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IEEE Transactions on Applied Superconductivity

YBCO-Constriction Hot Spot Modeling: DC and RF Descriptions for HEB THz Mixer Noise Temperature and Conversion Gain

Romain G. Ladret, Alain Kreisler, Annick F. Degardin

Published Jan 1, 2014• 7 citations
Publisher

Abstract

To investigate the THz mixing performance of YBCO hot electron bolometers (HEB), the influence of the local oscillator (LO) radiofrequency (RF) radiation has been considered in detail. As opposed to the usual hot spot modeling approach, where the LO power is assumed to be uniformly distributed over the HEB constriction length, a uniform RF current has been assumed. The local electron temperature-as obtained by solving the coupled electron and phonon thermal reservoir equations-could then be used to determine the local YBCO complex resistivity, hence the locally dissipated LO power. Besides, the use of a modified two-fluid description allowed to determine the RF-dependent temperature shift (~-1% THz-1) and broadening (~+20% THz-1) of the resistive transition. Finally, the impedance matching to the THz antenna was considered. For a typical constriction, the conversion loss and noise temperature TDSBwere computed, with TDSB× exp(0.32f) behavior up to 2.5 THz.

DOI
10.1109/tasc.2014.2374416

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To investigate the THz mixing performance of YBCO hot electron bolometers (HEB), the influence of the local oscillator (LO) radiofrequency (RF) radiation has been considered in detail. As opposed to the usual hot spot modeling approach, where the LO power is assumed to be uniformly distributed over the HEB constriction length, a uniform RF current has been assumed. The local electron temperature-as obtained by solving the coupled electron and phonon thermal reservoir equations-could then be used to determine the local YBCO complex resistivity, hence the locally dissipated LO power. Besides, the use of a modified two-fluid description allowed to determine the RF-dependent temperature shift (-1% THz-1) and broadening (+20% THz-1) of the resistive transition. Finally, the impedance matching to the THz antenna was considered. For a typical constriction, the conversion loss and noise temperature TDSBwere computed, with TDSB× exp(0.32f) behavior up to 2.5 THz.
High-TCsuperconductor (YBaCuO) hot electron bolometers (HEB) are promising THz mixers due to the large predicted bandwidth and the low local oscillator (LO) power requirement. Recently, we introduced the hot-spot model, initially dedicated to low-TCNbN devices, to predict YBaCuO mixer performance. Major improvements to the model have been introduced: local description of the power absorption along the HEB constriction, THz dependence of the resistive transition, impedance matching between the THz antenna and the constriction. Mixer noise temperature TNand conversion gain G were predicted up to 2.5 THz. For instance, TN= 2700 K (DSB) and G = -13 dB are obtained with 9 μW of LO power at 1 THz.
Hot electron bolometers (HEB) made from high-TC superconducting YBa2Cu3O7–x (YBCO) oxide nano-constrictions are promising THz mixers, due to their expected wide bandwidth, large mixing gain, and low intrinsic noise. The challenge for YBCO resides, however, in the chemical reactivity of the material and the related aging effects. In this paper, we model and simulate the frequency dependent performance of YBCO HEBs operating as THz mixers. We recall first the main hypotheses of our hot spot model taking into account both the RF frequency effects in the YBCO superconducting transition and the nano-constriction impedance at THz frequencies. The predicted performance up to 4 THz is given in terms of double sideband noise temperature TDSB and conversion gain G. At 2.5 THz for instance, TDSB ≅ 1000 K and G ≅ − 6 dB could be achieved at 12.5 μW local oscillator power. We then consider a standoff target detection scheme and examine the feasibility with YBCO devices. For instance, detection at 3 m through cotton cloth in passive imaging mode could be readily achieved in moderate humidity conditions with 10 K resolution.
High- T C hot electron bolometers (HEB) are promising THz mixers due to their expected wide bandwidth, large mixing gain, and low intrinsic noise. We have simulated the characteristics of YBaCuO HEBs with a hot spot model usually dedicated to low- T C phonon cooled devices. With respect to e.g., NbN, the high- T C specificities are mainly arising from the large values of YBaCuO phonon thermal conductivity, and the film to MgO substrate phonon escape time. The consequent effects on the electron temperature profiles along the YBaCuO constriction and the current voltage DC characteristics are considered. The conversion gain G and noise temperature T N were computed for two constriction dimensions. For a 100 nm long × 100 nm wide × 10 nm thick constriction at 9 microwatt local oscillator (LO) power, the expected double sideband (DSB) T N = 1520 K ( G = −13.7 dB). For a larger (but more realistic according to YBaCuO aging effects) 400 nm long × 400 nm wide × 35 nm thick constriction, minimum T N = 1210 K DSB at 35 microwatt LO power ( G = −13.1 dB).
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
We report on an experimental investigation of high-Tc superconducting hot electron bolometer (HEB) mixers of YBCO. These mixers were tested at 100 and 530 GHz LO for a range of temperatures around 77 K. The conversion gain of -32 dB was measured at an LO power of about 1 mW (530 GHz) and 0.3 GHz IF. The mixers were integrated with a logarithmic spiral antenna on a silicon lens, providing a broad frequency coverage (well above 1 THz). To measure the incident RF signal power we used the homodyne responsivity (see abstract "Terahertz response of YBCO HEB homodyne detectors") which is referenced to the input of the silicon lens where the bolometers were glued. Corrections were made for losses in the cryostat window and polarization losses between the signal and antenna. We made the measurements at different temperatures and different LO power levels which were measured using a quasi optical detector at room temperature. The 3 dB gain bandwidth was measured to be about 0.2 GHz. The bolometer bridges have nominal dimensions 1 μm x 2 μm x 50 nm and are fabricated on sapphire substrates using UV photolithography. Backward wave oscillators sources were used at 530 GHz and Gunn diodes at 100 GHz.