Root-of-area formula of electrical capacitance, for equivalent circuit of thermal conduction, from an HBT-IC through a GaAs substrate with temperature dependent conductivity

Like the field computation of capacitance, thermal resistance from an ICs is normally done by simulating over a very large region of the device and substrate, in 3D and with very fine meshing. This is especially necessary in a temperature dependent substrate such as GaAs [1]. Through the root-of-area capacitance formula of the electrical equivalent, this paper shows that the tedious 3D fine meshing may be replaced by a simple equivalent circuit.