SNSPDs detection mechanism

Figure 1.1: Meandered shaped nanowire (colored in blue). The circle represents the 3-sigma area of the optical mode of the fiber coupled to the detector, where 99.73% of the incident photons are located.

1.2 SNSPDs detection mechanism

Superconducting Nanowire Single Photon detectors were first introduced in 2001 [3].

This new type of detectors offers unprecedented quantum efficiencies [4, 5, 6] which have been pushed up to near unity very recently [7, 8]. Sub-Hertz dark count rates [9] can be obtained and a wide range of wavelength from X-Ray to mid-infrared can be detected.

SNSPD have a high temporal resolution, with timing jitter values typically under 100 ps and intrinsic jitter values below 10 ps have been demonstrated [10]. Detection rates of hundred of MHz can be obtained. However not all of these parameters can be obtained with the exact same device, and SNSPDs are typically designed to favor one or several characteristics above the others. Nevertheless SNSPDs currently offer the best combined performances among other existing single-photon detectors [11].

An SNSPD structure is fairly simple and the working principle of SNSPDs can be described in an intuitive manner. The detector consists, as the name suggest, in a thin superconducting film (typically few nm) of type-II superconductor, patterned into a long wire with a typical width of ∼100 nm. This nanowire is usually shaped as a meander which aims at covering a given surface area, usually much larger than the nanowire width itself, as shown on figure 1.1.

The meander area is usually chosen to match the optical mode diameter of an optical

is essential to reach high detection efficiencies. The percentage of the detection area effectively covered by the nanowires depends on the nanowire width and of the spacing between each meander line. This value is often referred to as the fill factor of the detector (FF) with :

F F = w

w+d (1.1)

withwthe nanowire width, and dthe distance separating two lines of the meander.

The nanowire is biased with aμA electronic currentI_b(represented on fig. 1.1). Absorption of a single photon into the superconducting film will make the superconducting nanowire switch to a resistive state, which will create a resistance of ∼1 kΩ, and will redirect the bias current to the readout circuit. Although the exact detection mechanism is not fully understood, the photo absorption process is usually described with the six consecutive steps shown on fig. 1.2 (see for example ref [3, 12, 13, 11]). However this is not the only description that has been done of the detection mechanism, and in particular the points (iii) and (iv) of fig. 1.2 are subject to discussion. Recent fundamental achievements on understanding the detection mechanisms can be found in ref. [14], but answering this question goes far beyond the scope of this thesis. The next paragraphs briefly presents important notions and definitions which will be used along this document.

(i)

(ii)

(iii) (iv)

(v)

t ≈ 6 nm w ≈ 150 nm

(vi)

I

Figure 1.2: Basic operation principle of an SNSPD (see [3, 12, 13, 11]) (i) A thin superconducting nanowire is biased near its critical current. (ii) An incoming photon is absorbed into the nanowire. (iii) The energy diffusion creates a cloud of excited electrons and phonons, so-called hotspot. (iv) This cloud then obstructs the current flow, leading to a non-superconducting cross-section in the nanowire that grows under the influence of Joule heating. (v) Because of the large resistive section (∼1 kΩ), the current is redirected in the readout electrics, producing a voltage pulse. (vi) The nanowire cools down and becomes superconducting again, ready to detect another photon.

1.2. SNSPDs detection mechanism

Superconductivity

The superconducting absorptive film is at the core of the detector. Important properties of superconductors such as the penetration length [15], the coherence length [16] and the bandgap [17] were described in the early 1950s. The properties of type I superconductors were modeled by John Bardeen, Leon Cooper, and Robert Schrieffer in 1957 in what is commonly called the BCS theory of superconductivity [18, 19]. The theory goes far beyond the scope of this work, but a few key principles are of interest to us. Superconductors carry pairs of electrons, called Cooper pairs, which travel without interacting with the superconductor’s lattice and hence move resistance-free. This phenomenon is related to the bandgap of the material : the charge carriers energy is quantized, so that they do not have any available energy levels withing reach of the energies of interaction with the lattice.

Increasing the temperature will bring energy to the particles and get carriers across the gap and break the superconductivity. This temperature is called the critical temperature T_c of the material, and is directly linked to the band gap∆ in type I superconductors such that∆(T = 0) = 1.764kbTc.

Increasing the energy of the pairs can be done in different ways. Similarly to the critical temperature, a critical external magnetic field H_c (orB_c) and critical current density J_c can be measured. This can be represented on a phase diagram figure where the boundary between the superconducting state and the resistive state depends on those parameters (fig. 1.3). Type I superconductors are pure metals with small bandgaps (with typical Tc

around 1 K) hence they exhibit a very fragile superconductivity state and have limited practical applications. Type II superconductor are compounds or alloys and exhibit a mixed-state where single quanta of magnetic flux are allowed through the material up to a critical fieldHc2 much higher than Hc. Type II superconductor typically have higher T_c and H_c values and exhibit a more stable superconducting state. They have been the materials of choice for SNSPDs and other kind of superconducting detectors¹. A consequence of the nature of the Cooper pairs as the charge carrier is the kinetic inductance of the superconducting film. Nanowire made of superconductivity material exhibit a non-negligible inductance related to the material, temperature, and shape of the nanowire. The inductivity can be estimated from measured values [22, 23], and the final inductance value then depends on the length l, width wand thicknesst of the nanowire as well:

Wherem is the mass of the electron,nsis the superconducting electron density and λ_L is the London penetration depth, which can be estimated from the value of the penetration

1It is interesting to note that so called superconducting superheated granular detectors (SSG) made of type I superconductors have been investigated in the past for neutrino detection [20, 21] and seemed

depth at T=0, λ₀: λ_L= λ₀

r 1−

T Tc

4 (1.3)

Based on this calculation and experimental measurements on our superconducting thin films, we estimate the inductance of our 16 μm x 16μm SNSPDs between 500 nH to 1μH.

