indicating that synaptic responses based on thesedetectors will be independent of the number of incident photons in a communication pulse. Sucha binary response is ideal for communication in neural systems. We further demonstrate that theresponse has a linear dependence of output current pulse height on bias current with up to a factor of1.7 tunability in pulse height. Throughout the work, we compare room-temperature measurementsto cryogenic measurements. The agreement indicates room-temperature measurements can be usedto determine important properties of the detectors. PACS numbers: 07.20.Mc, 42.79.Gn, 07.05.Mh, 85.25.j
I. INTRODUCTION
Superconducting-nanowire single-photon detectors(SNSPDs) have proven their utility in a number ofscientific and technological applications, including fun-damental tests of quantum mechanics [1, 2], quantuminformation processing [3], quantum [4] and classical[5–7] communication and high-energy physics experi-ments [8]. Large-scale spiking neural networks havealso been designed based on SNSPDs as receiver el-ements for photonic communication between neuronsand synapses [9–12]. SNSPDs are attractive for theseapplications due to their high detection efficiency, lowpower consumption, and ease of fabrication. In thecases of quantum and neural information processing,several system architectures are being pursued based onSNSPDs integrated with on-chip photonic structures.In these systems, SNSPDs are fabricated directly ontop of photonic waveguides and strongly absorb lightin the waveguide modes. The integration of SNSPDswith photonic structures leads to many opportunities forhighly functional systems in which photonic devices cangenerate, control, and route light, with detection beingperformed at the single-photon level.The system demands and design requirements ofwaveguide-integrated SNSPDs depend on the applicationbeing pursued. For quantum information applications,extremely high detection efficiency is paramount, whiledetector area may be less of a concern. By contrast, for ∗ [email protected] densely interconnected neural systems, area and powerefficiency are primary considerations. Interaction of lightin the waveguide with the detector leads to an attenua-tion length, leading to a trade off between area and de-tection efficiency. Similarly, the energy of a photon de-tection event is given by LI /
2, where L is the SNSPDinductance (proportional to length) and I is the bias cur-rent (proportional to wire width). Thus, smaller wiresare more energy efficient, but less absorptive, and pro-vide a lower current signal level. A system designer mustconsider these trade offs when choosing the parametersspecifying an SNSPD for a certain application.On the experimental side, it is necessary to character-ize the performance of SNSPDs in the context in whichthey will be utilized. We demonstrate several photonicstructures that facilitate the assessment of waveguide-integrated SNSPDs. We use branching trees of waveg-uides and beamsplitters to assess the absorption of thedetectors as a function of wire length and width. Mach-Zehnder interferometers are used to bound the splittingratio of the beamsplitters, providing confidence that alldetectors in a tree are receiving nearly equal numbers ofphotons. With these structures, we can use a single fiberinput to simultaneously characterize multiple detectors(up to fifteen in this work) to determine absorption anddetection efficiency properties as a function of nanowirelength and width. Such structures can also assess thefabrication yield. Apart from a layout error, 100% oftested detectors worked. As is typical, there was somevariation in critical currents and dark count rates due tofabrication imperfections.In addition to waveguide trees, we also explore a re- a r X i v : . [ phy s i c s . i n s - d e t ] J un lated device based on beamsplitters with an uneven split-ting ratio. At each splitter in this structure, the majorityof light is dropped to a detector, while a small fractioncontinues to the next stage. Such a structure provideshigh dynamic range, as the first detector in the struc-ture is sensitive at the single-photon level, while the finaldetector provides information about much higher lightlevels. Structures with between 40 dB and 120 dB of dy-namic range were designed. However, due to scatteredlight on the chip, the noise floor of -30 dB limits the util-ity of such a structure. This experiment reveals the sig-nificance of stray light that will affect any technology uti-lizing many light sources and detectors on a single chip.The stray light problem can be addressed by shieldingeach detector with opaque materials, allowing only thesingle port of a waveguide to couple to the detector. Ad-ditional metal layers have been shown to reduce the straylight to around 60 dB below the pump signal [13], and in-tegration of a metal layer below the detector can likelyreduce it to tolerable levels.We also directly measure two properties of SNSPDsrelevant to their use in synaptic circuits in spiking neu-ral systems. While for many applications in quantuminformation it would be advantageous if SNSPDs coulddetermine the number of photons present in an incidentpulse, for the spiking neuromorphic application the op-posite is desired. In such systems, it is important thatcommunication is binary so that noise on a neuron’s lightsource and stochasticity in the number of photons in acommunication pulse do not contribute to noise at thesynapse. For this purpose, we would like the response ofthe detector to be independent of the number of pho-tons being received. We measured the response of awaveguide-integrated SNSPD to pulses with average pho-ton numbers ranging from less than 10 − photons perpulse up to greater than 10 photons per pulse. We findthe response is identical across the entire range, confirm-ing that these detectors are ideal for binary detection ofsynapse-events. Furthermore, the wavelength of opera-tion of the sources used in the proposed superconductingspiking neural