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Journal of Applied Physics

Heating effects in high-frequency metallic Josephson devices: Voltage limit, bolometric mixing, and noise

M. Tinkham, Miguel Octavio, William J. Skocpol

Published Mar 1, 1977• 95 citations
Publisher

Abstract

In this paper, we analyze nonequilibrium effects within a simple heating approximation for the case of metallic Josephson weak links which have a favorable three-dimensional cooling geometry. Our principal conclusions are the following: (1) The temperature in the center of the junction with voltage V applied is Tm=[Tb2+3 (eV/2πk)2]1/2, where Tb is the bath temperature, e is the electronic charge, and k is Boltzmann’s constant. This Tm can be as high as 70 K in Nb point contacts on a high Josephson step; thus the device noise temperature TN? (1/2)(Tb+Tm) can greatly exceed Tb. (2) The critical current falls approximately as exp(−P/Po), where P is the power dissipated in the junction and Po is typically 10 μW for Al, Sn, Pb, and Nb, but much smaller for Nb3Sn. This leads to a decrease in the amplitude of Josephson steps at high voltages which is in good agreement with data on the best Sn variable-thickness microbridges and Nb point contacts. In a junction of optimized resistance level, the overall maximum voltage at which microwave-induced steps can still exceed the noise is predicted to be proportional to Tc[Ωξ (0)/ρo]2/7× (ν1/Tc)1/7, where Ω is the solid angle of the three-dimensional cooling, ξ (0) is the extrapolated coherence length at T=0, ρo is the residual resistivity of the metal, and ν1 is the microwave frequency. (3) The thermal response should be fast enough (∼τGL) to allow detection (heterodyne or square law) with bandwidth as large as the energy gap frequency; it is estimated that this bolometric detection effect will dominate true Josephson detection for carrier frequencies above ∼3 THz (i.e., λ≲100 μm) in junctions with resistance 10 Ω or less.