Figure 1.3: Phase diagram of type I and type II superconductor. Type II exhibit a mixed state (blue zone) in which vortex of magnetic flux can exist inside the superconducting material.

Image : Wikimedia Commons [24]

Energy-current relation and quantum efficiency

Intuitively, a photon bringing an energy lower than the bandgap of the superconducting thin film cannot break any Cooper pair. On the other hand, a high energy photon can bring enough energy to break multiples pairs. By applying a bias currentIb inside the nanowire, the energy of the pairs is increased so that a single photon can bring a sufficient amount of energy to break enough Cooper pairs and create a local resistive hotspot (step (ii) and (iii) of figure 1.2). There is therefore a specific threshold current which enables detections of photons at a given energy. The energy-current relation is a key feature of SNSPDs and was previously investigated with our devices using different incident wavelengths [25]. In the frame of this work, incident photons at 1550 nm were used for all the measurements. Typical detection vs. bias current curves (such as the one shown on figure 2.6) have a step-function shape. The transition region where the detection increases between 0 to its maximal value has been described as the consequence of Fano fluctuations, coming from the statistical nature of the quasiparticle creation process [26, 27, 28, 29]. The maximal value reached after the transition is referred to as the saturated efficiency of the detector, and it is crucial to use bias currents in this region to obtain the best performances of the thin film. The whole system detection efficiency (SDE) of the detector is one of the key characteristic of an SNSPD and is of course directly impacted by the quantum efficiency of the thin film. The SDE measurement setup and results obtained are presented in the next chapter, section 2.2.1.

1.2. SNSPDs detection mechanism

Electro-thermal behavior

Figure 1.4: Typical detector readout. The two inset curves illustrate the current vs time behavior in the SNSPD (red) and inside the readout resistor and transformer (blue). A DC coupling is created using a transformer connected to the ground.

The time dynamics of a detection event is an important feature to understand the recovery time and maximum counting rate of a detector. After the hotspot formation in a nanowire section, the high resistive impedance of the thin film of material will force the current into the readout circuit. This signal will be pre-amplified at 40 Kelvin and read by the photon counting electronics at room temperature. The time dynamics of the current and temperature of the nanowire is central to the functioning of the device. Typical current behavior and DC readout circuit is illustrated on fig. 1.4. The DC coupling ensures the functioning of the readout at high detection rates where an AC coupling will create an increase of the bias current inside the detector due to charge accumulation on the capacitor² [31]. After a detection event, the nanowire is in a highly resistive state due to local Joule heating in the resistive strip (P_{J oule} =I_b²·R). Hence the current inside the nanowire will drop with a time constant τf all = Lk/(Rhotspot+Rs). During this short time (τ_{f all} typically is∼100 ps) the Joule heating in the resistive nanowire strip will decrease as well. This in turns influences the resistance of the hotspot, which starts cooling down. During the cooldown, as soon as the critical temperature Tcis reached, the nanowire impedance will fall down and current will start flowing back with a timing constant τ =L_k/R_s [32], with τ typically in the range of tens of nanoseconds.

However if this dynamic is too fast, Joule heating of the hotspot will be self-sustaining, resulting in a stable resistive domain [13, 33]. Figure 1.5, taken from the work of Yang et al. [13], illustrate this phenomenon. It is essential to control this dynamic to ensure the proper functioning of the device. This can be done by adapting the resistance of the readout to the kinetic inductance created by the section and length of the nanowire, with L_k ∝ l

w·t. Nevertheless, increasing the bias current too much will always results in the formation of a self-heating hotspot, and the detector will remain in a latched state. This

Figure 1.5: Plot of the current I inside the nanowire depending on time (a) and tempera-ture (b), for a device with Lk = 60nH and different values of load resistorR.

Images : Yang et al. [13]

limit is commonly called the latching current I_L of the device, and particular care has to be taken so that its value is higher than the saturation current of the detector. Another regime exists, where the hotspot is not self-heating, but an excessively fast dynamic of the bias current leads to an increase of the current density above the critical value J_c(T) for a given temperature during the cool down. This results in an oscillation-relaxation regime. The current at which this effect is observed is referred as the critical current Ic

of the detector.

Important characteristics of SNSPDs are directly linked to the dynamic of the bias current.

Indeed, as described above, a too low bias current effectively leads to a zero efficiency of the detector after detection. The efficiency of the detector will recover over time, according to the bias current dynamic and the energy-current relation. The recovery-time (RT) of the efficiency will be discussed in greater details in section 2.2.3. The detection rate of conventional SNSPDs is ultimately limited by the recovery time, hence by the time dynamic of the bias current [32]. If consecutive photons are absorbed with short time intervals below the recovery time, the average detection probability of the second photon will be lowered as the detector full efficiency was not yet recovered. Consequently, at high detection rates where successive detections can happen in time intervals of the order of τ, the average SDE drops. Definition of the SNSPD maximum detection rate, measurement and results obtained with single-meander SNSPDs are presented in section 2.2.2. Improving the maximum detection rate has been a large part of this work, and extensive discussions on possible solutions and results obtained are presented in chapters 3 and 4.