Augmented finite element method (AFEM) for the linear steady-state thermal and thermomechanical analysis of heterogeneous integration architectures

The thermal and thermomechanical reliability analysis of a package is often performed under cyclic loading conditions. An enhanced finite element method to efficiently solve for the steady-state temperature and stress responses arising out of such analysis is presented in this paper. It belongs to and extends the harmonic balance finite element method (HBFEM) technique for the case of a periodic switched linear (PSL) system. The method captures the periodic time-varying nature in the spectral domain. By relying on the time-invariant basis, the method addresses the time-scale and coupling challenges that exist with the traditional time-domain methods for the multi-physics modeling and analysis of the electronic packages. Its computational efficiency is verified on the power-cyclic thermal and thermomechanical analysis of a panel-embedded package.