systems operate around 1.22 µ m [9, 14].Therefore, we design all devices for operation at boththe standard 1.55 µ m wavelength used for telecommuni-cations and most quantum optics experiments, as wellas 1.22 µ m. Finally, we explore the use of variation inSNSPD bias current across the detector plateau regionas a means of establishing a synaptic weight. We findthat variation by a factor of 1.7 can be achieved with theSNSPDs studied here. This functionality is unique tomaterials with a broad detection plateau. While synap-tic circuits combining SNSPDs with Josephson junctionshave been proposed that give an order of magnitude moredynamic range in synaptic weight and enable unsuper-vised learning techniques [11, 12], the technique of vary-ing the SNSPD bias current may be useful for supervisedlearning in a simpler fabrication process without Joseph-son junctions [15].Throughout the paper, we compare the cryogenic measurements of detector response to room-temperatureabsorption measurements using similar branching treestructures. The room-temperature and cryogenic ab-sorption measurements are compared to theoretical mod-els, and satisfactory agreement is found. We use thesemeasurements to quantify the difference in the nanowirematerial absorption between room temperature and 1 K.These comparisons indicate that future work can arriveat final designs with the support of room temperatureoptical characterization and minimal cryogenic testing. II. INTEGRATED PHOTONICCHARACTERIZATION OF SINGLE-PHOTONDETECTORS
Room-temperature and cryogenic measurements weremade on devices comprising both integrated photonicand superconducting nanowire components. For cryo-genic measurements, detector samples were wire-bondedand fiber-packaged by the method described in [16]. Thepackaged samples were then cooled to 800 mK in a closedcycle sorption pump He cryostat. Detectors were DC bi-ased and measured through AC-coupled amplifiers. Lightcould either be coupled onto the chip via the packagedfibers, or via a separate fiber that flooded the entire chipuniformly with light. Fabrication details, as well as pas-sive photonic component design and testing details canbe found in the Methods section (Sec. V).For each cryogenic measurement, a correspondingroom-temperature measurement was also performed ona similar device with output gratings in place of single-photon detectors. For these room-temperature measure-ments, we used a technique that has been previouslydescribed for characterization of photonic structures inRef. [17]. In this technique, light is coupled from an op-tical fiber to an input grating, and the device is charac-terized by measuring the intensity emitted from outputgratings at different points in the device on an infra-redcamera. The room-temperature measurements are di-rectly comparable to the cryogenic measurements.Due to variations in fiber coupling efficiency and thecomplexity of the fiber coupling/packaging procedure, itis helpful to make as many measurements as possible us-ing a single fiber input. We therefore use waveguidesand beamsplitters to route light to different devices froma single fiber input. In particular, in Sec. II A we de-scribe the tree device, which evenly divides input lightbetween seven detectors and can be used to compare dif-ferent detector designs. In Sec. II B we describe a high-dynamic-range detector array. We can measure three ofthese devices with a single fiber input. The full integratedcircuits consist of up to 15 detectors, integrated with upto 18 beamsplitters/beamtaps and several centimeters ofwaveguides. μ m input gratingoutputgrating Detector Array(a) (c) (d)(b)bond pad gnd FIG. 1. (a) An optical microscope image of the tree device.(b) Zoom-in view of a waveguide-integrated detector with as-sociated meander inductor. (c) Scanning electron micrographof the nanowire on the silicon waveguide. (d) Infrared cam-era image showing the passive tree device and the laser input.The green boxes are the automated detection of the outputports, and the white text is automated output from the pro-gram indicating the coordinates and intensity of the output.
A. Branching tree structures
The ‘branching tree’ structure provides a method forevenly distributing light to a number of different detec-tors. This allows comparison of the performance of sev-eral detectors under uniform waveguide-coupled illumi-nation. A microscope image of such a device is shown inFig. 1(a). Light from a single fiber input is split evenlyby a series of beamsplitters and routed to seven detectorsand an output grating. The output grating is used forfiber alignment during packaging at room temperature.The path lengths from the input grating to all detectorsare equal. A zoom-in of a detector is shown in Fig. 1(b),and a scanning electron micrograph of an SNSPD detec-tor on a waveguide is shown in Fig. 1(c). We have also im-plemented a version of this device for room-temperaturecharacterization. The room-temperature structures in-clude an output grating after the hairpin device, as wellas output reference gratings for normalization of the out-put power. Absorption of the hairpins at room tempera-ture can then be compared to measurements of hairpinsat cryogenic temperature. Figure 1(d) shows a micro-scope image of such a tree structure used for room tem-perature characterization. The measurements describedin this section were all performed at 1.55 µ m on devicesdesigned for operation at this wavelength. Once cooled,the current-voltage curves for each SNSPD detector weremeasured. From these data, the critical current of the A b s o r p ti on ( d B ) passive 1passive 2cryogenic SNSPD
160 dB/mm177 dB/mm175 dB/mm
Nanowire length [µm] N o r m a li ze d c oun t s uniform illuminationwaveguide coupledlinear fit Nanowire width [nm]400 1000600 8000.250.40.30.35 P l a t ea u w i d t h [I / I c ]
400 1000600 8000.410.60.8 uniform illuminationwaveguide coupledlinear fit N o r m a li ze d c oun t s Nanowire width [nm] C oun t s / s Bias current [µA]0 201010
