Modeling of Circuits with Strongly Temperature Dependent Thermal Conductivities for Cryogenic CMOS

TL;DR

This paper develops a SPICE model for cryogenic CMOS circuits that accurately predicts local heating effects by incorporating temperature-dependent thermal conductivities, validated through measurements at 4.2K.

Contribution

It introduces a novel lumped element SPICE model that accounts for strong temperature-dependent thermal conductivities in cryogenic CMOS circuits.

Findings

Model predicts local heating within 20% of measurements

Effective for temperatures from <1K to over 100K

Provides insights into thermal behavior at cryogenic temperatures

Abstract

When designing and studying circuits operating at cryogenic temperatures understanding local heating within the circuits is critical due to the temperature dependence of transistor and noise behavior. We have investigated local heating effects of a CMOS ring oscillator and current comparator at T=4.2K. In two cases, the temperature near the circuit was measured with an integrated thermometer. A lumped element equivalent electrical circuit SPICE model that accounts for the strongly temperature dependent thermal conductivities and special 4.2K heat sinking considerations was developed. The temperature dependence on power is solved numerically with a SPICE package, and the results are within 20% of the measured values for local heating ranging from <1K to over 100K.