  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.
