Establishing mode mix dependency of fracture toughness in microelectronic components with reduced experimental effort

Bulk material fracture and interface delamination are main failure modes observed in microelectronic components. Drivers are stresses during processing (e.g. soldering), testing (e.g. moisture sensitivity, thermal cycling) and operation in application environments. For quantitative modeling to predict failures the fracture toughness expressed as critical energy release rate G_c has to be known by measurements. As interface toughness depends on processing of materials, the mode mix of tensile and shear stress loads expressed by a mode angle Ψ with a reference length l_ref as additional parameter, further on temperature T and moisture condition C, this is a huge task and full data sets are rarely found. In summary G_c=G_c(Ψ(l_ref), T, C) is a function of four parameters. Usually just fit functions of measured data are reported. A physics based relation of the dependency of critical energy release rate G_c on mode angle Ψ is highly desirable, could drastically reduce the experimental effort, and provide a model to better understand influence factors. The present work suggests such a relation. Starting from an idealized layer stack of inert particles a hypothesis is derived, which leads to a basic relation for G_c(Ψ). We apply this function to four cases to fit own experimental results and data from literature or phenomenological expressions representing measured data. Good agreement is found. Then we extend the approach from an idealized flat interface to more realistic rough interfaces to explain adhesion promotion by roughening for asymmetric and symmetric roughness profiles. Finally we suggest an expression to cover also the effect of chemical adhesion promotion. The expressions derived cover all aspects of adhesion and depend on 1-3 parameters only. In principal a similar number of independent measurements at different mode angles Ψ is enough to establish - he whole G_c(Ψ) curve. More is safer. We suggest to do about five measurements at suitable mode angles Ψ. That should give all information needed. With more experience, and for extensions to different temperature and humidity conditions, three or in case of poor adhesion even one additional experiment can be sufficient. Overall the approach enables a tremendous reduction of the experimental characterization effort and a better understanding of interface adhesion.