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Applied Physics Letters

Hotspot mixing: A framework for heterodyne mixing in superconducting hot-electron bolometers

D. Wilms Floet, E. Miedema, T. M. Klapwijk, J. R. Gao

Published Jan 18, 1999• 73 citations
Publisher

Abstract

We propose a framework to interpret heterodyne mixing in superconducting hot-electron bolometers. The physical conversion process of the mixer is the result of an electronic hotspot, of which the length, and consequently the resistance, oscillates at the intermediate frequency. On the basis of this concept, we calculate the (un)pumped current–voltage relation, the dc voltage responsivity, and the mixer conversion efficiency.

DOI
10.1063/1.123052

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We propose a framework to interpret heterodyne mixing in superconducting hot-electron bolometers. The physical conversion process of the mixer is the result of an electronic hotspot, of which the length, and consequently the resistance, oscillates at the intermediate frequency. On the basis of this concept, we calculate the (un)pumped current–voltage relation, the dc voltage responsivity, and the mixer conversion efficiency.
We present the hotspot mixing as a new principle of heterodyne mixing in a superconducting hot-electron bolometer. Applying DC and LO powers to a superconducting bridge generates a hotspot within the bridge. The size of the hotspot, and thus the resistance of the bridge, oscillates with the heating power at intermediate frequency. By solving heat-conducting equations, we can predict the mixer performances, such as the conversion efficiency, as a function of dc bias voltage, LO power, or the bath temperature.
We present a study of the resistive behavior of hot-electron bolometers in two different regimes. At bath temperatures near the critical temperature and under the condition of a low current density, the behavior can be understood in terms of charge-imbalance, Andreev reflection, and the superconducting proximity effect. At lower temperatures, a high current density and the application of LO power result in the formation of a resistive electronic hotspot. We propose to interpret heterodyne downconversion as the result of the length oscillation of the hotspot at the intermediate frequency.
We present theoretical analysis of the performance of a superconducting hot-electron bolometer mixer with electron cooling due to electron phonon interaction. The analysis is based on a complete set of thermal balance equations for phonons and electrons. A non-thermal action of a dc current has been considered phenomenologically using an analytical fit of isothermal current-voltage characteristics of the mixer. The operation point of the mixer has been determined as a result of the heating by both the power of a local oscillator and the power dissipated by the current. Electron temperature fluctuations, Nyquist noise, and shot noise have been supposed to only contribute to the mixer noise. The conversion gain and the noise temperature of the mixer have been evaluated taking into account an electro-thermal feedback between the mixer and an intermediate frequency circuit with an arbitrary impedance. We have obtained general expressions for the conversion gain, noise temperature and impedance which enabled us to estimate ultimate performance of a superconducting hot-electron bolometer mixer. Theoretical predictions are in good agreement with experimental results obtained for a NbN hot-electron bolometer mixer at a radiation frequency of 2.5 THz.
Superconducting hot electron bolometer (HEB) mixers are the most sensitive heterodyne detectors at frequencies beyond 1 THz, and are used for many astronomical observations. HEB, consisting of a narrow and short superconducting thin film patch connected to an antenna via contact pads, is brought into a highly sensitive operating regime by applying a DC current and a certain amount of local-oscillator power. Potentially, superconducting HEB mixers are capable of exhibiting high sensitivity for frequencies up to several tens of THz, as their output noise and conversion gain are nearly frequency independent according to the mixing mechanism. Moreover, the understanding of mixing mechanism has evolved over time from lumped-element model to distributed hot-spot model. In this review, we provide an overview of theoretical and experimental studies on HEBs and their applications, especially in astronomical observations on ground, airborne and space telescopes.
Hot-electron bolometer devices, used successfully in low noise heterodyne mixing at frequencies up to 2.5 THz, have been analyzed. A distributed temperature numerical model of the NbN bridge, based on a local electron and a phonon temperature, is used to model pumped IV curves and understand the physical conditions during the mixing process. We argue that the mixing is predominantly due to the strongly temperature dependent local resistivity of the NbN. Experimentally we identify the origins of different transition temperatures in a real HEB device, suggesting the importance of the intrinsic resistive transition of the superconducting bridge in the modeling.
Superconducting hot-electron bolometers are presently the best performing mixing devices for the frequency range beyond 1.2 THz, where good-quality superconductor-insulator-superconductor devices do not exist. Their physical appearance is very simple: an antenna consisting of a normal metal, sometimes a normal-metal-superconductor bilayer, connected to a thin film of a narrow short superconductor with a high resistivity in the normal state. The device is brought into an optimal operating regime by applying a dc current and a certain amount of local-oscillator power. Despite this technological simplicity, its operation has found to be controlled by many different aspects of superconductivity, all occurring simultaneously. A core ingredient is the understanding that there are two sources of resistance in a superconductor: a charge-conversion resistance occurring at a normal-metal-superconductor interface and a resistance due to time-dependent changes of the superconducting phase. The latter is responsible for the actual mixing process in a nonuniform superconducting environment set up by the bias conditions and the geometry. The present understanding indicates that further improvement needs to be found in the use of other materials with a faster energy relaxation rate. Meanwhile, several empirical parameters have become physically meaningful indicators of the devices, which will facilitate the technological developments.