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Here, we propose a superconducting trigger that realizes signal amplification and code functions on-chip of the SNSPD. The trigger adopts the sandwich structure of input nanowire–insulator–output nanowires. The output channel enters the latching state affected by the Joule heat generated from the input channel, which can convert a small input current (<10 μA) to a large output impedance (>100 kΩ). The input and output channels are electronically well isolated to avoid signal crosstalk, and they are fabricated on the same layer of the superconducting film, increasing the homogeneity of the nanowires. The trigger is applied to the readout of a 4-pixel SNSPD, converting the parallel input signals to a serial impedance output signal and reconstructing the intensity distribution of the incident light.
The superconducting trigger consists of two superconducting nanowires with an interval of several tens of nanometers, as shown in Fig. 1(a). The input and output channels are independently provided with the bias currents Iin and Iout, which are slightly lower than the critical current Ic, and the dielectric is filled between them as both an electrical isolation layer and a thermally conductive medium. When the input channel enters the normal state due to the disturbance of the external current Ie, Joule heat is generated and then transferred to the output channel through the dielectric, causing the output channel to enter the latching state. Figure 1(b) elucidates the working principle of the trigger. In the initial state, both the input and output channels of the trigger are in the superconducting state. When disturbed by the external current Ie, the input channel switches to the normal state, and Joule heat is generated and continues to spread. Then, the output channel also switches to the normal state, and the output resistance Rout dramatically jumps to approximately 100 kΩ. The readout circuit detects the resistance change and immediately reduces the bias current to 0 μA, and the trigger is gradually restored to the initial state.We modeled and simulated the heat transfer process in the superconducting trigger. The energy relaxation process of the trigger is mainly controlled by the interaction of electron and phonon systems, as shown in Fig. 1(c). We adopted a simplified heat transfer model, ignoring the effect of diffusion and the nonequilibrium distribution of electrons and phonons,1515. R. Baghdadi, J. P. Allmaras, B. A. Butters, A. E. Dane, S. Iqbal, A. N. McCaughan, E. A. Toomey, Q. Y. Zhao, A. G. Kozorezov, and K. K. Berggren, Phys. Rev. Appl. 14, 054011 (2020). https://doi.org/10.1103/PhysRevApplied.14.054011 and obtained a reasonable result.For the input channel, the heat transfer equation for the electron–phonon system is Ce,nTe,n∂Te,n∂t=−∑e−ph,nTe,n5−Tph,n5+In2ρnwndn2,(1) Cph,nTph,n∂Tph,n∂t=∑e−ph,nTe,n5−Tph,n5−Gn−D4wnTph,n4−Tph,D4−Gn−sub4dnTph,n4−Tsub4,(2)where Ce,n = 240Te,n is the electron heat capacity,16,1716. A. D. Semenov, G. N. Gol'tsman, and A. A. Korneev, Physica C 351, 349 (2001). https://doi.org/10.1016/S0921-4534(00)01637-317. Y. P. Gousev, G. N. Goltsman, A. D. Semenov, E. M. Gershenzon, R. S. Nebosis, M. A. Heusinger, and K. F. Renk, J. Appl. Phys. 75, 3695 (1994). https://doi.org/10.1063/1.356060 Te,n is the electron temperature, and Σe-ph,n is the electron–phonon coupling strength of the input channel nanowire, which is a material-dependent constant on the order of 109 W/(m3 K5).1616. A. D. Semenov, G. N. Gol'tsman, and A. A. Korneev, Physica C 351, 349 (2001). https://doi.org/10.1016/S0921-4534(00)01637-3 Tph,n is the phonon temperature, In is the bias current of the input channel, ρn = 2.4 × 10−6 Ω m is the resistivity of the normal state, and wn and dn are the width and thickness of the input channel, respectively. Cph,n = 9.8Tph,n3 is the phonon heat capacity,1616. A. D. Semenov, G. N. Gol'tsman, and A. A. Korneev, Physica C 351, 349 (2001). https://doi.org/10.1016/S0921-4534(00)01637-3 Tph,D is the phonon temperature of the dielectric, Tsub = 2.3 K is the substrate temperature, Gn-D is the input-dielectric boundary conductance, and Gn-sub is the input-substrate boundary conductance, which is on the order of 700 W/m2 K4.1515. R. Baghdadi, J. P. Allmaras, B. A. Butters, A. E. Dane, S. Iqbal, A. N. McCaughan, E. A. Toomey, Q. Y. Zhao, A. G. Kozorezov, and K. K. Berggren, Phys. Rev. Appl. 14, 054011 (2020). https://doi.org/10.1103/PhysRevApplied.14.054011 Equation (1) describes the energy relaxation of the Joule heat generated by the bias current to the electrons at the input channel nanowire, and Eq. (2) reveals the relaxation process of the electron energy to the dielectric and substrate.The thermal transfer process for the insulating dielectric layer and the output channel is similar to that of the input channel, which can be found in the supplementary material. We solved Eqs. (1) and (2) and Eqs. (S1)–(S3) in the supplementary material, and the results are shown in Fig. 1(d). At the initial time, the external current Ie = 6 μA is input to the input channel of the trigger, causing the input channel to switch to the normal state immediately, and the temperature of the electron