Multiscale modelling of multilayer substrates

A multiscale (global-local) numerical method for the assessment of reliabilty issues in substrates is presented. The method allows for the calculation of accurate local quantities, without the need for heavy calculations. A global step is performed by first subdividing the substrate into cells. Next, the structure (circuit) of each cell is analysed and quantified and, based on the result, appropriate effective properties are assigned. In this way a homogenised finite element model of the substrate is constructed which is used to determine its global response. A local step is subsequently performed, where only a small ‘region of interest’ of the substrate is modelled in detail. The loading is accomplished by describing boundary conditions extracted from the global simulation.