Statistical approach to the elastic property extraction and planar elastic response of polycrystalline thin-films.

摘要

A system of numerical methods is proposed to predict planar elastic responses and/or the elastic property (modulus and Poisson's ratio) of polycrystalline thin-films for Micro-Electro-Mechanical Systems (MEMS) components. A lattice based stochastic model is employed to model the micro structural evolution (nucleation and growth) of thin-film deposition. Given a micrograph, depicting a grain distribution, key kinetics parameters for the deposition process can be extracted by the proposed inverse method within the system.; In order to connect the microstructure evolution simulation and the elastic behavior prediction by the finite element method, a mesh generation algorithm on the lattice based microstructure is developed. The edge matching, essential for the node location on the grain boundaries, is accomplished by a pixel-by-pixel marching scheme. The finite element method with planar anisotropic elasticity model is used to calculate statistically averaged values of Young's modulus and Poisson's ratio. The Chi-square test is adopted for the statistical convergence criterion, proven to be statistically admissible and logically reasonable. This criterion is not affected by the appearance order of the variables and well behaved regardless of the variable types considered.; The developed system of models (plane stress/strain), techniques and numerical algorithms are applied to the following polycrystalline materials to calculate statistically scattered effective elastic constants: polysilicon, barium titanate and zircon.; A micro-beam specimen is also analyzed for a statistically scattered elastic response (tip deflection and stress) and compared with classical solutions. The beam is assumed to have a known microstructure (Al2O3 ), in which each grain has a different planar orthotropic axis. The example approach can be applied directly to other MEMS components without bothering to determine statistically averaged elastic constants.; The effects of the polycrystalline specimen size and the anisotropy of the material on the statistical scatter of the effective elastic constants are studied. The larger scatter is observed for a smaller size of specimen and for a material with more severe anisotropy.