Theoretical and experimental characterization of self-heating in silicon integrated devices operating at low temperatures

The self-heating of Si devices operating in the 4 K<T<300 K range is discussed in this work. The temperature-dependent thermal time constant of a typical Si chip is calculated and compared to several electrical relaxation times. Thermal events may be indistinguishable from electrical events at low temperatures, and this makes the transient method an unreliable one for characterizing the cryogenic self-heating. A semi-analytical approach, which considers the temperature dependence of the thermal conductivity of Si, is used to calculate the steady-state thermal profile on the top surface of a Si IC where a device is dissipating power at different ambient temperatures. Theoretical results indicate that the temperature rises measured in earlier works cannot be due to the thermal properties of Si at low temperatures. A test chip containing several integrated Si devices is used to characterize experimentally the self-heating. The strong self-heating usually observed in Si devices operating at very low temperatures is dominated by the parasitic thermal resistance, of which the ceramic package is the main contributor. The dominance of this parasitic contribution decreases for an increasing ambient temperature and becomes similar to that of the Si device at 300 K