500 nm400 nm700 nm600 nm800 nm1 μm C oun t s / s Bias current [µA]0 201010
500 nm400 nm700 nm600 nm800 nm1 μm (f)(e) (d)(c) (b)(a)
FIG. 2. (a) Count rate versus bias current for six dif-ferent SNSPD widths with uniform illumination of the de-tectors. (b) Count rate versus bias current for six differentSNSPD widths with waveguide-coupled light. (c) The heightof the plateau versus the nanowire width for uniform illumina-tion (blue squares) and waveguide coupled light (red circles).The count rate is linearly proportional to the nanowire widthwhen the chip is uniformly illuminated, as shown by the lin-ear fit (black line). (d) The width of the plateau versus thenanowire width. (e) Count rate versus nanowire length forsix different SNSPD lengths for waveguide-coupled and not-waveguide-coupled light. The count rate is linearly propor-tional to the SNSPD length when the detectors are uniformlyilluminated, while the waveguide-coupled data saturates. (f)Absorption versus nanowire length for cryogenic and passivedevices measured at room temperature, showing absorptionbetween 160 dB/mm and 175 dB/mm. standard detectors (200 µ m long, 500 nm wide) was foundto be 10 µ A.With the light evenly divided, comparisons can bemade between detectors with different geometric param-eters. A layout error caused one of the seven detectors oneach tree to fail, so each tree in this work compares sixdetectors. For the first tree, the width of the SNSPDswas varied from 400 nm to 1.5 µ m, keeping the lengthof the nanowire constant (see Fig. 7(c)). The results areshown in Fig. 2. Detector count rate is plotted in Fig. 2(a)when the detectors are flood-illuminated from above andin Fig. 2(b) when the detectors are illuminated throughthe waveguide tree structure. In both the uniform andwaveguide illuminated plots the count rate is normal-ized to the count rate on the brightest detector. Thedetectors under uniform illumination required approxi-mately 50 dB more light for the same count rate as thewaveguide-coupled devices. A plateau region where thecount rate on the detector is independent of bias cur-rent is observed for every width measured, as expectedbased on the results in Ref. 18. This plateau region is thedesired bias current range of operation. The narrowerthe wire, the steeper the transition between the onsetof detection and the plateau region. This has also beencharacterized for this and different film compositions foruniformly illuminated detectors in Ref. 18.We further use the tree structure to investigate theheight and width of the plateau region. The height ofthese curves quantifies the relative detection efficiencyof wires with differing widths, while the width of theplateau quantifies the range of bias currents providingsaturated internal quantum efficiency. In Fig. 2 (c) theplateau height (averaged value of the data points withinthe plateau region) is plotted versus wire width. The bluesquares show the result when the chip is uniformly illu-minated. The black line is a linear fit, which is expecteddue to the fact that the detector area is proportional tothe wire width. The red circles in Fig. 2 (c) show thesame analysis for the waveguide-coupled data. Since allof the nanowires absorb more than 99% of the light, thereshould be no discernible difference between the values forthe different wire widths. However, the data indicates aslight drop in efficiency for wider wires. The cause ofthis drop in efficiency may be the tip of the wire, whichis approximately four times wider than the rest, absorb-ing some of the light without leading to detection events.This design is intended to avoid current crowding [19].For reference, a 4 µ m-length corresponds to 14% absorp-tion according to the measured absorption values (sim-ulated in Fig. 8 and measured in Fig. 2(f)). It may bepossible to narrow this tip length, although the cost maybe a lower switching current and narrower plateau region.Interestingly, the narrowest wire is also less efficient, pos-sibly due to edge roughness resulting from pushing thelimits of the photolithography tool used in fabrication.Figure 2(d) shows the width of the plateau versus thewire width. This width decreases as a fraction of theswitching current, but increases in absolute value due tothe increase in switching current for wider wires. The op-timal performance therefore depends on the applicationand the circuit used to read out the signal.Based on this analysis, any of the detector widths cho-sen would work for applications at 1.55 µ m. The widestwires are the least sensitive to lithography, but have thelargest area and highest energy consumption, while thenarrowest wires’ reduced performance suggests this isclose to the resolution limit of our 365 nm i-line lithogra-phy process.A second tree device with nanowires of different lengthswas also fabricated and measured. The nanowire lengthwas varied from 5 µ m to 200 µ m, based on simulationsof the nanowire absorption length (see Methods). Figure 2(e) shows the height of the nanowire pleateau versusthe nanowire length for the different length nanowires.Normalization is again performed against the highest-count-rate detector on that particular tree device. A lin-ear dependence versus length (proportional to area) isagain observed for the case of uniform illumination. Thesame nanowires show a saturating behavior with increas-ing length when the light is waveguide coupled, indicatingthat all light has been absorbed in the longest wires. Weuse this tree to quantify the absorption of the nanowiresversus length. Figure 2(f) shows 10 · log( A − R det ), where R det is the SNSPD count rate, versus length for the valueof A that gave the best linear fit (green dashed line). Thenanowire absorption per unit length calculated from theslope of this line is 160 dB/mm.We also measured the waveguide-integrated nanowireabsorption at room temperature. Separate photonictrees were fabricated for this purpose. Such a tree isshown in Fig. 1(d). In these structures, output grat-ing couplers were fabricated after each