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Investigating the feasibility of using nanobridge weak links as the active Josephson element in Rapid Single Flux quantum circuitry

Abubakar Adan

Published Mar 28, 2018• 0 citations
OpenAlex

Abstract

Josephson junctions are used in present day voltage standards. To extend their use to AC voltage standards a high bandwidth, low-noise detector is required. A candidate component for this detector is a superconducting comparator based on Rapid Single Flux Quantum (RSFQ) circuits. The work presented here is a study to determine if nanobridge weak links can be used as the active Josephson element in these circuits. In order to achieve this an understanding of the nanobridge properties and in particular their critical currents is fundamental. We present simulations of a simple comparator using the circuit simulation software JSIM in order to study the effect of varying nanobridge parameters such as width, length, and loop area. These geometrical variables have an affect on the critical currents and loop inductances which subsequently effect device performance. Particular emphasis is given to investigation of how these parameters affect a key figure of merit, the grey zone width.

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Abstract\nThis diploma work is about Rapid Single Flux Quantum (RSFQ) circuits. This\nsupercoducting digital circuitry has the most promising properties in terms of speed and\npower consumption. The active elements of the RSFQ circuits are Josephson junctions (JJ).\nFor their fabrication low temperature superconducting niobium films are used. Today the\ndesign and fabrication of RSFQ circuits are done in a standardized way with well-defined\ndesign rules. Nevertheless, to design complicated circuits with more than several hundred\njunctions a lot of practical problems must be solved.\nDifferent aspects of the RSFQ circuits design process were investigated in this work.\nIn the theoretical part we propose a new, more realistic model of the Josephson junction for\nphysical simulation (which is necessarily used for design of every RSFQ gate) in order to\nimprove its quality and precision. The new model for the JJ includes additional inductances,\nwhich must reflect a specific environment of the junction layout. The influence of parameter\ndeviations was investigated in the simulation. As sources of the deviation we chose the\nspread of c (the Stewart-McCumber parameter) and that of the inductances. Then the\noperational margins of the basic elements of the RSFQ logic SR flip-flop were determined\nand compared with the prediction of the previously used model. To prove the results of\nsimulations we designed a test structure of the SR flip-flop, with c=1 and c=2 for the wellestablished\nHYPRES technology (USA).\nAnother part of the work is practical measurements. A test chip, containing chains of 100\nJosephson junctions was designed and measured in order to estimate the spread of critical\ncurrents in real technology.

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Nanoscale superconducting quantum interference devices (nano-SQUIDS) where the weak links are made from nanobridges, i.e., nanobridge SQUIDs (NBSs), are one of the most sensitive magnetometers for nanoscale magnetometry. Because of very strong nonlinearity in the nanobridge-electrode joints, the applied magnetic flux (${\mathrm{\ensuremath{\Phi}}}_{a}$)--critical current (${I}_{c}$) characteristics of NBSs differ very significantly from conventional tunnel-junction SQUIDs, especially when the nanobridges are long and/or the screening parameter is large. However, in most of the theoretical descriptions, NBSs have been treated as the conventional tunnel-junction SQUIDs, which are based on the dc Josephson effect. Here, I present a model demonstrating that for long nanobridges and/or large screening parameters the ${I}_{c}({\mathrm{\ensuremath{\Phi}}}_{a})$ of a NBS can be explained by merely considering the fluxoid quantization in the NBS loop and the energy of the NBS; it is not necessary to take the Josephson effect into consideration. I also demonstrate that using the model, one can derive useful expressions such as the modulation depth and transfer function. I discuss the role of the kinetic inductance fraction ($\ensuremath{\kappa}$) in determining ${I}_{c}({\mathrm{\ensuremath{\Phi}}}_{a})$. I compare the predictions of the present model with the experimental data already published by several groups.

