Thermal impedance of microwave integrated circuits with localized small heat sources

The heat sinking of small active devices embedded in semiconductor chips is investigated. It is assumed that heat is dissipated only by conduction to the back of the chip and that no special thermal features are provided in the design of the device. This problem is usually approached with finite-element analysis or with involved analytical methods. In this paper, a simple closed-form equation for the thermal impedance from the heat source to the back of the chip is derived based on the equivalence of electrical and thermal fields. The electrical designer can use this equation to estimate the thermal impedance of critical devices. The equation shows that the design of embedded devices is thermally very limited. The equation contains only two design parameters: the periphery of the heat generating area and the chip thickness.