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Softwaretechnik-Trends

A Distributed Device Model for Phonon-Cooled HEB Mixers Predicting IV Characteristics, Gain, Noise and IF Bandwidth

P. Khosropanah, H. Merkel, Sigfrid Yngvesson, Aurèle J. L. Adam, Serguei Cherednichenko, E. Kollberg

Published May 1, 2000• 18 citations
OpenAlex

Abstract

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.

Related papers

A Large Signal Model for Phonon-Cooled Hot-Electron Bolometric Mixers for THz Frequency Applications

H. Merkel, E. Kollberg, K. S. Yngvesson

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.

•Mar 1, 1998•8 citations

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

Harald Merkel, P. Khosropanah, Pavel A. Yagoubov +1 more

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

Softwaretechnik-Trends•Mar 1, 1999•5 citations

A hot-spot mixer model for phonon-cooled NbN hot electron bolometric mixers

H. Merkel, P. Khosropanah, Pavel A. Yagoubov +1 more

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.

IEEE Transactions on Applied Superconductivity•Jun 1, 1999•30 citations

Frequency-Domain Analysis of Diffusion-Cooled Hot-Electron Bolometer Mixers

Anders J. Skalare, William R. McGrath, B. Bumble +1 more

A new theoretical model is introduced to describe heterodyne mixer conversion efficiency and noise (from thermal fluctuation effects) in diffusion-cooled superconducting hot-electron bolometers. The model takes into account the non uniform internal electron temperature distribution generated by Wiedemann Franz heat conduction, and accepts for input an arbitrary (analytical or experimental) superconducting resistance-versus-temperature curve. A non-linear large signal solution is solved iteratively to calculate the temperature distribution, and a linear frequency-domain small-signal formulation is used to calculate conversion efficiency and noise. In the small-signal solution the device is discretized into segments, and matrix algebra is used to relate the heating modulation in the segments to temperature and resistance modulations. Matrix expressions are derived that allow single-sideband mixer conversion efficiency and coupled noise power to be directly calculated. The model accounts for self-heating and electrothermal feedback from the surrounding bias circuit.

•Jan 1, 1998•0 citations

Rigorous Analysis of a Superconducting Hot-Electron Bolometer Mixer: Theory and Comparison with Experiment

Rainer S. Nebosis, Alexei D. Semenov, Yu. P. Gousev +1 more

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.

Softwaretechnik-Trends•Mar 1, 1996•21 citations

A frequency-domain mixer model for diffusion-cooled hot-electron bolometers

Anders J. Skalare, William R. McGrath

A new frequency domain hot-electron bolometer (HEB) mixer model is described, which takes into account the non-uniform temperature distribution found in superconducting diffusion-cooled devices. In this model the bolometer is discretized into a finite number of segments, and the non-linear large signal response to local oscillator and DC heating is found by an iterative algorithm. A frequency-domain coupling matrix is introduced to represent small-signal modulations around the large-signal values of temperatures and heat flows inside the device. The coupling matrix and a Norton representation of the mixer DC and intermediate frequency (IF) circuit allows the mixer conversion to be calculated.

IEEE Transactions on Applied Superconductivity•Jun 1, 1999•6 citations
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.
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 new theoretical model is introduced to describe heterodyne mixer conversion efficiency and noise (from thermal fluctuation effects) in diffusion-cooled superconducting hot-electron bolometers. The model takes into account the non uniform internal electron temperature distribution generated by Wiedemann Franz heat conduction, and accepts for input an arbitrary (analytical or experimental) superconducting resistance-versus-temperature curve. A non-linear large signal solution is solved iteratively to calculate the temperature distribution, and a linear frequency-domain small-signal formulation is used to calculate conversion efficiency and noise. In the small-signal solution the device is discretized into segments, and matrix algebra is used to relate the heating modulation in the segments to temperature and resistance modulations. Matrix expressions are derived that allow single-sideband mixer conversion efficiency and coupled noise power to be directly calculated. The model accounts for self-heating and electrothermal feedback from the surrounding bias circuit.
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.
A new frequency domain hot-electron bolometer (HEB) mixer model is described, which takes into account the non-uniform temperature distribution found in superconducting diffusion-cooled devices. In this model the bolometer is discretized into a finite number of segments, and the non-linear large signal response to local oscillator and DC heating is found by an iterative algorithm. A frequency-domain coupling matrix is introduced to represent small-signal modulations around the large-signal values of temperatures and heat flows inside the device. The coupling matrix and a Norton representation of the mixer DC and intermediate frequency (IF) circuit allows the mixer conversion to be calculated.