arXiv:1809.09510•Physical review. B./Physical review. B•Apr 5, 2019•11 citations
Josephson junctions are used in present day voltage standards. To extend their use to AC voltage standards a high bandwidth, low-noise detector is required. A candidate component for this detector is a superconducting comparator based on Rapid Single Flux Quantum (RSFQ) circuits. The work presented here is a study to determine if nanobridge weak links can be used as the active Josephson element in these circuits. In order to achieve this an understanding of the nanobridge properties and in particular their critical currents is fundamental. We present simulations of a simple comparator using the circuit simulation software JSIM in order to study the effect of varying nanobridge parameters such as width, length, and loop area. These geometrical variables have an affect on the critical currents and loop inductances which subsequently effect device performance. Particular emphasis is given to investigation of how these parameters affect a key figure of merit, the grey zone width.
We optimized a process to reliably fabricate thin Nb nanobridge weak links having a physical size comparable with Nb coherence length ξ(4.2K) ∼16 nm, controlled degraded superconductivity with respect to the electrodes, and excellent edge roughness. We then investigated the feasibility to use these nanobridges as the Josephson element for reduced footprints and efficient next-generation single flux quantum (SFQ) logic electronics. First of all, we demonstrated that in such thin Nb nanobridges, there is no thermal hysteresis in the current–voltage characteristics (IVC) that instead is usually observed in other weak links and prevents their use in SFQ electronics. We fitted the experimental IVCs of nanobridges with the resistively shunted junction model implemented with piecewise linear current–phase relation (CPR) finding a very good agreement with data. This allowed us to infer the CPR parameters and evaluate the product of critical current and normal resistance,IcRn∼mV, at varying temperatures. Using these data, we simulated the generation of voltage pulses at varying CPRs and verified that they still have a quantized area equal to the magnetic flux quantum Φ0and the productIcRnallows for speed of operationIcRN/ Φ0$\gg 100GHz.Moreover,theircriticalcurrentIc100 GHz. Moreover, their critical currentIc100GHz.Moreover,theircriticalcurrentIc\approx 100100100\mu A,comparablewiththatoftunnelJosephsonjunctions(JJs)usedinSFQelectronics,isordersofmagnitudelargerthanthermalcurrentnoiseITN=(2π/Φ0)kBTA, comparable with that of tunnel Josephson junctions (JJs) used in SFQ electronics, is orders of magnitude larger than thermal current noiseITN= (2π / Φ0)kBTA,comparablewiththatoftunnelJosephsonjunctions(JJs)usedinSFQelectronics,isordersofmagnitudelargerthanthermalcurrentnoiseITN=(2π/Φ0)kBT\approx 0.20.20.2\mu AattemperatureT=4.2K,forstableand,atthesametime,efficientoperationwithenergyperswitchofonlyEJ≈ICΦ0A at temperatureT= 4.2 K, for stable and, at the same time, efficient operation with energy per switch of onlyEJ≈ICΦ0AattemperatureT=4.2K,forstableand,atthesametime,efficientoperationwithenergyperswitchofonlyEJ≈ICΦ0\mathbin{\hbox{$\buildrel<\over {\smash{\scriptstyle \sim}\vphantom{_x}}$}} $1 aJ. To assess the potential use of these nanobridges in SFQ logic electronics with a large number of elements, we used an open-source simulation software (JSim) to simulate the behavior of a standard DC-to-SFQ converter circuit. From the simulation made by implementing the CPR inferred from experimental data, we observed that the circuit behaves exactly as intended. Our results strongly suggest that these nanobridges can be used to develop large-scale SFQ electronics with several advantages over tunnel JJs. The reduced footprint, just one-third or less than standard tunnel JJs, and simplified fabrication process, with only 2 steps involved against typically ∼20 for tunnel JJs, could allow for a better fabrication tolerance, higher control on operation parameters, higher circuit density, and easier integration with other technology platforms. These characteristics could be very appealing also to replace tunnel JJs in quantum technology devices like transmon qubits and superconducting parametric amplifiers.
This paper investigates the feasibility of using weak link nanobridges as Josephson junction elements for the purpose of creating Josephson circuits. We demonstrate the development of a single-step electron beam lithography procedure to fabricate niobium nanobridges with dimensions down to . The single-step process facilitates fabrication that is scalable to complex circuits that require many junctions. We measure the IV -characteristics (IVC) of the nanobridges between temperatures of and and find agreement with numerical simulations and the analytical resistively shunted junction (RSJ) model. Furthermore, we investigate the behaviour of the nanobridges under rf irradiation and observe the characteristic microwave-induced Shapiro steps. Our simulated IVC under rf irradiation using both the RSJ model and circuit simulator JSIM are in agreement with the experimental data. As a potential use of nanobridges in circuits requiring many junctions, we investigate the theoretical performance of a nanobridge-based Josephson comparator circuit using JSIM .