and phonon system of the trigger rises dramatically. After approximately 2 ns, the electron and phonon temperatures of the nanowire at the output channel both exceed 8 K, which is higher than the critical temperature Tc, and tend to saturate, resulting in nanowire switching to the latching state. After 2 ns, the active quenching circuit works to set the bias current to zero, and the trigger is gradually restored to the superconducting state.We fabricated the superconducting trigger on a thermally oxidized silicon substrate, and the detailed preparation process can be found in the supplementary material and our previous work.18–2018. Q. Chen, B. Zhang, L. B. Zhang, R. Ge, R. Y. Xu, Y. Wu, X. C. Tu, X. Q. Jia, D. F. Pan, L. Kang, J. Chen, and P. H. Wu, IEEE Photonics J. 12, 1 (2020). https://doi.org/10.1109/JPHOT.2019.295493819. B. Zhang, Q. Chen, L. B. Zhang, R. Ge, J. R. Tan, X. Li, X. Q. Jia, L. Kang, and P. H. Wu, Appl. Phys. B 126, 59 (2020). https://doi.org/10.1007/s00340-020-7408-420. B. A. Zhang, L. B. Zhang, Q. Chen, Y. Q. Guan, G. L. He, Y. Fei, X. H. Wang, J. Y. Lyu, J. R. Tan, H. C. Li, Y. Dai, F. Y. Li, H. Wang, S. L. Yu, X. C. Tu, Q. Y. Zhao, X. Q. Jia, L. Kang, J. Chen, and P. H. Wu, Phys. Rev. Appl. 17, 014032 (2022). https://doi.org/10.1103/PhysRevApplied.17.014032 Figure 2(a) is the false-color scanning electron microscopy image of the superconducting trigger with sample number S1, and Fig. 2(b) is the cross section diagram of the superconducting trigger. The lengths of the coupled nanowires at the four input channels are 48, 96, 192, and 384 μm, with a length ratio of 1:2:4:8. The widths of the input and output channel nanowires are 100 and 70 nm, respectively, and their interval is 70 nm, filled with an insulating dielectric. The four input channels are supplied with bias current independently, and the distance of each input channel is more than 10 μm to avoid thermal crosstalk.The device is installed in a Gifford–McMahon cryocooler with a base temperature of 2.3 K, and the electrical and optical system of the device characterization can be found in the supplementary material. The current–voltage (I–V) relationship of the output channel nanowire is shown in Fig. 2(c). The output channel is in the superconducting state when the four input channels work in the zero-current state, with Ic = 19 μA and retrapping current Ir = 2.5 μA. When the input channel switches to the latching state, the coupled part of the output channel also switches to the normal state, resulting in a corresponding resistance, and the I–V curve becomes a resistance line, which is similar to the work by McCaughan et al.2121. A. N. McCaughan, V. B. Verma, S. M. Buckley, J. P. Allmaras, A. G. Kozorezov, A. N. Tait, S. W. Nam, and J. M. Shainline, Nat. Electron. 2, 451 (2019). https://doi.org/10.1038/s41928-019-0300-8 The resistance of the output channel increases as the coupling length increases. Figure 2(d) shows the relationship between the output channel's resistance and the superconducting transition length. Lin is various superconducting transition length combinations of the input channels, resulting in different normal state resistances of the output channel. The superconducting states of the four input channels form a total of 15 different resistance outputs. Through this resistance-coding method, one can infer the working condition of the input nanowires from the output resistance values. The red circles are the experimental data, and the blue line is the linear fit with the coefficient of determination R2 = 0.99, which shows good linearity. The linear fitting result in Fig. 2(d) is R = 3.56Lin − 7.00, with the R in the unit of kΩ and the Lin in the unit of μm, and we can calculate that the sheet resistance of the output channel is 249.2 Ω/□ based on the fitting result. The corresponding sheet resistance of the niobium nitride film is 241.6 Ω/□, which is consistent with the fitting result, indicating that the nanowire undergoes a complete superconducting transition. The possible reason for the discrepancy is the side damage and partial oxidation of the nanowire during fabrication processes, resulting in a slightly larger sheet resistance of the nanowires than the film.Figure 2(e) shows the relationship between Ic, retrapping current Ir, and temperature T at the output channel nanowire of S2. The difference from S1 is that the width of the output channel nanowire of S2 is 100 nm. Ic and Ir both decrease with increasing temperature, and the blue and red solid lines are the fitting results using Bardeen's phenomenological equation Ic = Ic0(1−(T/Tc)2)3/2.2222. J. Bardeen, Rev. Mod. Phys. 34, 667 (1962). https://doi.org/10.1103/RevModPhys.34.667 The inset shows the relationship between Ic and Ir of the output channel nanowire and the heat power of input channel 3, which decreases gradually with increasing heat power. When the trigger is working, the actual temperature of the output channel is 6.2–7 K, corresponding to the gray area in Fig. 2(e). Although the Tc of the film (7.8 K) is not reached, this temperature is also sufficient to trigger the superconducting transition of the nanowire for the following two reasons: (1) the Tc of the nanowire is lower than the film itself due to the superconducting proximity effect2323. Q. Chen, B. Zhang, L.