nanowire. Eachwaveguide-integrated nanowire is also accompanied by areference waveguide with the same geometry but withouta nanowire. Light is coupled through a fiber to the inputgrating. A branching tree splits the light evenly along 16paths in this structure, with eight nanowires each accom-panied by a reference waveguide, for a total of 16 outputports. The light from the output gratings following thenanowires and reference paths is captured on an infrared-sensitive camera. Automated image processing is used tofind the output grating locations and extract the relativeintensities of light from these outputs. The intensity ofthe light after each nanowire is compared to the inten-sity from the associated reference grating to normalizeout the effect of the grating response as well as propaga-tion losses. The intensity of the laser can also be variedby four orders of magnitude and calibrated against a ref-erence to increase the measurement dynamic range. Thegreen boxes in Fig. 1(d) indicate the locations that havebeen automatically assigned as the outputs.The results of this measurement for the tree structurewith varying nanowire length are compared to cryogenicmeasurements of counts per second in Fig. 2(f), purplecircles and blue squares (indicating measurements of twoequivalent devices). The absorption in this case is di-rectly measured (unlike the case of the cryogenic mea-surement, where the total light to be absorbed is a fitparameter). We find 175 dB/mm attenuation (purpleand blue lines) from the SNSPD hairpin at room tem-perature, compared with the cryogenic measurement of160 dB/mm. This level of agreement may be satisfactoryfor some applications, in which case it would be suffi-cient to measure the absorption of prototype nanowireswith room temperature measurements. The simulationsshown in the Methods give a value of 165 dB/mm for thestructures studied in the experiment, which is in goodagreement with the experimental results. The absorp-tion depends exponentially on the thickness of the di-electric spacer between the waveguide and the nanowire, inputlight inputlight f - f μ m (c)(b)(a) FIG. 3. The HiDRA device used to test the dynamic rangeof the integrated SNSPD platform. (a) Optical microscopeimage of the HiDRA device. (b) Schematic of a 50/50 beam-splitter. (c) Schematic and optical microscope image of abeamtap. with a thinner spacer leading to larger absorption perunit length, and therefore smaller-footprint SNSPDs.For neural applications in which size matters, a thin-ner spacer may be used, with a correspondingly reducedover-etch tolerance during nanowire fabrication.Similar cryogenic/room-temperature comparison hasbeen performed previously for NbN SNSPDs on nanopho-tonic diamond waveguides [20], and room temperatureabsorption measurements of similar devices have beenperformed for NbN on diamond and SiN waveguides, al-though using a different experimental technique [21, 22].Discussion of room temperature characterization of treedevices at 1.22 µ m is in Methods (Section V D). B. High-dynamic-range detector arrays
The next device examined in this study is a high-dynamic-range detector array (HiDRA). An optical mi-croscope image of the device is shown in Fig. 3(a). Eachon-chip system consists of three HiDRAs with a sin-gle input grating and a single output grating used forfiber alignment during packaging. Light from the in-put grating is split evenly to four waveguides by three50/50 beamsplitters (see Fig. 3(b)). Three of these fourbranches are attached to a HiDRA, while the fourth is astraight waveguide connected to an output grating. TheHiDRA device works as follows. Input light is incidenton a beamtap (see Fig. 3(c)). The beamtap drops a frac-tion 1 − f of the light to an SNSPD while a fraction f of the light is passed to the next beamtap. After n such T r a n s m i ss i on ( d B )
1% nom., cryo0.1% nom. cryo0.1% nom., R.T.1% nom., R.T. T r a n s m i ss i on ( d B )
10% nom., R.T.10% nom., cryoDisconnected, cryo27% calculated tap29% calculated tap tap 3tap 5tap 4tap 2tap 1 C oun t s / s Bias current [μA]5 6 7 8 9 tap 3tap 5tap 4tap 2tap 1 C oun t s / s Bias current [μA]5 6 7 8 9 (a) (b) (c) (d)
FIG. 4. (a) Count rate versus bias current for the five de-tectors in a HiDRA device when the chip is uniformly illumi-nated. (b) Count rate versus bias current for the same deviceas in part (a) with the input light waveguide coupled. (c)Count rate versus port number for a HiDRA designed to havea 10% beamtap, including measurements of two cryogenic de-tector devices (green markers), two room temperature devices(blue markers). The black lines show linear fits to the cryo-genic (solid) and room temperature (dashed) data. The redstars show the result for a cryogenic device with intentionallydisconnected detectors. (d) Count rate versus port number forHiDRA with different designed beamtap ratios for both cryo-genic (green makers) and room-temperature (blue markers)operation. The scattered light prevents the dynamic rangefrom exceeding 30 dB. The black lines show how a 1% (solid)and 0.1% (dashed) measured device should perform, indicat-ing the nominal values are far from realized. beamtaps, an SNSPD should receive (1 − f ) f ( n − of thelight. The waveguide loss must also be included, whichis approximated by e α · l ( n − , where α = ln 1020 L , L is thewaveguide loss in dB/m, and l is the length of each seg-ment of the HiDRA. The total light intensity at the n thdetector is therefore (1 − f ) f ( n − e α · l ( n − .Figure 4 shows data acquired from such HiDRAs. Fig-ures 4 (a) and (b) show counts per second versus biascurrent for the five detectors on a HiDRA designed tohave a 10% beamtap ( f = 0 . n is a straight line, indi-cating that the tap fraction is constant. The tap fractioncan be calculated from the slope m of this plot, as wellas the known segment length l and waveguide loss L indB/m. The tap fraction f is then given by f = 10 m − Ll .We extract tap fractions of 0.26 and 0.28 from the twoHiDRAs designed to have taps with f = 0 .
