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arXiv:1912.00503 · IEEE Transactions on Applied Superconductivity

Study of Microwave Resonances Induced by Bias Lines of Shunted Josephson Junctions

Uğur Yılmaz, Sasan Razmkhah, Romain Collot, J. Kunert, Ronny Stolz, Pascal Febvre

Published Jun 25, 2020• 4 citations
arXivHTMLPDF

Abstract

Bias lines routed over a ground plane naturally form microstrip lines associated with the presence of a capacitance. This can lead to unwanted resonances when coupled to Josephson junctions. This article presents an electrical model of a shunted Josephson junction with its bias lines and pads, fabricated with the 1 kA/cm2rapid single flux quantum niobium process of the FLUXONICS foundry (J. Kunert, 2013), (J. Kunert, 2017). A T-model is used to simulate the microwave behavior of the bias line, predict resonances and design resonance-free superconducting circuits. The I-V characteristics of three shunted Josephson junctions have been obtained from time-domain simulations done with Josephson SIMulator (JSIM) (E. S. Fang and T. Van Duzer, 1989) and show a good match with the experimentally observed resonance at 230 GHz up to the normal resistance branch, measured at 4.2 K. The influence of the position and value of a series resistor placed on bias lines is studied to damp unwanted resonances at the junction.

DOI
10.1109/tasc.2020.3004781

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Bias lines routed over a ground plane naturally form microstrip lines associated with the presence of a capacitance. This can lead to unwanted resonances when coupled to Josephson junctions. This article presents an electrical model of a shunted Josephson junction with its bias lines and pads, fabricated with the 1 kA/cm2rapid single flux quantum niobium process of the FLUXONICS foundry (J. Kunert, 2013), (J. Kunert, 2017). A T-model is used to simulate the microwave behavior of the bias line, predict resonances and design resonance-free superconducting circuits. The I-V characteristics of three shunted Josephson junctions have been obtained from time-domain simulations done with Josephson SIMulator (JSIM) (E. S. Fang and T. Van Duzer, 1989) and show a good match with the experimentally observed resonance at 230 GHz up to the normal resistance branch, measured at 4.2 K. The influence of the position and value of a series resistor placed on bias lines is studied to damp unwanted resonances at the junction.
State-of-the-art RSFQ circuits consist of Josephson junctions, inductances and bias current sources, where the inductances are practically used as functional elements. Even more, their value defines the functionality and therefore the conventional design process requires strict conditions for the wiring between Josephson junctions. The present design and optimization process does not take into account their parasitic capacitances to ground. This becomes an important issue for ultra fast applications above 100 GHz, but also for circuits dedicated to control quantum electronics. We report on a theoretical and experimental investigation of the influence of ground capacitances. The impedance matching between the connecting microstrip lines and the Josephson junction is a key issue for the correct operation of these circuits. We performed circuit simulations and collected experimental data of correct and incorrect operating circuits to derive design criteria. The critical reflection coefficient is found to be 0.35 and the particular design must use a smaller value for transfer and a larger value for storage of SFQ pulses, respectively.
We have designed and characterized superconducting integrated circuits for the ac Josephson voltage standard that demonstrate significantly improved performance. The typical circuit consists of an array of superconductor-normal metal-superconductor Josephson junctions, which are placed in a transmission line and biased with a broad-band (dc-to-15 GHz) pulse-drive waveform. Additional low-speed (dc and audio frequency) bias and output leads contain on-chip inductors that act as low-pass filters. The operating margins of the array were improved by adding resistive shunts across these inductors to damp their intrinsic resonances. These resonances had previously degraded the integrity of the broad-band signal driving the array. We present simulations and measurements of these improved circuits that demonstrate no resonances in the range of 0.1-20 GHz. Moreover, the operating margins of the ac Josephson voltage standard were improved.
