Abstract In kinetic inductance detectors (KIDs) and other similar applications of superconducting microresonators, both the large and small-signal behaviour of the device may be affected by electrothermal feedback. Microwave power applied to read out the device is absorbed by and heats the superconductor quasiparticles, changing the superconductor conductivity and hence the readout power absorbed in a positive or negative feedback loop. In this work, we explore numerically the implications of an extensible theoretical model of a generic superconducting microresonator device for a typical KID, incorporating recent work on the power flow between superconductor quasiparticles and phonons. This model calculates the large-signal (changes in operating point) and small-signal behaviour of a device, allowing us to determine the effect of electrothermal feedback on device responsivity and noise characteristics under various operating conditions. We also investigate how thermally isolating the device from the bath, for example by designing the device on a membrane only connected to the bulk substrate by thin legs, affects device performance. We find that at a typical device operating point, positive electrothermal feedback reduces the effective thermal conductance from the superconductor quasiparticles to the bath, and so increases responsivity to signal (pair-breaking) power, increases noise from temperature fluctuations, and decreases the noise equivalent power (NEP). Similarly, increasing the thermal isolation of the device while keeping the quasiparticle temperature constant decreases the NEP, but also decreases the device response bandwidth.
Abstract In kinetic inductance detectors (KIDs) and other similar applications of superconducting microresonators, both the large and small-signal behaviour of the device may be affected by electrothermal feedback. Microwave power applied to read out the device is absorbed by and heats the superconductor quasiparticles, changing the superconductor conductivity and hence the readout power absorbed in a positive or negative feedback loop. In this work, we explore numerically the implications of an extensible theoretical model of a generic superconducting microresonator device for a typical KID, incorporating recent work on the power flow between superconductor quasiparticles and phonons. This model calculates the large-signal (changes in operating point) and small-signal behaviour of a device, allowing us to determine the effect of electrothermal feedback on device responsivity and noise characteristics under various operating conditions. We also investigate how thermally isolating the device from the bath, for example by designing the device on a membrane only connected to the bulk substrate by thin legs, affects device performance. We find that at a typical device operating point, positive electrothermal feedback reduces the effective thermal conductance from the superconductor quasiparticles to the bath, and so increases responsivity to signal (pair-breaking) power, increases noise from temperature fluctuations, and decreases the noise equivalent power (NEP). Similarly, increasing the thermal isolation of the device while keeping the quasiparticle temperature constant decreases the NEP, but also decreases the device response bandwidth.
In kinetic inductance detectors (KIDs) and other similar applications of superconducting microresonators, both the large and small-signal behaviour of the device may be affected by electrothermal feedback. Microwave power applied to read out the device is absorbed by and heats the superconductor quasiparticles, changing the superconductor conductivity and hence the readout power absorbed in a positive or negative feedback loop. In this work, we explore numerically the implications of an extensible theoretical model of a generic superconducting microresonator device for a typical KID, incorporating recent work on the power flow between superconductor quasiparticles and phonons. This model calculates the large-signal (changes in operating point) and small-signal behaviour of a device, allowing us to determine the effect of electrothermal feedback on device responsivity and noise characteristics under various operating conditions. We also investigate how thermally isolating the device from the bath, for example by designing the device on a membrane only connected to the bulk substrate by thin legs, affects device performance. We find that at a typical device operating point, positive electrothermal feedback reduces the effective thermal conductance from the superconductor quasiparticles to the bath, and so increases responsivity to signal (pair-breaking) power, increases noise from temperature fluctuations, and decreases the noise equivalent power (NEP). Similarly, increasing the thermal isolation of the device while keeping the quasiparticle temperature constant decreases the NEP, but also decreases the device response bandwidth.
In this thesis I describe work on developing theoretical and numerical models of supercon- ducting thin-film microwave resonators. Superconducting resonators are used in a variety of applications, one of which is as kinetic inductance detectors (KIDs). KIDs are ultra-low noise, highly sensitive, multiplexable detectors, with uses in a wide variety of fields including astrophysics, medical imaging, and particle physics. Resonators are also crucial for supercon- ducting qubit readout, superconducting mixers and parametric amplifiers, and as multiplexers for other devices. The results described in this thesis apply to all thin film resonators, but are primarily described in the context of KIDs. I develop models of how constant absorbed power affects superconducting thin films, driving them out of thermal equilibrium with the bath. Using the Chang & Scalapino equations, I calculate numerically the steady-state quasiparticle and phonon distributions for various sources of power (sub-gap and above-gap photons and phonons, single frequency and broadband). Many new results emerge, a few of which are: the quasiparticle heating effects of microwave power, explaining the experimentally measured saturation of resonator performance; the frequency dependence of the quasiparticle generation efficiency in the sub-mm wavelength range; and the importance of phonon trapping in thin films at low temperatures. I then use these nonequilibrium results in higher-level device models. Starting from a generic framework for resonators, I present and implement a model of a KID with variable thermal isolation. I calculate the effects of quasiparticle heating on both the large-signal and small-signal behaviour, highlighting the effects of electrothermal feedback caused by readout power. Electrothermal feedback is shown to be able to increase or decrease the magnitude and bandwidth of the responsivity and noise, depending on the operating point. Finally, I propose an experimental measurement of quasiparticle heating effects in a new device – a four-port ring resonator. In such a device, unlike in the standard two-port resonator, the device can be heated and read out independently. I develop detailed models for the thermal and electrical behaviour of these devices, and suggest a scheme by which the quasiparticle heating effects of microwave power, predicted in this thesis, can be measured.