1, with themean value (solid black line) of 0.27. This deviationfrom the designed value is likely due to the the gapscoming out narrower than designed. This in combina-tion with a slightly longer effective length due to the sinebends leading up to the beamtap could explain the dis-crepancy. A third device with intentionally disconnectedwaveguides was also measured (red stars). DisconnectedHiDRAs were identical aside from a 180 ◦ waveguide turnand taper that couples light into free space, away fromthe SNSPD. The disconnected device shows a relativelyconstant level at around 30 dB below the level of the firstwaveguide coupled detector on the connected HiDRA.This indicates that with our current fabrication processand packaging scheme there is a 30 dB noise floor. Previ-ous measurements of LEDs coupled to waveguides indi-cated a 40 dB noise floor [14]. Both the low fiber-couplingefficiency and high waveguide scattering loss contributeto this high background light level (see Methods for aprecise characterization of these losses).As in the case of trees, ‘passive HiDRA’ structures werefabricated for characterization at room temperature. Un-like the trees, in the case of the HiDRA structures mea-sured at room temperature, the SNSPD has been omit-ted, and the structure is intended to characterize the pho-tonic beamtap ratios. The structures measured on thiswafer have high dynamic range, with up to 30 dB atten-uation measured in the devices themselves. This posesan issue for the 8-bit camera used for characterization ofthe structures. We therefore used a calibrated attenu-ator to vary the input light and capture the light fromthe reference and measurement gratings over 50 dB ofattenuation. Figure 4(c) also shows the transmission foreach of the output ports of a passive, room-temperatureHiDRA. From the plot of transmission versus attenua-tion, the beamtap ratio at room temperature is deter-mined to be 0.29 for these devices, calculated from theslope of the dashed black line in the figure. This valueagrees well with the cryogenic measurements describedin the preceding paragraph.The results of cryogenic and room temperature mea-surements of HiDRA designed to have 1% and 0.1%beamtaps are shown in Fig. 4(d). The solid black line in-dicates where the data for a cryogenic HiDRA with a 1%tap ratio should fall, while the dashed black line indicatesthe same for a 0.1% tap ratio device. The data clearly donot follow this trend. For the cryogenic measurements,linear fits to the first two points of the 1% designed de-vice (green triangles) corresponds to a tap ratio of around6%, while a linear fit to the first two points of the 0.1%designed device (green circles) yields a fitted tap ratio of2.3%. However, the rest of the data points deviate signif-icantly from these linear fits due to scattered light in thechip. The scattered background light prevents such lowtap ratios from being useful. The passive HiDRA withbeamtap ratios designed to be 1% (blue triangles) and0.1% (blue circles) indicate similar trends. We again find -200 2000Time [ns]0120 Laser attenuation (dB)10 50 C oun t r a t e ( / s ) pulse heightHiDRA Port HiDRA Port
In the superconducting optoelectronic neuromorphicplatform proposed in Refs. 10 and 11, communicationis photonic, but computation is electronic. The signalscommunicated from each neuron to its synaptic connec-tions are binary, few-photon pulses, meaning the infor-mation communicated is independent of the number ofphotons in the pulse. Only the timing of spikes is rele-vant. Synaptic weighting of the pulses is done entirelyelectronically. This communication scheme requires thedetectors to be insensitive to the number of incident pho- A m p li f i e r ou t pu t ( A . U . ) -250 250Time [ns]01 A m p li f i e r O u t pu t ( A . U . ) Bias current [μA]10.65 6 10 (a) (b)
10 1.50.25 A m p li f i e r ou t pu t ( A . U . )
10 1.50.25 Time [μs] port 1port 2 port 3port 4 port 5port 6 port 7 A m p li f i e r ou t pu t ( A . U . ) Time [μs] (c) (d)
FIG. 6. (a) Pulses for three different values of bias currenton a single detector. (b) The pulse height versus bias currentfor the detector in (a). (c) Pulses on each of seven detectorson an even tree device with a fixed bias current of 7.7 µ A. (d)Pulses on the same seven detectors as in part (c) for sevendifferent values of bias current. The x-axis separation of thepulses in parts (c) and (d) are for visibility purposes only. tons. We use the tree and HiDRA structures to testwhether or not SNSPDs demonstrate this behavior bymeasuring their output electrical pulses when they areilluminated over a light intensity range of close to 50 dB.At the low end of this range, multi-photon absorptionevents are very improbable, with less than 10 − photonsper pulse on average, while at the high end multi-photonevents are likely, with greater than 10 photons per pulseon average. The measurement is performed with an in-put laser with 50 ps pulses operating at a pulse rate of200 kHz and wavelength of 1.57 µ m. The photon numberis changed via a calibrated variable fiber attenuator. Forcoherent light, the photon number should follow a Pois-son distribution given by p ( n >
0) = 1 − e −(cid:104) n ph (cid:105) . Sincethe laser pulse length is much shorter than the responsetime of the detector, at most one count is observed ev-ery time the photon number in a pulse incident on thedetector is greater than zero. Therefore p ( n >