-B. Zhang, F.-Y. Li, F.-F. Jin, H. Han, R. Ge, G.-L. He, H.-C. Li, and J.-R. Tan, Phys. Rev. B 105, 014516 (2022). https://doi.org/10.1103/PhysRevB.105.014516 and the edge defects in the nanowire's fabrication processes; (2) the bias current is lower than 1 μA when measuring the Tc of the film, while the bias current of the output nanowire is approximately 10 μA when operating, which is sufficient to trigger the nanowire's superconducting transition at 7 K.We constructed a 4-pixel SNSPD readout circuit using this superconducting trigger and reconstructed the intensity of incident light. A schematic diagram of the experiment is shown in Fig. 3(a). Each pixel of the array SNSPD is provided with the bias current Ib (6 μA) independently and connected to the input channel of the trigger through a 200 Ω resistor R0. A pulsed laser with a power of 100 nW and a wavelength of 1550 nm is coupled to the SNSPD through a multimode fiber. When an SNSPD pixel detects a photon, the bias current of the pixel is repelled to the input channel of the trigger so that the input channel switches to the normal state, and the coupled part of the output channel nanowire also switches to the resistive state. We used an oscilloscope to observe the current pulse of the SNSPD and the voltage pulse of the input and output channels. The results are shown in Fig. 3(b), numbered 1, 2, and 3. The voltage pulse at the output channel is approximately 0.4 V, which can be read out using a conventional time-to-digital converter. The readout results are shown in Fig. 3(c). The counting rate of the trigger increases as the incident light increases and finally tends to saturate. The counting rate of the four SNSPD pixels is different under the same light power, which is due to the uneven photon irradiation of the SNSPD. We reconstructed the light intensity distribution of each SNSPD pixel by integrating the counting rate under different incident light powers, and the result is shown in the inset.We measured the time characteristics of the four input channels, as shown in Fig. 3(d). Time delay refers to the time between the output signal of the trigger and the laser synchronization signal, including the photon transmission time in the optical fiber, the thermal transfer time of the trigger, and the transmission time of electrical signals on the coaxial line. The main discrepancy is caused by the thermalization time of the trigger nanowires, which increases with the nanowire length. We counted the time delay distribution of each channel and calculated the time jitter using Gaussian fitting, which is distributed between 0.6 and 0.7 ns. The inset shows the time delay statistics for input channel 3, and the time jitter is approximately 0.62 ns. When the input and output channels are latched, their bias current drops below 2 μA, and the input and output channel resistances exceed 100 kΩ. Thus, the power consumption of the trigger is approximately P = I2(Rin+ Rout) = (2 μA)2 × 200 kΩ = 0.8 μW, where Rin and Rout are the normal state resistances of the input and output channel nanowires, respectively.The exponential proportional relationship for the length of input channel nanowires of the trigger is designed to resolve signals generated by multiple input channels that respond simultaneously. As the number of input channels increases, the nanowire length will increase dramatically. To overcome this problem, we can set the length of input channels to a linear ratio to reduce the rapid growth of nanowire length and improve the scalability of the device. Although the linear-ratio trigger cannot resolve simultaneous responses of input channels, it can be applied to the field of few-photon detection, such as lidar. Due to the time uncertainty introduced by the electron–phonon coupling, quasiparticle diffusion, and ballistic phonon transport,2121. A. N. McCaughan, V. B. Verma, S. M. Buckley, J. P. Allmaras, A. G. Kozorezov, A. N. Tait, S. W. Nam, and J. M. Shainline, Nat. Electron. 2, 451 (2019). https://doi.org/10.1038/s41928-019-0300-8 this trigger based on thermal coupling has a relatively high time jitter, which can be reduced by changing the film material or lowering the operating temperature in the future. The trigger is not sufficient for the readout of SNSPDs with low time jitter, while it is suitable for applications, such as infrared imaging or quantum optics that do not require high time resolution.The detection efficiency in free mode is limited by the working speed of the quenching circuit. Currently, the maximum frequency of the quenching circuit is 100 kHz, which is limited by the digital-to-analog converter (DAC) operating speed and the parasitic inductance of the circuit. Thus, when the power of the continuous laser is too high, the detection efficiency of the trigger will decrease. We will improve the quenching method of the circuit to achieve a higher quenching speed in the future. We compared the SNSPD readout method performance based on SFQ, nanocryotron, and the superconducting nanowire trigger, as shown in Table I, demonstrating the trigger's application potential of the low-power on-chip readout of SNSPDs.
