Highspeed superconducting logic circuits EECS 713 presentation by

High-speed superconducting logic circuits EECS 713 presentation by Naveed Mahmud 10/7/2020 1

Background • Superconductor electronics (SCE) use Josephson junctions (JJs) as switching devices Properties of superconductors v Metals cooled (~4. 2 K) to very low temperatures v Essentially no electrical resistance v Expels all magnetic fields v Maximum supercurrent called the critical current 10/7/2020 A Josephson junction is made by sandwiching a thin layer of a nonsuperconducting material between two layers of superconducting material. Research into aluminum superatoms may lead to the discovery of a new class of high-temperature superconductors (Image: 2 Shutterstock)

Background • Josephson junction v. Supercurrent flows across barrier v. When current < critical current v. Voltage across junction zero v. When current > critical current A Josephson junction is made by sandwiching a thin layer of a nonsuperconducting material between two layers of superconducting material. v. AC voltage across junction ~ 500 GHz/m. V v. Change of state used for applications v. Digital circuits can be built from JJs 10/7/2020 Josephson junction array chip developed by the National Bureau of Standards as a standard volt 3

Background • Josephson junction is modeled by Resistively Capacitively Shunted Junction (RCSJ) • Total current is sum of • • 10/7/2020 Josephson tunnel current Quasi-particle tunnel current Displacement current through junction C Current through external shunt R 4

Circuit Fabrication v. Circuits made in the US and Japan historically the most successful v. Exponential growth (x 3 less than CMOS) v. Cryogenic Computing Complexity (C 3) targets greater exponential growth The largest demonstrated Single Flux Quantum (SFQ) circuits have only about 105 Josephson junctions 10/7/2020 The total number of Josephson junctions in fully-operational superconducting integrated circuits reported in journal publications and conference proceedings. 5

Single Flux Quantum (SFQ) circuits • Network of Josephson junctions interconnected by superconducting wires (inductors) • DC bias currents • Network of bias resistors • Common voltage rail • Network of bias inductors and JJs SFQ circuits are built using large networks of JJs, inductors, resistors, and transmission lines. • AC bias and clock signals • Network of passive transmission lines (PTLs) • Coupling transformers 10/7/2020 6

Single Flux Quantum (SFQ) circuits • Uses magnetic-flux quantization in superconducting loops • Three types of logic: § Rapid Single Flux Quantum (RSFQ) § ERSFQ § e. SFQ § Reciprocal Quantum Logic (RQL) § Quantum Flux Parametron (QFP) logic 10/7/2020 magnetic flux quantum Φ 0 = h/(2 e) ≈ 2. 067833848. . . × 10− 15 Wb is a combination of fundamental physical constants: the Planck constant h and the electron charge e. 7

Rapid Single Flux Quantum (RSFQ) • Voltage pulses using shunted JJs (SFQ pulses with quantized area) • Represents logic instead of using voltage state logic • Fast and scalable superconducting ICs • Complete RSFQ logic / memory family • Simplest SFQ pulse generator circuit (SQUID) 10/7/2020 8

Superconducting QUantum Interference Device (SQUID) • Magnetic flux through the loop is the difference between the external applied flux and flux generated in the loop by the circulating current • This flux is related to the phase difference across the Josephson junction (Faraday’s induction law) as: 10/7/2020 9

Superconducting QUantum Interference Device (SQUID) 10/7/2020 10

SFQ Voltage Pulse • An SFQ pulse with quantized area of pulse height is 1. 5. Ic. R and the FWHM is the ratio of quantized area to the pulse height 10/7/2020 11

General scheme of RSFQ circuits • Logic is defined by presence or absence of SFQ pulse • n-Data lines and an Output synchronized with a Clock signal. 10/7/2020 12

Frequency scaling of RSFQ circuits • 10/7/2020 13

Conclusion • RSFQ is the fastest digital technology capable of reaching ~ 70 GHz clock frequencies in the current technology node and over 100 GHz • The technology level of SCE circuits based on RSFQ is defined by the critical current density (jc) of Josephson junctions • Maximum operating speed of the circuits scales as the square root of jc • Need to increase jc while proportionally decreasing the junction size • Fast and compact JJ-based RAM should be investigated using advanced materials and smaller features 10/7/2020 14