Efficiency of SNSPD in terms of kinetic inductance: Optimization Analysis of Superconducting Nanowire Single-Photon Detectors (SNSPDs) Based on their Kinetic Inductance.
Abstract
Superconducting Nanowire Single-Photon Detectors (SNSPDs) have been established themselves as critical elements in present-day quantum systems, especially in quantum communications, quantum computers, and other quantum related optics. Indeed efficiency is one of the key aspects of SNSPD and one of parameters that defines it is kinetic inductance of the single superconducting nanowire. This article explains the effect of kinetic inductance on the efficiency of SNSPDs and adds further knowledge on how it affects the mechanism of photon detection. We then discuss motion of Cooper pairs in SNSPDs to get insights into the physical mechanism of the device operation and examine how the kinetic inductance, critical current of the nanowire, and speed of the detector response depend on each other. Further, the article discusses numerous optimization strategies to improve SNSPD performance by comparing the kinetic inductance with other material characteristics.
Introduction
Recently, Superconducting Nanowire Single-Photon Detectors have attracted a lot of consideration since they exhibit high efficiency of detection, low rate of dark counts, as well as high speed. These detectors utilize super conducting materials and nanowire geometry to discern individual photons, suitable for quantum applications as QKD and quantum computing.
Among the most critical factors that determine the properties of SNSPDs is their kinetic inductance – a parameter that characterizes the time response and energy dissipation in the nanowire when photon is absorbed and converted into an electric signal. Kinetic inductance is central to how fast the SNSPD can respond to photon events and the general efficiency in photon detection. In this article, we discuss the efficiency of SNSPDs with a particular emphasis on the kinetic inductance effect.
Background on SNSPDs
2.1 Principles of Operation
An SNSPD is composed of a superconducting nanowire, normally niobium nitride (NbN) or tungsten silicide (WSi), in which a meander structure is fabricated to enhance the photon’s interaction length. It runs at a condition below the critical temperature and the nanowire maintains a superconducting condition at normal conditions.
What happens when a photon is incident on the nanowire In the process, energy is deposited at one point, creating a hotspot, which kills the superconducting state. This forms a resistive area and hence temporarily interrupts the superconducting loop. The disrupted region creates voltage pulse, and this voltage pulse is extracted by a cryogenic amplifier. The detector efficiency is determined by the geometry of the wire, the physical properties of the nanowire, physical effects of the different mechanisms involved, and more specifically kinetic inductance.
2.2 Role of Kinetic Inductance
Kinetic inductance is produced by the movement of Cooper pairs in the superconductor and as unique from magnetic inductance which is produced by current flow through a magnetic field. The kinetic inductance in a superconducting material is an entity that exists in inverse proportion to the density of superconducting carriers, also known as Cooper pairs, of the wire in question, proportional to the current through the wire.
That is why kinetic inductance plays a significant role in defining the speed of the SNSPD detector, its response and recovery times after photon absorption. The total inductance in the SNSPD is the geometric inductance and the kinetic inductance because of the superconductivity of the material used in fabrication of the wire. It increases the understanding of how kinetic inductance operates so that an improved design of the detector can be achieved.
The absorption of kinetic inductance and SNSPD efficiency
3.1 Impact On Photon Detection Efficiency
In SNSPDs the efficiency of photon detection is expressed as the probability that the incident photon leads to the appearance of the detectable signal – voltage pulse. This probability depends on the kinetic inductance of the nanowire that modulates the features of the superconducting state at the time of photon absorption.
Whenever a photon is being absorbed by the nanowire, a temporary heat source for the nanowire current is generated thereby ridiing the wire. This current response contains the kinetic inductance in its time constant. Higher kinetic inductance causes longer recoverable time period because the current requires extra time to go back to a basic SRF condition. This slowing of the response can diminish the rate of photon detection especially where high detection rate or fast repetition rates are need.
On the other hand a low kinetic inductance tends to result in faster recoveries, this may increase the detector’s speed and minimize the likelihood of after pulsing, that is false signals arising from the fact that the detector has not fully recovered before the arrival of the next photon. Thus, there is kinetic inductance range that provides an appropriate level of speed with proper efficiency.
3.2 Consequence on the Recovery Time and Dead Time
The dead time, or recovery time, is the interval of time after the first detection of a photon when the SNSPD will not be able to detect another photon. Dead time is thus a function of the time it takes for the nanowire to reset to the superconducting state, which is determined by kinetic inductance. In general, the increase in the kinetic inductance results an increased recovery time as the time for current to damp down and system to evolve to equilibrium.
If the dead time is too long, the effective detection rate of the detector is low and the operation efficiency of the SNSPD decreases.
The Optimization of SNSPD Efficiency with Respect to Kinetic Inductance
4.1 Coherent Kinetic And Geometric Inductance
Therefore for efficient functioning of the SNSPD the kinetic inductance and geometric inductance must be well managed. The geometrical inductance depends on physical dimensions of the nanowire, its width and length and the kinetic inductance is embedded or inherent in the material properties and the level of super conductivity of the wire used. When designing the detector it is therefore important that both factors are well balanced for peak efficiency to be attained.
As mentioned above in most designs, wire length can be used to increase geometric inductance and light coupling or photon absorption but also increases the total inductance degrading the speed of the detector. As such, there is the need to carefully model the dimensions of the wire and the materials properties in order to achieve the right balance of the system efficiency and response time at the same time.
4.2 What Material Should Be Used And Other Superconducting Characteristics
It is evident that for the Efficiency of SNSPD in terms of kinetic inductance the kinetic inductance depends on the type of superconducting material selected for the device. Critical temperature higher and critical current density indicate that the kinetic inductance is lower and responds to a stimulus more quickly, although intrinsic photon absorption efficiency can also be lower. However, materials with low critical temperature and high kinetic inductance might offer even higher photo-detection efficiency at the cost of time resolution.
4.3 Technical Parameters: Cryogenic Temperatures and Kinetic Inductance
Efficiency of SNSPD in terms of kinetic inductance work at cryogenic temperatures, in the range between 1 and 4 Kelvin, at which superconductivity is preserved. Above such temperatures, the electrical resistance of the material is extremely low and the kinetic inductance defines the device behavior. However, results show that changes in temperature are effective in affecting the kinetic inductance through the changes in the density of Cooper pairs in the material. Hence, a high degree of stability of the cryogenic temperature is required to achieve a uniform performance and achieve a high detection efficiency.
