Thermomechanical stress analysis of laminated thick-film multilayer substrates

As an increasing number of polymer dielectric layers were laminated, the maximum bow values were measured layer by layer using a laser profilometry during thermal cycling. In the lamination process, a polymeric film is overlaid on a silicon substrate using a polymeric adhesive. Since the lamination process uses relatively thick polymer films, the classical stress analyses assuming infinitesimally thin films, are no longer effective. In this letter, a simple model based on the composite beam theory is presented to analyze the experimental results, and compared with the well-known Stoney's formula. The thermomechanical behavior of the laminated multilayer polymer films on a silicon substrate was better described by the proposed model, while an error as much as 30% was involved using Stoney's formula. The model can be applied for the design and fabrication of multilayer multichip module substrates. (C) 1999 American Institute of Physics. [S0003-6951(99)03623-2].