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Journal of Applied Physics

Model of superconducting alternating current bolometers

M. A. Lindeman, P. Khosropanah, R. A. Hijmering

Published Feb 15, 2013• 10 citations
Publisher

Abstract

We present a model of the response of superconducting AC bolometers to signal and noise using parameters and matrix formalism that were previously adopted in modeling DC bolometers and microcalorimeters. The model was developed to investigate novel AC bolometer designs, which have properties not described by previous models. It is applicable to kinetic inductance devices, kinetic inductance thermometers, AC transition edge sensors, and other technologies based on AC read out and frequency mixing. The AC bolometer model includes the temperature and current dependence of both resistive and inductive bolometers and microcalorimeters. The bolometers may be thermal or athermal. The model compactly describes the complex relationships between electrical and thermal signals and it simplifies the associated calculations. This model is useful for characterizing bolometers, predicting the effects of various noise sources on performance and designing new detectors. Additionally, a measurement technique is developed for characterizing these devices.

DOI
10.1063/1.4790146

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We present a model of the response of superconducting AC bolometers to signal and noise using parameters and matrix formalism that were previously adopted in modeling DC bolometers and microcalorimeters. The model was developed to investigate novel AC bolometer designs, which have properties not described by previous models. It is applicable to kinetic inductance devices, kinetic inductance thermometers, AC transition edge sensors, and other technologies based on AC read out and frequency mixing. The AC bolometer model includes the temperature and current dependence of both resistive and inductive bolometers and microcalorimeters. The bolometers may be thermal or athermal. The model compactly describes the complex relationships between electrical and thermal signals and it simplifies the associated calculations. This model is useful for characterizing bolometers, predicting the effects of various noise sources on performance and designing new detectors. Additionally, a measurement technique is developed for characterizing these devices.
Complex impedance measurements are widely used to characterize superconducting transition edge sensors (TESs) in bolometers and microcalorimeters. Typically, models are fit to impedance data to find parameters which pertain to the performance of these detectors. After the parameters are determined, the models are then used to compute the response and noise of these devices. In this paper, we present general relationships between the measured impedance, the thermal response to power in the TES, and noise. We describe a method for measuring αIand βIof the superconducting phase transition, which does not require model fitting. We find bolometer response is determined from the impedance provided that the absorber is strongly coupled to the TES electron system. We also demonstrate how to calculate upper and lower limits on the noise directly from the impedance data without modeling. Additionally, the relations can be used to check the validity of the models and to understand what information can and cannot be obtained from measurements of impedance, response, and noise.
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We present a theoretical analysis and experimental evaluation of a transition-edge superconducting bolometer for detecting infrared and millimeter waves. The superconducting film is voltage biased and the current is read by a superconducting quantum interference device ammeter. Strong electrothermal feedback maintains the sensor temperature within the transition, gives a current responsivity that is simply the inverse of the bias voltage, and reduces the response time by several orders of magnitude below the intrinsic time constant C/G. We evaluated a voltage-biased bolometer that operates on the Tc∼95 mK transition of a tungsten film with a thermal conductance of G∼1.2×10−9 W/K. As expected, the electrical noise equivalent power of 3.3×10−17/W√Hz is close to the thermal fluctuation noise limit and is lower than that of other technologies for these values of G and temperature. The measured time constant of 10 μs is ∼100 times faster than the intrinsic time constant.
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It has been recently demonstrated that superconducting transition edge-sensors behave as weak-links due to longitudinally induced superconductivity from the leads with higher Tc. In this work we study the implication of this behaviour for transition-edge sensors (TES)-based bolometers and microcalorimeter under ac bias. The TESs are read-out at frequencies between 1 and 5 MHz by a frequency domain multiplexer based on a linearised two-stage SQUID amplifier and high-Q lithographically made superconducting LC resonators. In particular, we focus on SRON TiAu TES bolometers with a measured dark noise equivalent power of 3.2 \\times 10 -19 W/\\sqrt{Hz} developed for the short wavelength band for the instrument SAFARI on the SPICA telescope.