Fig. 1. (a) Cross-section schematic diagram of the NbN SMSPD. From top to bottom, optical stacks correspond to a NbN microstrip, a 13-layer SiO2/Ta2O5 distributed Bragg reflector, and a Si substrate, respectively. (b) Simulated microstrip thickness dependence of optical absorptance at different f (0.4, 0.6, and 0.8), with a fixed strip width of 1 μm. (c) Simulated wavelength dependence of optical absorptance for microstrips with varied f in a wavelength range of 1300–1900 nm at two different polarizations of light: TE (solid lines) and TM (dashed lines).

Fig. 2. Layouts [top panels, (a)–(d)] and magnified SEM images [bottom panels, (e)–(h)] of four different SMSPDs: (a) and (e), the short micrometer bridge; (b) and (f), the modified double spiral strip; (c) and (g), the regular double spiral strip; (d) and (h), the conventional meandered strip. The f of the microstrips [(b)–(d), (f)–(h)] is 0.8. The blue arrows mark the directions of the current flow.

Fig. 3. (a) Current and voltage (I-V) trace for NbN SMSPD with (red line) and without (blue line) 6.8 Ω shunt resistor at 2.1 K. The switching currents are 80 μA for shunt (Iswshunt) and 66 μA for non-shunt (Isw). (b) Switching currents without a shunt resistor versus different geometric structures (Bridge, Spiral-1, Spiral-2, and Meander) with error bars measured also at 2.1 K.

Fig. 4. Comparison of SDE (solid scatters) and DCR (open scatters) of the SMSPDs fabricated with irradiated and unirradiated NbN thin films as a function of bias current (Ib) at 2.1 K. Inset: optical coupling image of the tested device captured by an infrared camera after the laser spot (emitted from a lens SMF) eccentrically aligned to the active area of the detector (marked with a dashed circle).

Fig. 5. (a) Bias current dependences of SDE and DCR of the SMSPD (“irradiated” chip), measured at two different temperatures, with 1550 nm light illumination. (b) Maximum (solid sphere) and minimum (solid square) SDEs measured at two different polarizations of light at 0.84 K. Inset: a microscope image of the SMSPD with an active area of 50 μm in diameter. Dashed lines are sigmoid function fits in both figures.

Fig. 6. DCR of the best SMSPD with and without fiber (i.e., the intrinsic DCR) as a function of the normalized bias current (Ib/Isw), recorded at ∼0.84  K.

Fig. 7. Histogram of time-correlated photon counts measured at 1550 nm. (a) Ib=95  μA (red circle). The blue line is the Gaussian distribution fit, with the FWHM of 47.5 ps. (b) Ib=76  μA (red triangle). The black line is superposition of two peaks with the FWHM of 142.4 ps. The green-dashed and orange-dotted lines are the Gaussian distribution fits for the main peak and secondary peak, respectively. (c) The bias current dependence of the TJ in a range of 70–95 μA.

Fig. 8. (a) Oscilloscope single pulse waveform graph of response versus time. The exponential fitting of the falling edge is given as 36 ns. (b) The dependence of SDE and count rate of SMSPD at 0.84 K. The count rate is ∼5.7  MHz at the 3 dB point. (c) Wavelength dependencies of the absorptance and SDE at TE polarization and 0.84 K for simulated absorptance (red dashed line) and the measured values with error bars (red stars). (d) The SDE and DCR versus Ib with an MMF coupling at 0.84 K, recorded at two different photon fluxes: 10⁵ photons/s (blue square) and 10⁶ photons/s (red sphere). The dashed line is the sigmoid fit for the data recorded at 10⁵ photons/s. Inset: the MMF coupling TJ is 50 ps at Ib=95  μA.

Fig. 9. Simulated wavelength dependence of optical absorptance for microstrips with two different widths (w=1 and 3 μm) and two different filling factors (f=0.80 and 0.88) in a wavelength range of 1300–1900 nm, respectively.

Fig. 10. (a) Bias current dependence of normalized detection efficiency (NDE) for the irradiated SMSPD, recorded under the 1064 nm and 1550 nm photons’ illumination, while operated at 0.84 K with a shunt resistor. Arrows indicate the locations of the Idetmax–sh determined for the two different wavelengths. The dashed line is a sigmoidal fit for the data measured at 1550 nm. (b) Dependence of the maximal detection current on the photon’s energy at different γ and width (w). The open dots are the calculated data obtained from Vodolazov’s paper (inset of Fig. 11 in Ref. [19]), with γ=10, ξc=6.4  nm, and Tc=10  K for NbN. The solid star symbols are our experimental results, with estimated γ=14, ξc=7.7  nm, and Tc=6.4  K for the irradiated NbN device.