0) canbe approximated by the count rate on the detector R det divided by the repetition rate of the laser, R laser . Theaverage photon number in the pulse received on the de-tector should therefore be related to these quantities by (cid:104) n ph (cid:105) = − log (cid:16) − R det R laser (cid:17) . Since this is the mean pho-ton number received on the detector, no assumptions sofar have been made about the absolute value of the laserpower. Next, we assume the laser power is proportionalto the mean photon number, and therefore the plot ofcount rate versus attenuation can be used to extract themean photon number incident upon the detector at each set laser power. Figure 5(a) shows pulses from an SNSPDwith waveguide-coupled light with mean photon numbersof 0.003 and 12. The difference is indistinguishable onthis scale. The inset shows the count rate versus laser at-tenuation for that SNSPD, from which the mean photonnumbers were calculated. Figure 5(b) shows pulse heightversus mean photon number for the detector in part (a).One hundred pulses were averaged to obtain the pulseheight at each photon number. The pulse height variesby less than 2% over almost five orders of magnitude inincident photon flux, with no discernible dependence onthe number of incident photons. Figure 5(c) and (d) showthe results using the same laser configuration for detec-tors on a HiDRA device. Part (c) shows the count rateversus port number on the HiDRA, while part (d) showsthe pulse height for each of the five detectors for thecount rates shown in part (c). The pulse height varies byless than 5% over the HiDRA, despite using five differentdetectors with mean photon numbers varying from 0.02to 6. Mean photon numbers were calculated for each de-tector in the HiDRA by the procedure described for thedata in Fig. 5 (a) and (b).In the synaptic weighting scheme described in Ref. [15],the magnitude of the SNSPD current pulses are used asthe weights. This pulse amplitude can be controlled withthe bias current applied to the SNSPD. In this case, itis very simple to generate synapses with a bit depth ofone by simply biasing the SNSPD or not. However, fur-ther weighting can also be achieved by varying the biascurrent within the detection range of the synapse. Ithas also been shown that neural networks that performsimple tasks can be designed with these simple integrate-and-fire neurons [15]. In Fig. 6(a), pulses on an SNSPDfor three different bias currents are shown. Figure 6(b)plots the pulse height versus bias current for the detec-tor over the available range of bias currents, indicatinga range of 6-10 µ A. The black line shows a linear fit tothe curve. In Fig. 6(c), pulses from seven detectors onan symmetrical tree are shown. This is a tree devicewith all seven detectors fabricated with the same geo-metric parameters. The pulses are separated on the x -axis (in time) for clarity, this separation has no physicalmeaning. Figure. 6(d) shows the pulses on the sameseven detectors with bias currents changed to give differ-ent pulse heights. In Ref. [15] the spiking neural net-work model assumed that bias currents could be var-ied between 5 µ A and 15 µ A (or set to zero). This isaround twice the range that is observed here. It wouldbe necessary to re-simulate networks with these valuesto ensure that this is still a viable method for controllingthe weights. Calculating the bit depth in a quasi-analogsystem is challenging, especially before building the sys-tem and determining what constitutes the minimum rea-sonable change in weight value. This is a challenge formany emerging technologies, such as magnetic Joseph-son junctions, which have > ,
000 internal states per µ m and are therefore quasi-analog [23], and spin-torquenano-oscillators [24] where frequencies are tuned using anapplied current. Memristor technologies have similar is-sues, with typically reported bit depths of 4-6 [25], withbit depths of up to eight reported for phase-change mem-ory [26]. However, even in these technologies, argumentshave also been made for operating in a binary mode [27],for which these synapses are well suited. Superconduct-ing loop neurons [11] use SNSPDs to generate the electri-cal pulses and then Josephson junctions add current to anintegrating loop in integer quantities of fluxons (althoughthermal noise will play a role, and further investigationis required). The maximum number of fluxons that canbe added determines the bit depth, with an upper limitof around 10 bits. IV. DISCUSSION
The work presented here introduces several tools forthe characterization of waveguide-integrated SNSPDs.The integration of the detectors with photonic struc-tures provides a powerful toolbox to rapidly assess largenumbers of detectors with various design parameters ina context similar to that in which the detectors will beutilized. Such measurement technologies are likely to beindispensable in the maturation of advanced computingtechnologies using photons for communication.Realization of the hardware necessary for several formsof advanced cryogenic computing involves integratingnew devices in a scalable fabrication process. One of themain elements required for computing hardware involv-ing photonic communication is high-yield, high-efficiencydetectors. In this paper, we have described the fabri-cation of waveguide-coupled SNSPDs that can be usedas components in synapses in superconducting optoelec-tronic networks. We have demonstrated several inte-grated photonic structures that can be used to assessimportant properties of waveguide-integrated SNSPDs.We have shown how room-temperature measurementscan be correlated with cryogenic measurements, and wehave demonstrated the effects of photon number and biascurrent on SNSPD pulse height, which are relevant tosynaptic operation.WSi SNSPDs operating in the telecommunicationswavelength have typically been fabricated with widthsof around 100 nm [28], which leads to a correspondinglysmaller footprint than the current work. However, formost academic cleanrooms, 100-nm-wide wires requireelectron beam lithography for fabrication, and the smallfeature size makes integration more challenging. Formicron-wide wires, photolithography can be employed(as in this work), which allows much easier integrationand fabrication. While this larger size is undesirable forlarge-scale systems in the long-term, it may be acceptablefor near-term demonstrations. More significant materialchanges, such as materials with a larger superconductingenergy gap enabling higher temperature operation, mayalso be beneficial. These photonic structures and mea-surement techniques will be valuable in the search for optimal materials and device designs to determine thebest detectors for a variety of applications.While the detectors in the present work had very largeadded inductances to ensure resetting, in a practical neu-ronal circuit the inductance may be very different de-pending on the circuit context. In these measurements,SNSPD pulses were read out across a 50 Ω transmissionline. The inductance must set so the
