BEM calculation of the complex thermal impedance of microelectronic devices

This paper presents a numerical method for modelling the dynamic thermal behaviour of microelectronic structures in the frequency domain. A boundary element method (BEM) based on a Green's function solution is proposed for solving the 3D heat equation in phasor notation. The method is capable of calculating the AC temperature and heat flux distributions and complex thermal impedance for packages composed of an arbitrary number of bar-shaped components. Various types of boundary conditions, including thermal contact resistance and convective cooling, can be taken into account. A simple benchmark case is investigated and a good convergence towards the analytical solution is obtained. Simulation results for a thin plate under convective cooling are compared with a theoretical model and an excellent agreement is observed. In a second example a more complicated three-layer structure is investigated. The BEM is used to analyse the thermal behaviour if delamination of the package occurs, and a physical explanation for the results is given.