Finite element method

As the size of the semiconductor devices is getting smaller with advanced technology, self-heating effects in power semiconductor devices are becoming important. An electrothermal simulation of complete power electronic systems that include Si chips, thermal packages, and heat sinks is essential for an accurate analysis of the behavior of these systems. This paper presents a rational approach to construct thermal circuit networks equivalent to a discretization of the heat equation by the finite element method. Elemental thermal circuit networks are developed, 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 thermal circuit networks are to be connected to the electrical networks of power electronic systems to provide complete electrothermal models that can be conveniently used in any circuit simulator package. Verification examples are presented to demonstrate the accuracy of the proposed formulation.