Modeling of circuits with strongly temperature dependent thermal conductivities for cryogenic CMOS

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. Local heating effects of a CMOS ring oscillator and current comparator were investigated at T=4.2 K. 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 4.2 K heat sinking considerations was developed. The temperature dependence on power is solved numerically with a SPICE package, and the results are typically within 3σ3σ of the measured values for local heating ranging from <1K to over 100 K.