Juergen Kunert

Design centering methods for yield optimization of cryoelectronic circuits

We present the results of comparison of different design centering methods, e.g. simplicial approximation method and centers-of-gravity method. The effectiveness of the proposed yield optimization strategies is demonstrated by application to various RSFQ circuits and analytical test functions. A SPICE-type program which includes the possibilities of analog behavior modeling and transient noise simulation was used for circuit simulation. Based on these methods, an interactive yield optimization framework for cryo-electronic circuits was developed and tested.

Reduced Power Consumption in Superconducting Electronics

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.

Formal description of the functional behavior of RSFQ logic circuits for design and optimization purposes

For being used in the design of Rapid Single Flux Quantum (RSFQ) circuits in a multipurpose manner, we developed a systematic and consistent approach for modeling the nominal circuit behavior using hardware description languages. We are presenting a method for establishing evaluation criteria for the circuits behavior which can directly be used in the input for circuit simulation and serve as a behavioral reference in yield-driven optimization cycles. Furthermore, this behavioral modeling technique allows for mixed-mode simulation with its advantages of both analysis speed-up and error localization. Finally, we demonstrate the application in high-level circuit synthesis which will be necessary to manage complex design problems.

Recent Developments in Superconductor Digital Electronics Technology at FLUXONICS Foundry

In Europe, the FLUXONICS Foundry develops fabrication processes and design kits for superconductor digital and mixed-signal circuits. We describe the implementation of the “European Roadmap for Superconductor Electronics” into the recent foundry process for superconductor digital electronics. Following the hierarchical cell-based design strategy, we developed a design kit with basic cells. We present experimental results of the process quality, the verified operation margins of the library cells, and the results of low- and high-speed investigations of test circuits. The process is suitable for the integration of complex digital and mixed-signal circuits for smart multichannel superconductor sensor applications with a digital interface.

Experimentally verified design guidelines for minimizing the gray zone width of Josephson comparators

We investigated the gray zone width of Josephson comparators by means of circuit simulations and experiments, looking at the dependences on different circuit parameters and topologies. Eight different comparator circuits were simulated and designed for a 1 kA cm − 2 niobium device. With our sophisticated measurement set-up, the lowest reported gray zone width of 3.2 µA at 4.2 K was measurable. Moreover, the results obtained allow us to derive a set of design rules for further reduction of the gray zone width, which was the original goal of our investigations.

Linearity of a Digital SQUID Magnetometer

A digital SQUID magnetometer measures the magnetic field amplitude by counting integer magnetic flux quanta within its superconducting input loop. Although resolution is limited in comparison to analog SQUID systems, the digital SQUID is able to outrange its analog counterpart with regard to parameters such as slew rate and dynamic range. In this work we evaluate the performance of a digital SQUID based on a three-level logic. Due to this basic principle, we face a combination of two comparator grayzones leading to hysteretic behavior of the sensor that produces a “dead zone” in the signal reversal point. The dependence of the comparator threshold on design parameters is investigated by simulation studies and reconfirmed by experimental results. We were able to reach a total dynamic range of more than 540,000 flux quanta (about 19 bit) with a linearity error of about 5 bit due to the mentioned hysteretic behavior. We discuss the results of our investigations and provide guidelines to extend dynamic range and linearity for future sensor designs.

On-chip integrated SQUID readout for Superconducting bolometers

We present the first steps toward a 288 pixel sub-millimeter wavelength bolometer camera. We have used bolometers of the transition edge type, choosing a thermometer made of a proximity bilayer of Mo and the alloy Au/Pd with a designed transition temperature of about 500 mK. We have adapted our well-developed niobium based technology for SQUID manufacturing in order to be able to fabricate the current sensor and the bolometer on a common substrate. The function of both devices was successfully tested at the operating temperature of 300 mK.

Operation of Low-

Low-Tc rapid single flux quantum (RSFQ) digital circuits without magnetic shielding fabricated with the FLUXONICS Foundry have been studied in the presence of external magnetic fields. Magnetic fields parallel to the plane of the chip are shown to influence more drastically the nominal behavior of the circuits above 5 μT, while perpendicular magnetic fields can reach 15 μT without affecting significantly their operation. This is confirmed by experimental SQUID interference patterns.

T_{c}

The rapid single-flux quantum electronics (RSFQ) is a superconducting, naturally digital circuit family which is currently close to being commercially applied. RSFQ is outstanding because of its very low switching energy resulting in very low power consumption. This advantage causes, however, a significant influence of thermal noise. For industrial applications, a certain noise immunity is required which is still a challenge, especially for circuits of higher complexity. Integrating phase-shifting elements is a new concept for further improvements concerning stability against the influence of thermal noise. We have already shown that the implementation of phase-shifting elements significantly reduces the influence of thermal noise on circuit behavior by experimentally analyzing the bit-error rate (Mielke et al 2009 IEEE Trans. Appl. Supercond. 19 621–5). Concepts which are easily implementable in standard niobium technology are especially promising. The π-phaseshifter consists of a superconducting loop which is able to store a single flux quantum. The loop current related to the stored flux creates a well-defined phase shift. To achieve the correct functionality of complex circuits it is essential to store exactly one flux quantum in each π-phaseshifter during the cooling down of the chip. Thus, for studying the feasibility of this new approach, the initialization reliability of the π-phaseshifter needs to be verified. We present an experimental investigation of this reliability to obtain a general assessment for the application of the π-phaseshifter in niobium technology. Furthermore, we compare the configuration shielded by a solid ground plane with a configuration with a ground-plane hole below the π-phaseshifter. Justified by the experimental results we suggest programmable RSFQ circuits based on π-phaseshifters. The characteristics of these devices can be influenced by a controlled initialization of the π-phaseshifter. The fabrication was performed by FLUXONICS Foundry.

Circuits in a Magnetic Environment

The design of single flux-quantum (SFQ) circuits requires well-defined inductances. In many cases these are created by irregular geometries and a computer-aided design tool is necessary for inductance calculations. This becomes a challenging task in cases where no ground plane is used and thus three-dimensional calculations are required. For this purpose, InductEx was developed and verified successfully for simple structures. In this work we take the next step and demonstrate the applicability of InductEx to the design of rapid single flux-quantum (RSFQ) cells. We use InductEx for inductance modeling as an integral part of the design cycle for an RSFQ cell with flux quantum transfer via mutual inductance and for a DC-reprogrammable logic circuit with similar inductive coupling. The relation between coupling factor and self-inductance is optimized in the circuit layout. All coupling structures are duplicated in SQUID modulation test circuits to measure and verify calculation accuracy. We find excellent agreement between the calculated and measured inductance values. Furthermore, the operational area of the basic cell is determined and compared with similar investigations reported earlier. Based on this comparison we conclude that InductEx is a valuable inductance design tool, and that mutual coupling in structures using ground plane holes and RSFQ-compatible self-inductances can be modeled and designed reliably.