TABLE I. Performance of SFQ, nanocryotron, and superconducting trigger readout methods.
Readout methodCore elementCodingPower consumptionSFQJosephson junctionPulse amplitude coding2424. K. Ota, M. Naruse, T. Taino, J. Chen, L. Kang, P. Wu, and H. Myoren, in 15th International Superconductive Electronics Conference (ISEC) ( IEEE, 2015), pp. 1–3. https://doi.org/10.1109/ISEC.2015.7383479Approximately 1 μW2525. T. Ortlepp, M. Hofherr, L. Fritzsch, S. Engert, K. Ilin, D. Rall, H. Toepfer, H.-G. Meyer, and M. Siegel, Opt. Express 19, 18593 (2011). https://doi.org/10.1364/OE.19.018593NanocryotronWeak link2626. A. N. McCaughan and K. K. Berggren, Nano Lett. 14, 5748 (2014). https://doi.org/10.1021/nl502629xPulse position coding1414. K. Zheng, Q. Y. Zhao, H. Y. B. Lu, L. D. Kong, S. Chen, H. Hao, H. Wang, D. F. Pan, X. C. Tu, L. B. Zhang, X. Q. Jia, J. Chen, L. Kang, and P. H. Wu, Nano Lett. 20, 3553 (2020). https://doi.org/10.1021/acs.nanolett.0c00498Less than 1 μW1414. K. Zheng, Q. Y. Zhao, H. Y. B. Lu, L. D. Kong, S. Chen, H. Hao, H. Wang, D. F. Pan, X. C. Tu, L. B. Zhang, X. Q. Jia, J. Chen, L. Kang, and P. H. Wu, Nano Lett. 20, 3553 (2020). https://doi.org/10.1021/acs.nanolett.0c00498Superconducting nanowire triggerSuperconducting nanowirePulse position codingApproximately 0.8 μWIn summary, we proposed an encodable superconducting trigger based on double nanowires, which can convert a small-current signal to a large-resistance signal using the latching effect of the superconducting nanowire. We applied the trigger for the readout of a 4-pixel SNSPD and reconstructed the light density distribution of incident photons, where the total power consumption is approximately 0.8 μW. The superconducting trigger is promising for application in integrated superconducting electronics and quantum optics in the future.
See the supplementary material for the complete analysis, the device fabrication, and the characterization setup of the superconducting trigger.This work was supported by the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0303401), the National Natural Science Foundation of China (Grant Nos. 12033002, 62071218, 62101240, and 62071214), the Natural Science Foundation of Jiangsu Province (Grant No. BK20210177), the Key-Area Research and Development Program of Guangdong Province (Grant No. 2020B0303020001), the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), and the Jiangsu Provincial Key Laboratory of Advanced Manipulating Technique of Electromagnetic Waves.
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Biao Zhang and Qi Chen contributed equally to this paper.
Biao Zhang: Conceptualization (equal); Writing – original draft (lead); Writing – review & editing (equal). Xuecou Tu: Writing – review & editing (equal). Qingyuan Zhao: Writing – review & editing (equal). Xiaoqing Jia: Writing – review & editing (equal). Jian Chen: Writing – review & editing (equal). Lin Kang: Writing – review & editing (equal). Peiheng Wu: Writing – review & editing (equal). Qi Chen: Writing – review & editing (equal). Labao Zhang: Conceptualization (equal). Rui Yin: Writing – review & editing (equal). Wenlei Yin: Writing – review & editing (equal). Yanqiu Guan: Writing – review & editing (equal). Xiaowen Hu: Writing – review & editing (equal). Chengxiu Li: Writing – review & editing (equal). Hao Wang: Writing – review & editing (equal).
The data that support the findings of this study are available from the corresponding author upon reasonable request.
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