Universal Minimum Heat Leak on Low-Temperature Metallic Electrical Leads

TL;DR

This paper derives a universal relation for minimizing heat leaks in low-temperature metallic leads, balancing electrical and thermal resistances, with broad applications in cryogenic systems including superconducting circuits and sensors.

Contribution

It introduces a simple universal approximate formula for the optimal heat leak in low-temperature metallic leads based on the Wiedemann-Franz law.

Findings

Q/I = V = 3.6 kT[hot]/e for optimal leads

Applicable to superconducting circuits and sensor arrays

Balances electrical bias and thermal insulation

Abstract

Low-temperature electronic systems require electrical leads which have low electrical resistance to provide bias current I without excessive voltage drop V. But proper cryogenic design also requires high thermal resistance to maintain a minimum heat leak Q from the hot temperature T[hot] to the cold temperature T[cold]. By the Wiedemann-Franz law, these requirements are in direct conflict, and the optimal configuration takes a particularly simple universal approximate form for the common case that T[cold] << T[hot]: Q/I = V = 3.6 kT[hot]/e. This is applied here to the cryopackaging of RSFQ superconducting circuits on a 4K cryocooler, but is equally applicable to other cryogenic systems such as a superconducting sensor array at low and ultra-low temperatures.