A New Analytical Method for Calculating Maximum Junction Temperature of Packaged Devices Incorporating the Temperature Distribution at the Base of the Substrate

All current analytical methods for calculating junction temperature of field effect transistor (FET) and monolithic microwave integrated circuits (MMIC) devices have assumed a constant uniform temperature at the base of the substrate. In a packaged device, however, where the substrate is attached to a carrier, finite element thermal analyses have shown that the temperature distribution along the base of the substrate is not uniform but has a bell-shaped distribution. Consequently, current analytical methods which attempt to predict the junction temperature of a packaged MMIC device by assuming a constant uniform temperature at the base of the substrate have been found to be inaccurate. In this paper, it is found that the temperature distribution along the base of a substrate can be well approximated by a Lorentz distribution which can be determined from a few basic parameters of the device such as the gate length, gate pitch, number of gates, and length of substrate. By incorporating this Lorentz temperature distribution at the base of the substrate with a new closed-form solution for the three-dimensional temperature distribution within the substrate, a new analytical method is developed for accurately calculating the junction temperature of MMIC devices. The accuracy of this new method has been verified with junction temperatures of MMIC devices measured using thermoreflectance thermography (TRT) as well as those calculated using finite element analysis (FEA).