Modelling the reaction behavior in reactive multilayer systems on substrates used for wafer bonding

Exothermic self-propagating high-temperature synthesis of intermetallic compounds attain increasing interest in the field of wafer bonding in microelectronics and microsystems technology due to local heat generation. Numerical models of self-sustaining reactions in thin multilayer films can be used to predict velocity and shape of the reaction front. This work deals with heat losses to various substrate materials and material compounds used for wafer bonding as well as the prediction of minimal numbers of bilayers required for a self-propagating reaction front. We introduced a cylindrically symmetric finite element approach. In addition to that, the effect of temperature-dependent specific heat capacities was investigated. Numerical computations were performed for Pd/Al multilayers and are compared to experimental data. It was found that the developed formalism is suitable to determine the mutual influence of heat losses and reaction properties. Furthermore, it was demonstrated that minimal numbers of bilayers can be determined more precisely by including temperature-dependent specific heat capacities.