Working Principle and LTspice Simulations

As multipixel detectors, series and para SNSPDs also take advantage of shorter nanowires.

Figure 3.5 shows the equivalent schematic of both solutions. Simulations helped us define approximate kinetic inductances and resistor values. Designs with resistors from 2 to 20 Ωand kinetic inductances from 3 nH to 200 nH have recovery time in the same order of magnitude or shorter than longer single-meander SNSPDs. An important point to take into account is that, unlike multipixels detectors presented above, the different nanowires used in series and parallel designs are not galvanically independent from each other.

Hence, when one nanowire becomes resistive after a photodetection, the bias current in the remaining nanowires will also be impacted. The LTspice simulation gives an important insight on the working principle and bias current behavior of the two different designs.

Series SNSPDs

The series SNSPD design was first proposed as a photon-number resolving solution [59, 60]

and have been mainly used for this task since [63, 64, 65]. In this case, the output signal is created by the voltage drop on the parallel resistor when one or more of the nanowire becomes resistive. LTspice simulations shows an output signal high enough for amplification and discrimination, although slightly lower than what is expected with single-meander SNSPDs, as the parallel resistor reduces the total impedance seen by the nanowire after a detection event. An advantage of this design is the low electronic crosstalk between the nanowires after detection. As shown on fig. 3.6a when a nanowire

3.3. Parallel and Series SNSPDs

(a) Series SNSPD equivalent schematic. Each nanowire is connected to an integrated resistor in parallel, which is necessary to prevent latch-ing after detection in a nanowire. The parallel resistor will act as a low impedance path.

(b) Parallel SNSPD equivalent schematic.

Series resistors are used to insure that the bias current is evenly distributed among the nanowires.

Figure 3.5: Schematics of the designs tested for improved detection rates and low readout complexity. Both designs only require a single coaxial line and amplification channel.

The value of the resistors used will have a direct impact on the recovery time of each nanowire. Low resistance values will decrease the timing constant τ, hence slow down the recovery time of the nanowire. However, too high resistance values will make the device re-trigger and eventually get blocked in a latched state.

0 10 20 30 40 50 60 70

Figure 3.6: LTspice simulation results for series and parallel designs ran with different number of nanowires N. The curve show the variation of bias current in the N −1 superconducting nanowires (inside the blue rectangle in the insets schematics) in the event of a photo absorption by a single nanowire.

absorbs a photon, the bias current flows mainly into the integrated parallel resistor and only part of it is flowing through the readout circuit. Therefore, the remaining nanowires experience only a small variation of the bias current, in the order of hundreds of nA. However, the design suffers from the asymmetry between the different pixels : the propagation path of the signal is different for each nanowire, and high frequency signals will travel through a number of nanowire and resistor pairs that depends on the position of the photo absorption. The simulation does not take into account parasitic capacitance and high frequency impedance of the different components, so this impact was difficult to predict. Jitter measurements presented in section 3.3.4 show that indeed, this has an impact on the shape and timing of the output signal which travels through the different parts of the structure after a detection.

Parallel SNSPDs

Parallel designs have been used to demonstrate photon-number-resolving detection [66], as well as fast recovery time and ultrashort output pulses [61, 62]. However, to the best of our knowledge, their potential for achieving larger detection rates has not been fully explored. Indeed, the above mentioned works on ultrafast SNSPDs report measurements at a detection rate of only 100 kHz [61, 62] and an efficiency of 0.01% [62]. As we observed, the problem seems to be that at high detection rate, electronic crosstalk between the different nanowires (which was reported in the literature since the first designs [61, 67]) cumulates, and this leads to a cascading effect between the different nanowires. Ultimately, this can lead to latching, i.e. all nanowires can end up in a steady resistive state and the whole detector is effectively disabled.

Indeed, the working principle of parallel design is different from the series SNSPDs described previously. When a nanowire switches to its resistive state after a detection event, its bias current is redirected to the parallel remaining nanowires as well as in the readout. The kinetic inductance of the parallel nanowires prevents high frequency components of the signal to be shorted to the ground, hence a signal high enough for amplification will flow through the readout. Nevertheless a non-negligible part of the bias current will be directed in the parallel nanowires and add to their own bias current.

Simulation results on fig. 3.6b show that this effect has to be taken into account when designing a parallel SNSPD. The results presented on fig. 3.6b are obtained with a kinetic inductance of 50 nH per nanowire and series resistors of 5Ω. Increasing the resistor value do not solve the crosstalk issue, however this is expected to decrease the critical current below the saturation current (for values ∼20 Ω) as the timing of the recovering current decreases. The readout load is simulated with a 10 nF capacitor and a 50 Ωresistor to the ground. The bias current per nanowire is 40 μA. In this case, a device made of 5 wires in parallel will experience an increase of almost 9 μA after a detection. Increasing the number of nanowires helps reduce the electronic crosstalk as the current is divided into more paths. To avoid latching, the bias current per nanowire I_b should be kept lower

3.3. Parallel and Series SNSPDs

Figure 3.7: Simulation of the cumulative crosstalk in a parallel SNSPD design. Two photons are absorbed in the two left-most nanowires at time t1= 10 ns andt2 = 20 ns.

The blue curve shows the bias current in each remaining nanowire. In this event, a detector with nanowires designed such thatIc= 32 μA will latch even though it would have withstood a single photoabsorption. Decreasing the nominal bias current below 30 μA would solve this issue, but the device could still be impacted by consecutive detections at shorter time intervals or with more consecutive photons.

thanIcby a margin of at least the same value as the expected crosstalk. The expected crosstalk can be estimated from the poissonian distribution of the incoming photons, for an average rate µ.

However this observation is only valid at low detection rate where only single photodetec-tion can happen in short time interval. It is likely that at higher rates, where consecutive photodetection can happen in time intervals lower than the recovery time of each nanowire, this effect will cumulate, as shown on fig 3.7. We consider this is a plausible explanation to why high detection rates were not achieved with similar structure before. Experimental tests have been done with parallel detectors and we could confirm that they have a latching point which is dependent on the detection rate, bias current, and number of nanowires, as will be explained in section 3.3.3.