A RATIONAL FORMULATION OF THERMAL CIRCUIT MODELS FOR ELECTROTHERMAL SIMULATION .1. FINITE-ELEMENT METHOD

As the size of the semiconductor devices is getting smaller with advan ced technology, self-heating effects in power semiconductor devices ar e becoming important, An electrothermal simulation of complete power e lectronic systems that include Si chips, thermal packages, and heat si nks is essential for an accurate analysis of the behavior of these sys tems, This paper presents a rational approach to construct thermal cir cuit networks equivalent to a discretization of the heat equation by t he finite element method, Elemental thermal circuit networks are devel oped, which correspond to the linear and cubic Hermite elements in the 1-D case, to the triangular and rectangular elements in the 2-D case, and to the tetrahedral and cube elements in the 3-D case, These therm al circuit networks are to be connected to the electrical networks of power electronic systems to provide complete electrothermal models tha t can be conveniently used in any circuit simulator package, Verificat ion examples are presented to demonstrate the accuracy of the proposed formulation.