We demonstrate strong negative electrothermal feedback accelerating and linearizing the response of a thermal kinetic inductance detector (TKID). TKIDs are a proposed highly multiplexable replacement to transition-edge sensors and measure power through the temperature-dependent resonant frequency of a superconducting microresonator bolometer. At high readout probe power and probe frequency detuned from the TKID resonant frequency, we observe electrothermal feedback loop gain up to L≈16 through measuring the reduction of settling time. We also show that the detector response has no detectable non-linearity over a 38% range of incident power and that the noise-equivalent power is below the design photon noise.
Kinetic Inductance Detectors (KIDs) consist of thinfilm superconducting resonators. An incoming photon breaks Cooper pairs, and causes the surface impedance of the resonator to change. The resonant frequency shifts, and the absorption event is recorded by monitoring the change in microwave transmission amplitude and phase. In this paper, we show that the power deposited by the microwave readout signal can cause the temperature of the quasiparticles in the superconducting film to switch between well-defined states. Experimentally, the effect appears as a discontinuity in the resonance curve, but is actually a hysteretic switching between thermal states as the readout frequency is swept up and down. We present numerical simulations that predict, quite clearly, the existence of hysteretic switching in low Tc superconducting resonators. The switching occurs as a direct consequence of the relationship between the readout power absorbed by the resonator as a function of temperature, and the finite thermal impedance of the quasiparticle-phonon coupling. This work may lead to an improvement of the power handling in KIDs, which is the easiest way of noise reduction in these devices, and to a better understanding of electron-phonon coupling in superconductors.
Low temperature microwave superconducting resonators (SRs) are attractive candidates for producing quantum-sensitive, arrayable energy or power detectors for astrophysical and other precision measurement applications. Their readout uses a microwave probe signal with quanta of energy well below the threshold for pair-breaking in the superconductor. We have calculated the non-equilibrium quasiparticle and phonon distributions generated by the photons of the probe signal of a resonator operating well below its superconducting transition temperature T c as the absorbed probe power was changed using the coupled kinetic equations described by Chang and Scalapino. The calculations give insight into a rate equation estimate which suggests that the quasiparticle distributions can be driven far from their thermal equilibrium value for typical readout powers. From the driven quasiparticle distribution functions, the driven quasiparticle number densities and lifetimes were calculated. An effective temperature to describe the driven quasiparticles was defined. The non-equilibrium lifetimes were compared to the distribution-averaged thermal lifetimes at the effective temperature and good agreement was found typically within a few per cent. We used the non-equilibrium quasiparticle distribution to model a representative SR. The complex conductivity and hence the frequency dependence of the experimentally measured forward scattering parameter S 21 of the SR as a function of absorbed power were found. The non-equilibrium S 21 cannot be accurately modeled by a thermal distribution even at its own elevated temperature, having a higher quality factor in all cases studied, although for low absorbed powers the two effective temperatures are similar. From the non-equilibrium lifetimes and number densities we determined the achievable noise equivalent power (NEP) of the resonator used as a power detector as a function of absorbed microwave power. Simpler expressions to evaluate the effective quasiparticle temperature as a function of absorbed power have also been derived. We conclude that multiple photon absorption from the microwave probe increases the quasiparticle number above the thermal background and ultimately limits the achievable NEP of the resonator at temperatures well below T c .
Microwave Kinetic Inductance Detectors (MKIDs) are extremely sensitive radiation detectors based on superconducting resonators that can be combined in large arrays on a single readout line within a limited frequency bandwidth. This makes MKIDs ideal detectors for the ultimate far-infrared observatory: a future space-based actively cooled telescope with its performance solely limited by the low universe background radiation. However, to reach these detector requirements, state-of-the-art MKIDs still need a order of magnitude improvement in device sensitivity. In this work, the MKID sensitivity is improved by reducing the aluminium volume that absorbs pair-breaking radiation into quasiparticle excitations, while making sure all radiation is still absorbed. Furthermore, a key requirement is sufficient reduction of excess noise as to keep the device intrinsically limited by thermally driven random fluctuations in the number of quasiparticles in absence of radiation, or Generation-Recombination (G-R) noise. To this end, a model is developed that describes the noise contributions as function of device geometry, readout power, material properties and radiation power. Subsequently, a realistic MKID design is presented and tested that reduces excess noise and maximises the sensitivity, expressed as Noise Equivalent Power (NEP). At high temperatures, good overall agreement is found between the measured noise spectra and the model. At low temperature T = 120 mK, the measurement results give an optical NEP similar to current state-of-the-art MKIDs. The NEP is not as low as expected due to short quasiparticle lifetimes, an unexpected decrease in the G-R noise level and a very high excess noise attributed to Two-Level Systems (TLS) noise that starts to dominate the already low G-R noise spectrum at low temperatures. Possibly, the quick quasiparticle lifetime saturation and noise level drop are caused by a strong readout power effect, as the readout power is known to create excess quasiparticles and to cause a strongly non-thermal electron energy distribution in the aluminium strip of the MKID. However, the exact microscopic details of these effects are unknown and not studied in this project. Based on the current chip design, a straightforward way to improve device performance and study the readout power effect in more detail is a reduction of the high TLS noise levels, which is possibly fabrication related. This would allow an unobstructed view of the G-R noise spectrum at low temperatures, thereby allowing both a study of the readout power effect on the quasiparticle system, and ultimately achieving the improvement in NEP needed reach the detector requirements for the ultimate space-based far-infrared observatory.