Interaction integral and mode separation for BEoL-cracking and -delamination investigations under 3D-IC integration aspects

As a consequence of increasing functional density and miniaturization in microelectronics new low-k and ultra-low-k materials are going to be increasingly used in Back-end of line (BEoL) layers of advanced CMOS technologies. These ongoing trends together with the transition to the use of TSVs for 3D-IC-integration cause novel challenges for reliability analysis and prediction of relevant electronics assemblies. The optimization of fracture and fatigue resistance of those BEoL structures under manufacturing/packaging (during lead-free reflow-soldering, in particular) as well as chip package interaction (CPI) aspects is a key for further enhancements - see also [1]. In particular in this context the evaluation of the risk of delamination at bi-material interfaces and damaging and cracking of materials needs to be improved. The application of advanced finite element techniques combined with experimental observations and validations, provide a way to gain more fundamental knowledge and ultimately, to understand, predict and prevent reliability issues. However, cracking and delamination risk evaluations hang behind the needs - especially for nonlinear, transient, thermal loading of bi-material interface fracture. At this point, the correct mode mixity separation at bi-material interface cracks is a precondition for proper delamination risk evaluation. However, different approaches are known to be dependent on mesh density, integration path and/or reference length. We discuss the use of VCCT and integral fracture concepts for bulk and bi-material interface fracture in multi-scale and multi-failure modeling approaches. Energy release rate (ERR), stress intensity factors (SIF) and the related phase angles as results of the different approaches will be investigated and compared. Analytic relations between them will be pointed out and verified. Therefore, the frequently investigated role of reference length, normalizing length and path dependence for the calculation of the fracture parameters is discussed. Effects on the fracture parameters are finally discussed related to the cracking risk of BEoL structures. The authors combine these numerical approaches with experimental results in order to optimize the toughness for bulk material fracture and interface delamination with regard to structural modifications.