Ambient Temperature and Self-Heating Scaling Laws for Materials With Temperature-Dependent Thermal Conductivity

Two of the primary variables affecting junction temperature of semiconductor devices are the self-heating due to internal power dissipation within the device and the device's base (or ambient) temperature. For materials with temperature-independent material properties, the junction temperature is a linear function of these two variables, which allows for simple "scaling" of the junction temperature for arbitrary dissipation and/or base temperatures. In materials with temperature-dependent material properties, however, the relationship between junction temperature and either variable is nonlinear. The scaling law between junction temperature and dissipated power and base temperature for materials with temperature-dependent material properties are developed in this work. This scaling law allows for fast computation of junction temperature for any values of power dissipation and/or base temperature given the junction temperature for one specific instance of power dissipation and base temperature and hence may find applicability in fast electrothermal solvers.