L/R time constantis sufficiently long to avoid latching. In the context ofsynapses, these detectors will be in parallel with a muchsmaller resistance, and the inductance (and therefore thesize) can be reduced while maintaining the same
L/R time constant for resetting. If the synapses of Ref. [15]are employed, the resistance affecting the SNSPD
L/R time constant is related to the integration time of theneuron. If the synapses of Refs. [10, 11] are employed,the normal-state resistance of the Josephson junctions(on the order of 1 Ω) establishes a minimum functionalvalue of SNSPD inductance (on the order of 100 nH), sothe SNSPD must be designed consistently with the criti-cal current of the junctions used in the circuit. Since theenergy consumption of the detectors is given by LI / V. METHODSA. Fabrication
In this work, the SNSPDs were made from WSi (shownin orange in Fig. 7 (a)), while the waveguides were silicon(blue). The substrate was a silicon-on-insulator (SOI)wafer with a 220 nm device layer and a 3 µ m buried oxidelayer. A 40 nm SiN layer (green) was sputtered on theSOI to act as an etch stop for the WSi etch. Electron-beam and photolithography alignment marks were thenetched into the wafer. A 2 nm/30 nm/2 nm Ti/Au/Tilayer was patterned via liftoff (red). This metal layerwas used to make electrical contact to the SNSPDs.A 2.1 nm W . Si . film was then co-sputtered as de-scribed in Ref. 18. An amorphous silicon capping layerwas then deposited without breaking vacuum to protect Ti/AuWSiSiN SU8Si SiO (a)(b) widthlengthgap tip (c)
FIG. 7. A schematic of the fabrication process used in thepaper showing (a) a cross section and (b) a top view. (c) Thegeometry of the waveguide nanowire. the thin WSi film. This WSi recipe has been demon-strated to allow saturated internal quantum efficiencyfor nanowires as wide as 1.2 µ m at 1.55 µ m [18]. Thenanowires were patterned with photolithography using a365 nm, i-line stepper and etched with Ar and SF chem-istry.A partial silicon etch was performed to create thegrating used for coupling light from an optical fiber tothe waveguides. This patterning was performed withelectron-beam lithography. The etch depth was de-signed to be 50 nm and measured at 65 nm - 70 nm. A100 nm SiO hardmask was then deposited using plasma-enhanced chemical vapor deposition (PECVD) and thewaveguides were patterned and etched with electron-beam lithography using a positive tone resist with 2 µ mclearance around the photonic devices. The remainder ofthe Si was then cleared out with photolithography. Allsilicon etches used SF and C F chemistry.Following the waveguide etch, vias were etched throughthe waveguide oxide hard mask to make electrical contactto the Au layer using CHF /O chemistry. A wiring layerof 2 nm/440 nm/2 nm Ti/Au/Ti was then deposited andpatterned with liftoff. A 1.8 µ m cladding oxide (white)was then deposited using PECVD. Openings to the wire-bond pads and the ground plane were then etched usingthe same CHF /O dry etch. Finally, a 50- µ m-thick SU8packaging layer (light blue) was spun on and patternedwith photolithography [16].Fig. 7 shows (a) cross sectional and (b) top view di-agrams of a fabricated device, indicating some of the Waveguide width [ μ m]0.4 0.5 0.6 Beamtap gap [μm]0 0.2 0.4 T r a n s m i ss i on [ d B ] -60-40-200 Beamtap gap [μm]0 0.2 0.4 0.6 (b)(c) Waveguide width [μm]0.2 0.3 0.45 0.5 n e ff TE1TM1TE2TM2 (a) n e ff L e ng t h [ μ m ] L e ng t h [ μ m ] -2 % c oup li ng
50% coupling 0.1 % coupling1% coupling % c oup li ng
50% coupling
TE1TM1TE2 -60 T r a n s m i ss i on [ d B ] -40-200 SNSPD Length [μm] SNSPD Length [μm]
FIG. 8. (a) Simulated waveguide modes at 1.22 µ m and1.55 µ m. (b) Simulated beamtap length versus gap for dif-ferent values of splitting ratio at 1.22 µ m and 1.55 µ m. (c)Simulated transmission versus nanowire length for differentvalues of the SiN spacer thickness. main features. Optical microscope images and scan-ning electron-microscope images of fabricated devices areshown throughout this paper alongside measured data.The geometry of a typical SNSPD is shown in Fig. 7 (c).The geometric parameters are indicated in the diagram.Length and width were varied in this paper to determineoptimal device performance. B. Photonic device design
The devices described in this paper required design ofa number of components. These devices include waveg-uides, beamsplitters, beamtaps and SNSPD hairpins.Photonic devices were designed for operation at both1.55 µ m (standard telecommunications wavelength), andat 1.22 µ m, where the proposed spiking neural net-works [9–12] are designed to operate. Simulations ofthe photonic waveguides were performed using a finite-difference frequency-domain eigenmode solver. The ef-fective index of waveguide modes in 220 nm thick waveg-uides of different widths for 1.55 µ m and 1.22 µ m wave-0lengths are shown in Fig. 8 (a). Based on these simu-lations, single-mode waveguide widths were chosen to be450 nm (350 nm) for waveguides designed for operation at1.55 µ m (1.22 µ m). For branching-tree and high-dynamicrange array structures, the beamtaps were simulated us-ing the eigenmode method described in Ref. 29. Theresults of the simulations are shown in Fig. 8 (b). Forthe 1.55 µ m beamtaps, the waveguide width was broughtdown to 400 nm at the beamtap region. The beam-splitter gap widths and interaction lengths were chosenbased on the plots in Fig 8(b). The 1.55 µ m beamsplit-ters were chosen based on the optimized design in