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Superconductor Science and Technology

Non-linear microwave effects in thin superconducting films

T. B. Samoǐlova

Published May 1, 1995• 47 citations
Publisher

Abstract

The available experimental data on non-linear microwave effects in superconductors and some theoretical explanations of these, published since 1964, are reviewed. Various mechanisms of non-linearity observed under a wide variety of external conditions and in a broad spectrum of materials are discussed. Some examples of application of the non-linearity to frequency mixing are considered and analysed in the framework of a simple model of a fast-response resistive mixer.

DOI
10.1088/0953-2048/8/5/001

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The available experimental data on non-linear microwave effects in superconductors and some theoretical explanations of these, published since 1964, are reviewed. Various mechanisms of non-linearity observed under a wide variety of external conditions and in a broad spectrum of materials are discussed. Some examples of application of the non-linearity to frequency mixing are considered and analysed in the framework of a simple model of a fast-response resistive mixer.
Non-linear behaviour of NbN and YBa 2 Cu 3 O 7-x films at microwave frequencies is considered. Basic non-linearity mechanisms in wide superconducting films and the corresponding cut-off frequencies are discussed. Non-linear microwave properties of the films are analysed on the basis of dynamic current-voltage characteristics derived from the film response to short current pulses. The mixing effect is observed on superconducting NbN and YBa 2 Cu 3 O 7-x thin-film microbridges and coplanar lines. The intermediate-frequency conversion loss is analysed as a function of the local oscillator power. The experimental data are compared with simulation results.
Since the discovery of the high-transition-temperature (T c ) superconductive oxide materials, there has been very substantial progress in the understanding and control of these materials in thin film form. Although the initial projections of rapid and pervasive applicability of the high T c materials in the market place have not been met, the sensibly reproducible synthesis of high-quality thin films on substrate wafers of up to 50.8 mm diameter has generated a wide variety of preprototype microwave components, some of which are already edging into the market place. The current state of the microwave properties of low T c and high T c thin film materials will be reviewed and selected examples of preprototype devices drawn from low T c and high T c technology will be described. These components include transmission lines, filters, mixers and amplifiers for microwave signals, and information processing circuits for wideband analogue and high-speed digital waveforms. Speculation is offered on the long-term applications of superconducting electronics. Despite the substantial progress in materials, much more is required. The technology which must be developed in order to deliver practical superconducting circuits will be highlighted.
Abstract We discuss how reactive and dissipative nonlinearities affect the intrinsic response of superconducting thin-film resonators. We explain how most, if not all, of the complex phenomena commonly seen can be described by a model in which the underlying resonance is a single-pole Lorentzian, but whose centre frequency and quality factor change as external parameters, such as readout power and frequency, are varied. What is seen during a vector-network-analyser measurement is series of samples taken from an ideal Lorentzian that is shifting and spreading as the readout frequency is changed. According to this model, it is perfectly proper to refer to, and measure, the resonant frequency and quality factor of the underlying resonance, even though the swept-frequency curves appear highly distorted and hysteretic. In those cases where the resonance curve is highly distorted, the specific shape of the trajectory in the Argand plane gives valuable insights into the second-order physical processes present. We discuss the formulation and consequences of this approach in the case of nonlinear kinetic inductance, two-level-system loss, quasiparticle generation, and a generic model based on a power-law form. The generic model captures the key features of specific dissipative nonlinearities, but additionally leads to insights into how general dissipative processes create characteristic forms in the Argand plane. We provide detailed formulations in each case, and indicate how they lead to the wide variety of phenomena commonly seen in experimental data. We also explain how the properties of the underlying resonance can be extracted from this data. Overall, our paper provides a self-contained compendium of behaviour that will help practitioners interpret and determine important parameters from distorted swept-frequency measurements.
We discuss how reactive and dissipative nonlinearities affect the intrinsic response of superconducting thin-film resonators. We explain how most, if not all, of the complex phenomena commonly seen can be described by a model in which the underlying resonance is a single-pole Lorentzian, but whose centre frequency and quality factor change as external parameters, such as readout power and frequency, are varied. What is seen during a vector-network-analyser measurement is series of samples taken from an ideal Lorentzian that is shifting and spreading as the readout frequency is changed. According to this model, it is perfectly proper to refer to, and measure, the resonant frequency and quality factor of the underlying resonance, even though the swept-frequency curves appear highly distorted and hysteretic. In those cases where the resonance curve is highly distorted, the specific shape of the trajectory in the Argand plane gives valuable insights into the second-order physical processes present. We discuss the formulation and consequences of this approach in the case of nonlinear kinetic inductance, two-level-system loss, quasiparticle generation, and a generic model based on a power-law form. The generic model captures the key features of specific dissipative nonlinearities, but additionally leads to insights into how general dissipative processes create characteristic forms in the Argand plane. We provide detailed formulations in each case, and indicate how they lead to the wide variety of phenomena commonly seen in experimental data. We also explain how the properties of the underlying resonance can be extracted from this data. Overall, our paper provides a self-contained compendium of behaviour that will help practitioners interpret and determine important parameters from distorted swept-frequency measurements.
The mixing of 20 GHz radiation in a Nb superconducting film in the resistive state was studied. The experiment gave evidence of electron-heating to be the origin of the non-linear phenomenon. The requirements on the operation mode and on the film parameters in order to obtain small conversion losses or even gain are determined. Our measurements indicate a conversion loss of about 6-8 dB. The hot-electron bolometer is considered to be very promising for use in heterodyne receivers in a wide frequency range from microwaves to terahertz frequencies.