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Softwaretechnik-Trends

A Hot Spot Mixer Model for Superconducting Phonon-Cooled HEB Far Above the Quasiparticle Bandgap

Harald Merkel, P. Khosropanah, Pavel A. Yagoubov, E. Kollberg

Published Mar 1, 1999• 5 citations
OpenAlex

Abstract

Abstract — A hot spot mixer model for phonon cooled hot electron bolometers is set up to accurately determine the dependence of the bolometer resistance on bias and absorbed LO power. An one-dimensional power balance for the nonequilibrium electrons containing an electron heat conduction term along the film and a loss term due to phonon escape to the substrate is solved. In the device's operating region of interest the absorbed heating power is usually large enough to heat a part of the bolometer bridge above the critical temperature forming a normal conducting hot spot. In this model heating due to the LO is assumed to be uniform whereas bias heating takes place in the hot spot region only. Solving the nonlinear power balance for the hot spot length allows to predict current-voltage characteristics, required heating powers and regions of optimal operation. Applying a small signal model in a given operating point yields an estimate for the intrinsic conversion gain. I. LARGE SIGNAL MODEL Existing device models for hot electron bolometers [1,2] treat the bolometer as a lumped element. It is assigned an effective temperature for the phonons and another for the electrons at a given bath temperature. In terms of heating bias power and RF power are equivalent and exchangeable. From this a method [3,4] to calculate the absorbed RF power is derived. This method is referred to as "isotherm " method: Operating points with identical device resistance must have identical temperatures since R(To„,,(,,, ) is a single valued monotonous function. Identical temperature implies identical power losses and identical 592

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RF heating efficiency of the terahertz superconducting hot-electron bolometer

S. N. Maslennikov

We report results of the numerical solution by the Euler method of the system of heat balance equations written in recurrent form for the superconducting hot-electron bolometer (HEB) embedded in an electrical circuit. By taking into account the dependence of the HEB resistance on the transport current we have been able to calculate rigorously the RF heating efficiency, absorbed local oscillator (LO) power and conversion gain of the HEB mixer. We show that the calculated conversion gain is in excellent agreement with the experimental results, and that the substitution of the calculated RF heating efficiency and absorbed LO power into the expressions for the conversion gain and noise temperature given by the analytical small-signal model of the HEB yields excellent agreement with the corresponding measured values.

arXiv:1404.5276•Apr 21, 2014•3 citations
Abstract — A hot spot mixer model for phonon cooled hot electron bolometers is set up to accurately determine the dependence of the bolometer resistance on bias and absorbed LO power. An one-dimensional power balance for the nonequilibrium electrons containing an electron heat conduction term along the film and a loss term due to phonon escape to the substrate is solved. In the device's operating region of interest the absorbed heating power is usually large enough to heat a part of the bolometer bridge above the critical temperature forming a normal conducting hot spot. In this model heating due to the LO is assumed to be uniform whereas bias heating takes place in the hot spot region only. Solving the nonlinear power balance for the hot spot length allows to predict current-voltage characteristics, required heating powers and regions of optimal operation. Applying a small signal model in a given operating point yields an estimate for the intrinsic conversion gain. I. LARGE SIGNAL MODEL Existing device models for hot electron bolometers [1,2] treat the bolometer as a lumped element. It is assigned an effective temperature for the phonons and another for the electrons at a given bath temperature. In terms of heating bias power and RF power are equivalent and exchangeable. From this a method [3,4] to calculate the absorbed RF power is derived. This method is referred to as "isotherm " method: Operating points with identical device resistance must have identical temperatures since R(To„,,(,,, ) is a single valued monotonous function. Identical temperature implies identical power losses and identical 592
Based on a one dimensional heat transport equation for the electrons in a super-conducting hot electron bolometer (HEB) a model for a hot spot mixer is see up. The hot spot parameters are applied in a small signal oscillator model predicting IV curves and conversion gain. Besides its normal resistance and its IF bandwidth a HEB around its optimal operating point is sufficiently characterized by its hot spot length as a function of heating power. All mixer properties can be derived from this parameter set.
A distributed model for phonon-cooled superconductor hot electron bolometer (HEB) mixers is given, which is based on solving the one-dimensional heat balance equation for the electron temperature profile along the superconductor strip. In this model it is assumed that the LO power is absorbed uniformly along the bridge but the DC power absorption depends on the local resistivity and is thus not uniform. The electron temperature dependence of the resistivity is assumed to be continuous and has a Fermi form. These assumptions are used in setting up the non-linear heat balance equation, which is solved numerically for the electron temperature profile along the bolometer strip. Based on this profile the resistance of the device and the IV curves are calculated. The IV curves are in excellent agreement with measurement results. Using a small signal model the conversion gain of the mixer is obtained. The expressions for Johnson noise and thermal fluctuation noise are derived. The calculated results are in close agreement with measurements, provided that one of the parameters used is adjusted.
Phonon cooled hot electron bolometers (HEB) show smaller noise temperatures in mixer applications above 1THz compared to Schottky diodes or SIS devices. To determine the optimal bias point for maximum IF bandwidth and lowest noise of a FEB detailed understandin g of the current-voltage characteristic is indispensable. A complete nonlinear model for a hot electron bolometric (HEB) mixer is derived. The dynamic resistance of a superconducting film is calculated under stron g demagnetization conditions. The resistance is modeled due to vortex flow and phase slip lines. Self heating gives rise to normal domains in the film. In addition the resistance due to thermally activated flux creep and thermal fluctuations is taken into account. All these relations form a large si gnal model for the iv-characteristics and the bias points of the device. A small signal linearization yields then conversion gain and noise temperatures. Furthermore a quality measure for HEB devices is set up by deriving the thermal coupling of the film to the substrate and the achieved critical current density from measured current-voltage characteristics.
A hot spot model for superconducting hot electron bolometers is presented based on a two-dimensional heat transport equation for electrons and phonons including heat trapping due to quasiparticle bandgap gradients. Skin effect concentrates the RF heating in lateral regions of the bridge and the bias current in the center. A reduction in conversion gain compared to a one-dimensional hot spot model is explained by the RF and bias heating profiles not being identical. An experimentally verified increase of the IF bandwidth from 3.5 GHz to 8 GHz when increasing bias voltage is predicted. IV curves, gain and noise are in very good agreement with measurements.
We report results of the numerical solution by the Euler method of the system of heat balance equations written in recurrent form for the superconducting hot-electron bolometer (HEB) embedded in an electrical circuit. By taking into account the dependence of the HEB resistance on the transport current we have been able to calculate rigorously the RF heating efficiency, absorbed local oscillator (LO) power and conversion gain of the HEB mixer. We show that the calculated conversion gain is in excellent agreement with the experimental results, and that the substitution of the calculated RF heating efficiency and absorbed LO power into the expressions for the conversion gain and noise temperature given by the analytical small-signal model of the HEB yields excellent agreement with the corresponding measured values.