Ref. 30.The 1.22 µ m beamsplitters are multi-mode interferome-ters that were optimized in separate fabrication runs tominimize loss.The waveguide-integrated nanowire geometry is shownin Fig. 7(c). We refer to this structure as a hairpin. Un-less otherwise noted, the measured width of the nanowirewas 500 nm and the length was 200 µ m. There was an800 nm gap between the wires in the hairpin, with a400 nm gap on either side. Waveguides were adiabaticallytapered from their single-mode widths up to 2.6 µ m overa 100 µ m length to accommodate the SNSPD. The de-tectors also have a meandering section of 3 µ m-wide wirefor extra inductance to achieve a total value 1.25 µ H.Nanowire absorption was calculated for a 500 nm-widenanowire with the geometry shown in Fig. 7(c). The realand imaginary parts of the refractive index of the WSiwas measured and used to simulate the real and imag-inary propagation constant in the nanowire on waveg-uide structure. The resulting absorption versus lengthat 1.22 µ m and 1.55 µ m are shown in Fig. 8 (c) for dif-ferent thicknesses of SiN spacer. Based on the results ofthis plot in combination with concerns about ensuringelectrical isolation of the superconducting layer, the SiNspacer was designed to have a 40 nm thickness. C. Component characterization
For every aspect of the integrated devices describedin Sec. II, test structures were also fabricated to charac-terize performance and losses. These test structures aredescribed below and in Fig. 9. All of these test deviceswere fabricated on the same wafer as the devices withintegrated nanowires. Insertion losses of the grating cou-plers varied from 5-7 dB at 1.55 µ m, and 8-10 dB at 1.22 µ m.The transmission of meandering waveguides of vari-ous lengths was used to measure the propagation lossof the waveguides (cutback method). The transmissionas a function of waveguide length is shown in Fig. 9(a).Each device has an input, a reference port, and an out-put grating, as shown in the optical microscope image inthe inset. The intensity of the light from the referenceand output gratings is measured with an infrared cameraand compared for devices of different lengths to obtainthe data in Fig. 9(a). The measured losses are 24 dB/cm loss = 10.3 dB/cmWavelength [nm]1261 1265 1269 T r a n s m i ss i on [ d B ] -20-100 -25-15-5 -30-10-20 loss = 24 dB/cm-45-35-25 10 20 30 40loss = 0.7 dB/beamsplitterpaperclip length [mm] loss = 0.65 dB/beamsplitter-10-22-14-18 T r a n s m i ss i on [ d B ] Wavelength [nm]1510 1514 1518 -2-6-10-14 T r a n s m i ss i on [ d B ] (b) (c) paperclip length [mm]2 6 10 14 (a) i n p u t r e f . o u t p u t FIG. 9. (a) Measured waveguide loss at 1.22 µ m and 1.55 µ mwith an optical microscope image of the structure used for lossmeasurement inset (scalebar = 200 µ m). (b) Measured beam-splitter loss at 1.22 µ m and 1.55 µ m with left inset showingan SEM of a beamsplitter (scalebar = 1 µ m) and right insetshowing an optical microscope image of the structure usedfor measuring beamsplitter loss (scalebar = 5 µ m). (c) Mea-sured transmission spectrum of Mach-Zehnder interferometerat 1.22 µ m and 1.55 µ m. at 1.22 µ m and 10.2 dB/cm at 1.55 µ m. These losses canbe improved with well-known processes [31].The loss per beamsplitter was measured using a similartechnique to waveguide propagation loss. Transmissionthrough sequences of various numbers of beamsplitterswas measured. The data are shown in Fig. 9(b), and theinsets show a scanning electron micrograph of a singlebeamsplitter as well as a microscope image of a seriesof four beamsplitters. For this measurement, light wascollected through a second fiber and detected with a pho-todiode. The loss of 0.7 dB per beamsplitter is arounddouble the insertion loss simulated [29]. To quantifythe power splitting ratio of the beamsplitters, they wereembedded in unbalanced Mach-Zehnder interferometers(MZIs). The extinction of such an interferometer canbe used to bound the splitting ratio [29]. Transmissionspectra of MZIs at 1.22 µ m and 1.55 µ m are shown inFig. 9(c). The extinction at 1.55 µ m was nearly 30 dB,while at 1260 nm (measured at this wavelength due tothe availability of an O-band laser) it was near 20 dB.From these values we get approximate splitting ratiosof 48%/52% at 1.55 µ m and 45%/55% at 1260 nm. The1extinction values measured with the MZIs were similarto the noise floor observed with SNSPDs at those wave-lengths (see Secs. II A and II B). This result may indicatethe beam splitting ratios were closer to 50%/50% thancalculated from these measurements. D. Waveguide-integrated nanowire measurementsat 1.22 µ m Nanowire length (μm) T r a n s m i ss i on ( d B )
165 dB/mm146 dB/mm T r a n s m i ss i on ( d B ) (b) -10-20-30
10% designed10% designed10% designed (a)
FIG. 10. Measurements of (a) length trees and (b) HiDRAat room temperature at 1.22 µ m. The values of absorption and dynamic range mea-sured with the passive tree and HiDRA devices measured at 1.55 µ m matched the active devices, and thereforewe measured the 1.22 µ m devices at room temperaturewithout also performing cryogenic measurements. Themeasurement technique is the same as that described inthe room-temperature measurements portions of SectionsII A and II B of the main text, but with a 1.22 µ m in-put laser. We found that the measured absorption ofthe nanowires at 1.22 µ m was similar to that measuredat 1.55 µ m, giving 146 dB/mm and 165 dB/mm for twodifferent (nominally identical) devices, as shown in Fig.10(a). The large variation may be due to the fact thatthere is more scattering from the 1.22 µ m waveguides dueto edge roughness, which affects the accuracy of the cam-era intensity measurements.The HiDRA devices designed to have 10% beamtapssuffered from a very high background, with the intensityflattening out at around 20 dB, as shown in Fig. 10(b).This reduced extinction ratio is likely due to the veryhigh waveguide scattering loss. ACKNOWLEDGMENTS
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