Thin-film superconductors with thickness ∼30–500 nm are used as non-equilibrium quantum detectors for photons, phonons or more exotic particles. One of the most basic questions in determining their limiting sensitivity is the efficiency with which the quanta of interest couple to the detected quasiparticles. As low temperature superconducting resonators, thin films are attractive candidates for producing quantum-sensitive arrayable sensors and the readout uses an additional microwave probe. We have calculated the quasiparticle generation efficiency η s for low energy photons in a representative, clean thin-film superconductor (Al) operating well below its superconducting transition temperature as a function of film thickness, within the framework of the coupled kinetic equations described by Chang and Scalapino (1978 J. Low Temp. Phys. 31 1–32). We have also included the effect of a lower frequency probe. We show that phonon loss from the thin film reduces η s by as much as 40% compared to earlier models that considered relatively thick films or infinite volumes. We also show that the presence of the probe and signal enhances the generation efficiency slightly. We conclude that the ultimate limiting noise equivalent power of this class of detector is determined by the thin-film geometry.
Thin-film superconductors with thickness ∼30–500 nm are used as non-equilibrium quantum detectors for photons, phonons or more exotic particles. One of the most basic questions in determining their limiting sensitivity is the efficiency with which the quanta of interest couple to the detected quasiparticles. As low temperature superconducting resonators, thin films are attractive candidates for producing quantum-sensitive arrayable sensors and the readout uses an additional microwave probe. We have calculated the quasiparticle generation efficiency η s for low energy photons in a representative, clean thin-film superconductor (Al) operating well below its superconducting transition temperature as a function of film thickness, within the framework of the coupled kinetic equations described by Chang and Scalapino (1978 J. Low Temp. Phys. 31 1–32). We have also included the effect of a lower frequency probe. We show that phonon loss from the thin film reduces η s by as much as 40% compared to earlier models that considered relatively thick films or infinite volumes. We also show that the presence of the probe and signal enhances the generation efficiency slightly. We conclude that the ultimate limiting noise equivalent power of this class of detector is determined by the thin-film geometry.
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 .
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.
Abstract We calculate nonequilibrium quasiparticle and phonon distributions for a number of widely-used low transition temperature thin-film superconductors under constant, uniform illumination by sub-gap probe and pair-breaking signal photons simultaneously. From these distributions we calculate material-characteristic parameters that allow rapid evaluation of an effective quasiparticle temperature using a simple analytical expression, for all materials studied (Mo, Al, Ta, Nb, and NbN) for all photon energies. We also explore the temperature and energy-dependence of the low-energy quasiparticle generation efficiency η by pair-breaking signal photons finding in the limit of thick films at low bath temperatures that is material-independent. Taking the energy distribution of excess quasiparticles into account, we find as the bath temperature approaches the transition temperature in agreement with the assumption of the two-temperature model of the nonequilibrium response that is appropriate in that regime. The behaviour of η with signal frequency scaled by the superconducting energy gap is also shown to be material-independent, and is in qualitative agreement with recent experimental results. An enhancement of η in the presence of sub-gap (probe) photons is shown to be most significant at signal frequencies near the superconducting gap frequency and arises due to multiple photon absorption events that increase the average energy of excess quasiparticles above that in the absence of the probe.
While experimental studies of kinetic-inductance sensors have been limited so far by the temperature range near the superconducting transition, these detectors can be very sensitivity at temperatures well below the transition, where the number of equilibrium quasiparticles is exponentially small. In this regime, a shift of the quasiparticle chemical potential under radiation results in the change of the kinetic inductance, which can be measured by a sensitive SQUID readout. We modeled the kinetic inductance response of detectors made from disordered superconducting Nb, NbC, and MoRe films. Low phonon transparency of the interface between the superconductor and the substrate causes substantial re-trapping of phonons providing high quantum efficiency and the operating time of approximately 1 ms at 1 K. Due to the small number of quasiparticles, the noise equivalent power of the detector determined by the quasiparticle generation-recombination noise can be as small as approximately 10(exp -19) W/Hz(exp 1/2) at He4 temperatures.
Low temperature Kinetic Inductance Detectors (KIDs) are attractive candidates for producing quantumsensitive, arrayable sensors for astrophysical and other precision measurement applications. The readout uses a low frequency probe signal with quanta of energy well-below the threshold for pair-breaking in the superconductor. We have calculated the detailed non-equilibrium quasiparticle and phonon energy spectra generated by the probe signal of the KID when operating well-below its superconducting transition temperature Tc within the framework of the coupled kinetic equations described by Chang and Scalapino.[1] At the lowest bath temperature studied Tb/Tc = 0.1 the quasiparticle distributions can be driven far from equilibrium. In addition to the low frequency probe signal we have incorporated a high frequency (~ 1 THz) source signal well-above the pair-breaking threshold of the superconductor. Calculations of source signal detection efficiency are discussed
While experimental studies of kinetic-inductance sensors have been limited so far by the temperature range near the superconducting transition, these detectors can be very sensitive at temperatures well below the transition, where the number of equilibrium quasiparticles is exponentially small. In this regime, a shift of the quasiparticle chemical potential under radiation results in the change of the kinetic inductance, which can be measured by a sensitive SQUID readout. We modeled the kinetic inductance response of detectors made from disordered superconducting Nb, NbC, and MoRe films. Low phonon transparency of the interface between the superconductor and the substrate causes substantial re-trapping of phonons providing high quantum efficiency and the operating time of ∼1 ms at ≈1 K. Due to the small number of quasiparticles, the noise equivalent power of the detector determined by the quasiparticle generation-recombination noise can be as small as ∼10−19 W/√Hz at He4 temperatures.