Josephson junctions (JJs) with non-hysteretic I-V characteristic and high critical parameters are required for many applications; in particular, they are needed to create tunable THz range oscillators. We fabricated and studied shunted superconductor-insulator-superconductor (SIS) Nb-AlOx-Nb tunnel junctions with an area of about 1μm2, estimated their parameters, and compared them with theoretical models. To assess the performance of shunted junctions in the terahertz range, their characteristics were studied under the influence of a high-frequency signal; the estimated value of the characteristic voltage for the shunted junction at a high frequency is about 1 mV. To improve the circuit parameters, a new type of the shunting based on application of NIS junctions was proposed, which reduces the influence of parasitic inductance, expands the frequency range of the generator, and decreases the size of the structure. The JJs with a new type of shunting have been fabricated and studied. The niobium integrated circuits intended for matching the superconducting oscillator and an SIS junction as a microwave detector were designed, fabricated, and tested. Such structures are required for studying the spectral characteristics and analyzing the operation of the oscillator. The developed circuits have demonstrated efficient operation at frequencies from 300 to 700 GHz; the experimental results are in good agreement with the simulated characteristics. The results obtained will be implemented for further development of the THz range oscillators.
Superconducting digital circuits based on Josephson junctions with amorphous niobium-silicon (a-NbSi) barriers have been designed, fabricated, and tested. Single-flux-quantum (SFQ) shift registers operated with ±30% bias margins, confirming junction reproducibility and uniformity. Static digital dividers operated up to 165 GHz for a single value of bias current, which was only marginally slower than circuits fabricated with externally shunted AlOx-barrier junctions having a comparable critical current density of 4.5 kA/cm2. In comparison, self-shunted a-NbSi junctions enabled a doubling in circuit density. This and their relatively thick 10 nm barriers could increase the yield of complex SFQ circuits.
Measurements have been made of the low-frequency spectral density of the voltage noise in current-biased resistively shunted Josephson tunnel junctions under conditions in which the noise mixed-down from frequencies near the Josephson frequency (${\ensuremath{\nu}}_{J}$) to the measurement frequency ($\ensuremath{\ll}{\ensuremath{\nu}}_{J}$) is in the regime $h{\ensuremath{\nu}}_{J}>{k}_{B}T$. In this limit, quantum corrections to the mixed-down noise are important. The spectral densities measured on junctions with current-voltage characteristics close to the Stewart-McCumber model were in excellent agreement with the predicted values, with no fitted parameters. The mixed-down noise for a wide range of bias voltages was used to infer the spectral density of the current noise in the shunt resistor at frequency $\ensuremath{\nu}$. With no fitted parameters, this spectral density at frequencies up to 500 GHz was in excellent agreement with the prediction $(\frac{2h\ensuremath{\nu}}{R})coth(\frac{h\ensuremath{\nu}}{2{k}_{B}T})$. The presence of the zero-point term, $\frac{2h\ensuremath{\nu}}{R}$, at frequencies $h\ensuremath{\nu}>{k}_{B}T$ was clearly demonstrated. The current-voltage characteristics of a junction with ${\ensuremath{\beta}}_{L}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{L}_{s}{I}_{0}}{{\ensuremath{\Phi}}_{0}}\ensuremath{\sim}1$ and ${\ensuremath{\beta}}_{C}\ensuremath{\equiv}\frac{2\ensuremath{\pi}{I}_{0}{R}^{2}C}{{\ensuremath{\Phi}}_{0}}\ensuremath{\ll}1$, where I0{I}_{0}I0​ is the critical current, CCC is the junction capacitance, and Ls{L}_{s}Ls​ is the shunt inductance, showed structure at voltages where the Josephson frequency was near a subharmonic of the LsC{L}_{s}CLs​C resonant frequency. The additional nonlinearity of the $I\ensuremath{-}V$ characteristic caused mixing down of noise near higher harmonics of the Josephson frequency, thereby greatly enhancing the voltage noise. The measured noise was in good agreement with that predicted by computer simulations.
Interaction between two Josephson junctions and a microstrip resonator is investigated using a resonator shunted junction (RLCSJ) model. A sharp current step resulting from coupling with the resonator is observed in simulated I-V characteristics. There is strong phase-locking and decreasing of dynamic resistance at the current step. We design and fabricate two types of Josephson array oscillators using these effects to obtain stable phase locking and narrow linewidth for the oscillation. The fabricated oscillators are formed with nine shunted Nb/AlOx/Nb tunnel junctions and Nb microstrip resonators. The power of the oscillator delivered to the load resistor was estimated to be about 3.6 /spl mu/W at 330 GHz. A composite linewidth of the oscillators is also measured at about 19 MHz at 4.2 K using two oscillators with a log-periodic antenna and a SIS detector.