Due to the thermal expansion mismatch of the different parts of multilayered structures, thermal stresses build up in the structure while it is manufactured and used. The problems such as delamination (interfacial crack) and excessive thermal bowing are related to the level of thermal stresses. Hence, the thermal stress and deformation problems should be understood and controlled precisely during the fabrication in order to manufacture high-reliability multilayered structure.
A multi-chip module (MCM) substrate is an example of multilayered structure subjected to thermal loading. In MCM substrate, various thin film technologies are used and the number of layers increases to meet the demands of electronics industry. This multilayer substrate has the properties which are not well taken care of in the usual thermal stress analysis; that is, (i) each layer experiences the different thermal history because the multilayered structures are made by the sequential build-up of the alternating layers of polymer dielectric and metal conductor films, (ii) a single film thickness cannot be assumed to be infinitesimal any more compared to the others, (iii) the polymer films seem to undergo the relaxation of stress.
In this study, a simple model for the thermomechanical behavior of multilayered structure is presented and verified with experiments. The proposed model, composite beam analysis (CBA) is based on the ‘cut and paste’ technique and the composite beam theory. The thermomechanical bowing of MCM substrates was experimentally measured layer-by-layer, and it is compared with the result of the thermomechanical stress analysis by CBA. The analytical results presented here provide the good estimation of the thermomechanical bowing as a function of temperature. The CBA accounts for the stress relaxation effect of polymer dielectric films as well as the different thermal history of each layer and the effect of the film thickness.
The energy release rate of an interfacial edge crack in multilayered structure under thermal loading is also evaluated in this study. The conservation integral J, which is physically the same as the energy release rate of a crack, is calculated using the stress field of multilayered structure obtained by CBA without the additional finite element analysis.
