Thermal budget of superconducting digital circuits at sub-kelvin temperatures

TL;DR

This paper investigates the thermal challenges of superconducting SFQ circuits operating at sub-kelvin temperatures, providing a thermal model and experimental data to guide design improvements for ultra-low-temperature quantum applications.

Contribution

It introduces a thermal model for SFQ circuits at sub-kelvin temperatures and presents experimental validation, addressing overheating issues in ultra-low-temperature superconducting electronics.

Findings

Overheating limits dissipated power in SFQ circuits at sub-kelvin temperatures.

Experimental data supports the thermal model of electron and substrate overheating.

Design modifications are needed to mitigate overheating in ultra-low-temperature superconducting circuits.

Abstract

Superconducting single-flux-quantum (SFQ) circuits have so far been developed and optimized for operation at or above helium temperatures. The SFQ approach, however, should also provide potentially viable and scalable control and read-out circuits for Josephson-junction qubits and other applications with much lower, milli-kelvin, operating temperatures. This paper analyzes the overheating problem which becomes important in this new temperature range. We suggest a thermal model of the SFQ circuits at sub-kelvin temperatures and present experimental results on overheating of electrons and silicon substrate which support this model. The model establishes quantitative limitations on the dissipated power both for "local" electron overheating in resistors and "global" overheating due to ballistic phonon propagation along the substrate. Possible changes in the thermal design of SFQ circuits in view of the overheating problem are also discussed.