DOI
10.1063/1.323776

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In this paper, we analyze nonequilibrium effects within a simple heating approximation for the case of metallic Josephson weak links which have a favorable three-dimensional cooling geometry. Our principal conclusions are the following: (1) The temperature in the center of the junction with voltage V applied is Tm=[Tb2+3 (eV/2πk)2]1/2, where Tb is the bath temperature, e is the electronic charge, and k is Boltzmann’s constant. This Tm can be as high as 70 K in Nb point contacts on a high Josephson step; thus the device noise temperature TN? (1/2)(Tb+Tm) can greatly exceed Tb. (2) The critical current falls approximately as exp(−P/Po), where P is the power dissipated in the junction and Po is typically 10 μW for Al, Sn, Pb, and Nb, but much smaller for Nb3Sn. This leads to a decrease in the amplitude of Josephson steps at high voltages which is in good agreement with data on the best Sn variable-thickness microbridges and Nb point contacts. In a junction of optimized resistance level, the overall maximum voltage at which microwave-induced steps can still exceed the noise is predicted to be proportional to Tc[Ωξ (0)/ρo]2/7× (ν1/Tc)1/7, where Ω is the solid angle of the three-dimensional cooling, ξ (0) is the extrapolated coherence length at T=0, ρo is the residual resistivity of the metal, and ν1 is the microwave frequency. (3) The thermal response should be fast enough (∼τGL) to allow detection (heterodyne or square law) with bandwidth as large as the energy gap frequency; it is estimated that this bolometric detection effect will dominate true Josephson detection for carrier frequencies above ∼3 THz (i.e., λ≲100 μm) in junctions with resistance 10 Ω or less.
We report a systematic, comprehensive set of measurements on the dynamics and noise processes in diffusion and phonon-cooled superconducting hot-electron bolometer mixers which will serve as ultralow noise detectors in THz heterodyne receivers. The conversion efficiency and output noise of devices of varying lengths were measured with radio frequency between 8 and 40 GHz. The devices studied consist of 100-Å-thin film Nb bridges connected to thick (1000 Å), high conductivity normal metal (Au) leads. The lengths of the devices studied range from 0.08 to 3 μm. For devices longer than the electron–phonon interaction length Le–ph≡Dτe–ph, with D the diffusion constant and τe–ph−1 the electron–phonon interaction rate, the hot electrons are cooled dominantly by the electron–phonon interaction, which in Nb is too slow for practical applications. If the device length is less than πLe–ph(≈1 μm at 4.2 K), then out diffusion of heat into the high conductivity leads dominates the cooling process. In this limit, the intermediate frequency (IF) bandwidth is found to vary as L−2, with L the bridge length, as expected for diffusion cooling. The shortest device has an IF bandwidth greater than 6 GHz, the largest reported for a low-Tc superconducting bolometric mixer. The dominant component of the output noise decreases with frequency in the same manner as the conversion efficiency, consistent with a model based on thermal fluctuations. The noise bandwidth is larger than the gain bandwidth, and the mixer noise is low, ranging from 100 to 530 K (double sideband). The crossover from phonon dominated to diffusion dominated behavior is also demonstrated using noise thermometry measurements in the normal state. Scalar measurements of the device differential impedance in the intermediate state agree with a theoretical model which takes into account the thermal and electrical dynamics. We also present detailed comparisons with theoretical predictions of the output noise and conversion efficiency.
Point-contact Josephson junctions with a submicron contact diameter have been used as high-frequency mixers (170–220 GHz) under high thermal background conditions. The junction is formed across a full height (0.56×1.06 mm2) waveguide between a 3–5-μm thick Nb whisker and a 0.2-mm diam Nb center conductor of a coaxial line. The best single-side band mixer-noise temperature that was measured is 165 K (± 25%) with a corresponding single-side band conversion efficiency of 0.36±0.03 (a loss of 4.5 ±0.4 dB) at a signal frequency of 185 GHz, including losses in the coupling horn and the waveguide. The performance was measured with the hot-cold source technique. The effects of nonheterodyne response in that situation were investigated in detail. The junctions have been operated in a coherent receiver that can be used on a telescope with only small adaptations. The instantaneous bandwidth of the receiver is about 20 GHz.
Detection mechanisms in Josephson junctions with energies Ej comparable to thermal energies kT have been studied. The responses ΔV of YBa2Cu3O7−x bicrystal junctions to monochromatic radiation with frequencies f ranging from 94 GHz to 3.1 THz can be described in terms of classical rectification on a static nonlinear V–I curve at low frequencies and frequency modulation of the ac Josephson current at high frequencies, with an interplay between these mechanisms at intermediate frequencies. An electrical noise-equivalent power of (9 ± 3) × 10−15 W/Hz1/2, a responsivity of (3.4 ± 0.5) × 105 V/W, and a dynamic power range of 5 × 104 have been demonstrated for the square-law classical detection of 94 GHz radiation with the junctions at 50 K. The effect of background radiation on the V–I curves of YBa2Cu3O7−x bicrystal junctions was found to have an optical noise-equivalent temperature of ≤30 mK/Hz1/2. The main contribution to the effect comes from the interplay between the classical and Josephson detection mechanisms. The spectral and power dependencies of the responses ΔV of Josephson junctions have been numerically simulated within the resistively shunted junction model at various values of kT/Ej, and the results are in acceptable agreement with the experimental data.
Nb hot-electron bolometers (HEBs) with critical temperature T. = 5 to 6 K have previously demonstrated good heterodyne mixing performance at THz frequencies. HEBs with a lower critical temperature are predicted to have improved performance with lower noise. We present microwave (30GHz) mixing measurements on Nb HEB mixers with T, between 1.4 and 5.3 K. The reduced T, is obtained by application of a magnetic field, or by use of a bi-layer microbridge of Nb and Au with 'F e = 1.6 K. The mixer output noise and voltage range of low mixer noise are observed to decrease approximately linearly with reduction of T. The Nb-Au mixer has a mixer noise temperature TM = 50K (DSB) with reasonable dynamic range, and thus is promising for future single pixel and array receivers for THz spectroscopy.
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.
The subject of electronic noise in high- superconducting Josephson devices and in their applications is considered. Several types of grain boundary junctions, prepared in different ways by four separate international laboratories, are fully characterized in terms of their electrical and noise properties at a range of temperatures, frequencies, magnetic fields and in the presence of microwaves. Similar characterization is carried out for multijunction Josephson flux-flow arrays, and bi-epitaxial SQUIDs. The theory of Likharev and Semenov for thermal noise in low- junctions is adopted as a reference against which excess noise can be identified in high- junctions. It is combined with theoretical models of excess noise based on fluctuations of critical current and resistance to provide accurate fitting of the observed noise curves. It is shown that the normalized levels of critical current and normal resistance fluctuations for all of the junction types examined are remarkably close (typically around and at 100 Hz) and are nearly independent of temperature in the range T = 30 - 80 K. The frequency dependence is close to the universal 1/f law with some deviations due to trapping of charge carriers at discrete states in the tunnelling barrier. Measurements of voltage noise levels and critical current fluctuations in multijunction flux-flow amplifiers, reported for the first time, are consistent with levels in single junctions of the same type. Excess noise is studied as a function of external magnetic field, in a way that has not been previously described. A new interpretation of the magnetic field-dependent noise data indicates that absolute levels of critical current fluctuations are nearly independent of applied magnetic field. This observation does not appear to have been reported elsewhere. It has important implications for the operation of grain boundary Josephson devices in real applications. Voltage noise in the presence of microwave irradiation, at operating points between Shapiro steps, is consistent with a modified form of the Likharev - Semenov equation which takes into account the known level of critical current fluctuations as measured in field-free conditions. The implications of these results for further improvements in device performance are discussed, and directions for further work are suggested.