Computer-aided thermal analysis of power semiconductor devices

Thermal analysis of power semiconductor devices is often complicated by odd geometries and the nonlinear properties of materials. It is the type of problem that can best be handled by a computer. Fortunately, numerous general-purpose heat transfer programs have been written that can be applied to power semiconductor deyices. The majority of programs were written for other technologies (aircraft engines, nuclear energy, and space) but they are sufficiently general for electronic applications. These programs are most often based on the method of finite differences. While this method can yield results to any degree of accuracy required, it is not readily apparent just how accurate the results are. In general, a user desires results as accurate as necessary while minimizing the cost of the problem solution. This paper deals with methods of achieving that goal. Descriptions of truncation and convergence errors are given along with methods of estimating their magnitude. Various forms of the finite difference method are discussed. Methods for speeding convergence are shown, including acceleration algorithms and simple guidelines for ordering matrices and selecting node boundaries. Convenient methods of displaying and interpreting the results are also discussed.