SNSPD characterization

5.3.3.1 Detection efficiency

In this section, we aim to estimate the waveguide-coupled SNSPDs detec-tion efficiency for the relevant wavelength of the PbS/CdS QDs emission at cryogenic temperature. We first used a commercial FDTD solver

(Lumer-Figure 5.13: (a) Schematic of the waveguide cross section with its dimensions and the materials used. (b) Simulation of the absorption of NbTiN nanowires below silicon nitride waveguides as function of the length of the nanowire. The dashed lines show an exponential fit to the simulated absorption data.

ical) to simulate the optical absorption of the superconducting nanowire located below the waveguide as presented in the previsous section 5.2.3.1.

The waveguide is designed with a height of 300 nm and a width of 1000 nm with 1µm of SiO2top cladding (Figure 5.13(a)) while the dimension of the superconducting detector is similar than section 5.2. With a scattered power of 1.1%(1.5%) for TE(TM) polarization, the simulations suggest that the reduction of the detection efficiency due to light scattering is minor. In practice, fabrication imperfections might lead to an increased contribution.

Figure 5.13(b) shows the simulated absorption for TE and TM polariza-tion, overlaid with an exponential fit of the data points. For the fabricated nanowire length of 25µm the absorption reaches 98%(82%) for the TE(TM) mode respectively. The simulated TE(TM) mode profiles propagating in

Figure 5.14: Cross-sections of the silicon nitride waveguide overlayed with the normalized electromagnetic field power of the mode. Optical mode profiles in the waveguide for TE (a) and TM (d) mode. (b) and (c)( (e) and (f) ) show the TE(TM) mode when a 1µm long NbTiN nanowire is introduced below the waveguide.

the waveguide are displayed in Figure 5.14(a) and (d), respectively. The TE mode in Figure 5.14(a) turns into a distorted mode as shown in Fig-ure 5.14(b)-(c) when a 1µm long NbTiN nanowire is introduced below the waveguide. The TM mode in Figure 5.14(d) shows the corresponding dis-tortion depicted in Figure 5.14(e)-(f). The intensity of the electromagnetic field is maximum at the NbTiN wires sides for the TE mode (Figure 5.14(c)) while below the superconducting film for the TM mode. This effect illus-trates a strong coupling of the guided optical modes to the superconducting nanowires and confirms the value of absorption obtained by simulations.

Figure 5.15: Normalized photon counts rate and dark count rates as function of the bias current for two different SNSPDs for 1050 nm and 1300 nm.

Then, we estimate the internal efficiency of the SNSPDs trough exper-imental testing. We used two attenuated lasers with wavelengths of 1050 nm and 1300 nm, enclosing the QD emission (see Figure 5.10). Figure 5.15 shows the normalized photon counts rate and dark count rates as function of the bias current for two different SNSPDs at the wavelengths of 1050 nm and 1300 nm. In Figure 5.15(a), the detector1presents unity internal effi-ciency for 1050 nm resulting in a saturation of the PCR whilst increasing the bias current. Even though the saturation regime was not reached at 1300 nm for detector1and at both wavelength for detector2, we were still able to estimate the internal detection efficiency. Recent publications on the de-tection mechanism of SNSPDs [35, 36] attribute the shape of the PCR curve as function of bias current for low energy photons, to the Fano-fluctuations.

In this model, a detection event for a certain bias current is produced if enough quasi-particles are generated. Therefore, the PCR as function of the bias current is expected to follow a sigmoidal shape. The counts are fitted with an error function (straight lines in Figure 5.15) after subtraction of the dark counts and the coefficients are used for the normalization. For a bias current corresponding to a DCR of∼100 cp, the extracted internal detection efficiency for detector1(Figure 5.15(a)) is between 99% and 95%

for 1050 nm and 1300 nm. Detector2(Figure 5.15(b)) has a significantly lower internal efficiency between 95% and 70% at the wavelength range of interest. A variety of detectors have been characterized and these results present the range of performance for our detectors.

Presuming that spherical PbS/CdS QDs show isotropic emission from their three-fold degenerate bright exciton state [37] in a homogeneous environ-ment, we argue that the high LRDOS in the antenna gap will force an emis-sion polarization along the antenna dipole axis d (Figure 5.11(a)). There-fore, the SNSPD detection efficiency is estimated at 0.9 ±0.1 for the TE mode. Since the isolated pillar of QDs equally couples to the TE and TM

mode of the waveguide, the SNSPD detection efficiency is the average of both efficiencies and yields to 0.8±0.1.

5.3.3.2 Timing jitter and dead time

Figure 5.16: (a) Typical temporal resolution of a superconducting nanowire. The Gaussian fit displayed in red gives a timing jitter of 43 ± 3 ps. (b) Trace of the detection pulse used for the timing jitter measurement. The fitted data is an exponential with a decay constant of∼9 ns. A zoom of the front-edge of an electrical pulse.

Figure 5.16(a) shows the temporal resolution of SNSPD located on the chip and the Gaussian fit gives an timing jitter of 43±3 ps. Figure 5.16(b) shows the correspond detection pulse used to perform the temporal resolu-tion measurement which is recorded with a fast digital oscilloscope (Lecroy Waverunner 640Zi). From the exponential decay of the detection pulse we extracted a dead time of∼9 ns which is used to calculate the kinetic induc-tance of the entire superconducting nanowire detector. It is defined as the product of the dead time of the detector and the load resistance (50 Ω) and yields to Lk = 450 nH. The inset of Figure 5.16(b) displays a zoom of the front edge of the detection pulse. The dashed lines indicate the 20% and 80% of the output pulse amplitude and the difference of the corresponding time gives a rise time of 400 ps.

The waveguide-integrated SNSPDs provide high detection efficiency and excellent timing resolution to characterize the emission lifetime of the Pb-S/CdS QDs.

5.3.4 Experimental set-up for on-chip measurements