The sensitivities, saturation powers, and response times of Kinetic Inductance Detectors depend on the degree to which the quasiparticle and phonon temperatures differ when readout and signal power are applied. Previously, we proposed a model for saturation in KIDs, and found that hysteretic switching, which is seen experimentally, emerges from the model in a natural way. Here we extend our work, and show through a diagrammatic rep- resentation of operating-point trajectories that output pulse shapes can be calculated for non-hysteretic and hysteretic changes of state driven by readout-frequency, readout-power, and signal-power pulses. The work has several applications: (i) Understanding quasiparticle and phonon relaxation, and their dependence on film and substrate thickness. (ii) Recovering quasiparticle cooling functions from measurements. (iii) Understanding the relationship between optimum readout power and device and material parameters. (iv) Characterising the time-dependent behaviour of photon-counting KIDs, including nonlinearity and pile up.
The sensitivities, saturation powers, and response times of Kinetic Inductance Detectors depend on the degree to which the quasiparticle and phonon temperatures differ when readout and signal power are applied. Previously, we proposed a model for saturation in KIDs, and found that hysteretic switching, which is seen experimentally, emerges from the model in a natural way. Here we extend our work, and show through a diagrammatic rep- resentation of operating-point trajectories that output pulse shapes can be calculated for non-hysteretic and hysteretic changes of state driven by readout-frequency, readout-power, and signal-power pulses. The work has several applications: (i) Understanding quasiparticle and phonon relaxation, and their dependence on film and substrate thickness. (ii) Recovering quasiparticle cooling functions from measurements. (iii) Understanding the relationship between optimum readout power and device and material parameters. (iv) Characterising the time-dependent behaviour of photon-counting KIDs, including nonlinearity and pile up.
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.
We consider the effects of quasiparticle heating on the dynamical behaviour of superconducting microresonators operating with high readout powers. It is seen that resonance-curve distortion and hysteretic switching are an inevitable consequence of the forms of the quasiparticle heating and cooling functions. The model uses a diagrammatic representation of dynamical behaviour to gain an insight into how the instantaneous operating point moves in response to step changes in readout power, signal power, bath temperature, and frequency. The coupling quality factor has a marked effect on non-linear behaviour. The model is used to calculate the waveforms generated when a device switches between hysteretic states. The work suggests that measured response times need not be representative of intrinsic quasiparticle relaxation rates.
A model is presented for readout-power heating in kinetic inductance detectors. It is shown that the power dissipated by the readout signal can cause the temperature of the quasiparticle system in the superconducting resonator to switch between well-defined states. At low readout powers, only a single solution to the heat balance equation exists, and the resonance curve merely distorts as the readout power is increased. At high readout powers, three states exist, two of which are stable, and the resonance curve shows hysteretic switching. The power threshold for switching depends on the geometry and material used but is typically around −70 dBm for Aluminum resonators. A comprehensive set of simulations is reported, and a detailed account of the switching process is given. Experimental results are also shown, which are in strong qualitative agreement with the simulations. The general features of the model are independent of the precise cooling function, and are even applicable for resonators on suspended, thermally isolated, dielectric membranes, where an increase in quasiparticle lifetime is expected. We discuss various extensions to the technique, including the possibility of recovering the cooling function from large-signal measurements of the resonance curve.
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.
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.