Estimation of passivated metal stack modulus through simulations of Micro-indentation

The determination of the passivated metal stack modulus, and in particular the modulus of thin films in a stack, is of great importance in the assessment of the reliability of Back-End-of-Line (BEOL) structures. Micro-indentation, which enables estimation of the modulus of thin films without needing (difficult to fabricate) free-standing film specimen, is utilized to extract the modulus of the top-most film on double-layer and multilayer stacks in the present study. Finite element modeling is used to simulate indentation tests and to extract the film modulus. Two double-layer and four multi-layer stack structures (differing in number of layers and materials) are characterized to study the influence of film/substrate modulus ratio, yield strength and layer configuration on the estimated modulus. Comparison of the results obtained by four different regression functions shows that the reciprocal of Gao's function and the reciprocal of linear function can, in general, produce more accurate results for double-layer stacks and multilayer stacks, respectively. In the special case where a great amount of sink-in is developed, the modulus obtained from a single low-depth test may be more accurate.