Abstract\nThis diploma work is about Rapid Single Flux Quantum (RSFQ) circuits. This\nsupercoducting digital circuitry has the most promising properties in terms of speed and\npower consumption. The active elements of the RSFQ circuits are Josephson junctions (JJ).\nFor their fabrication low temperature superconducting niobium films are used. Today the\ndesign and fabrication of RSFQ circuits are done in a standardized way with well-defined\ndesign rules. Nevertheless, to design complicated circuits with more than several hundred\njunctions a lot of practical problems must be solved.\nDifferent aspects of the RSFQ circuits design process were investigated in this work.\nIn the theoretical part we propose a new, more realistic model of the Josephson junction for\nphysical simulation (which is necessarily used for design of every RSFQ gate) in order to\nimprove its quality and precision. The new model for the JJ includes additional inductances,\nwhich must reflect a specific environment of the junction layout. The influence of parameter\ndeviations was investigated in the simulation. As sources of the deviation we chose the\nspread of c (the Stewart-McCumber parameter) and that of the inductances. Then the\noperational margins of the basic elements of the RSFQ logic SR flip-flop were determined\nand compared with the prediction of the previously used model. To prove the results of\nsimulations we designed a test structure of the SR flip-flop, with c=1 and c=2 for the wellestablished\nHYPRES technology (USA).\nAnother part of the work is practical measurements. A test chip, containing chains of 100\nJosephson junctions was designed and measured in order to estimate the spread of critical\ncurrents in real technology.
The Josephson comparator is one of the fundamental building blocks of rapid single flux quantum (RSFQ) electronics. Within this circuit family it is the exclusive device which provides logical data processing. The Josephson comparator is also the basic decision element for very fast analog-to-digital converters and sampler circuits for low input power and high-bandwidth signals based on the RSFQ technique. The performance of those devices is fundamentally determined by the characteristics of the Josephson comparator. In this study the gray zone dependency on the clock frequency of a Josephson comparator is investigated by simulations concerning the influence of thermal noise. This investigation is performed for a series of operating points defined by the bias current and different noise levels defined by the operating temperature. In contrast to former investigations, we analyzed the comparator embedded in a realistic environment for output data processing. We identified a characteristic clock frequency f c for a comparator topology designed for a 1 kA cm − 2 niobium fabrication technology. The gray zone of 8 µA remains constant for clock frequencies below f c = 15 GHz and starts to increase for larger frequencies. We also found out that this characteristic frequency is independent of the intensity of thermal noise and therefore independent of temperature.
Rapid single flux quantum (RSFQ) electronics is based on the Josephson junction as an active switching element. In standard RSFQ circuits its switching energy is much lower than the static power consumption caused by the resistive current distribution network. Due to this thermal heating of the chip, the maximum number of junctions on a single chip is limited to about 1 million. The frequency-dependent contribution to power dissipation from junction switchings is only about 2 percent of the static one. This fact limits the direct construction of VLSI systems for high-performance computing as well as small-scale circuit applications in the vicinity of ultra-sensitive detectors or even quantum circuits. We present an assessment of different approaches for reducing the static power consumption by investigating the potential of inductive bias distribution networks as well as reduced critical currents. We analyse the operation stability of simple digital circuits with 5 times smaller critical currents at 4.2 K. The combination of the reduced critical currents and inductive biasing can provide digital superconductive circuits with significantly reduced static power consumption.
Nanoscale superconducting quantum interference devices (nano-SQUIDS) where the weak links are made from nanobridges, i.e., nanobridge SQUIDs (NBSs), are one of the most sensitive magnetometers for nanoscale magnetometry. Because of very strong nonlinearity in the nanobridge-electrode joints, the applied magnetic flux (${\mathrm{\ensuremath{\Phi}}}_{a}$)--critical current (Ic{I}_{c}Ic​) characteristics of NBSs differ very significantly from conventional tunnel-junction SQUIDs, especially when the nanobridges are long and/or the screening parameter is large. However, in most of the theoretical descriptions, NBSs have been treated as the conventional tunnel-junction SQUIDs, which are based on the dc Josephson effect. Here, I present a model demonstrating that for long nanobridges and/or large screening parameters the ${I}_{c}({\mathrm{\ensuremath{\Phi}}}_{a})$ of a NBS can be explained by merely considering the fluxoid quantization in the NBS loop and the energy of the NBS; it is not necessary to take the Josephson effect into consideration. I also demonstrate that using the model, one can derive useful expressions such as the modulation depth and transfer function. I discuss the role of the kinetic inductance fraction ($\ensuremath{\kappa}$) in determining ${I}_{c}({\mathrm{\ensuremath{\Phi}}}_{a})$. I compare the predictions of the present model with the experimental data already published by several groups.