Elastic Properties and Representative Volume Element of Polycrystalline Silicon for MEMS

Abstract

A nanoscale mechanical deformation measurement method was employed to obtain the Young’s modulus and Poisson’s ratio of polycrystalline silicon for Microelectromechanical Systems (MEMS) from different facilities, and to assess the scale at which these effective properties are valid in MEMS design. The method, based on in situ Atomic Force Microscope (AFM) imaging and Digital Image Correlation (DIC) analysis, employed 2–2.5 μm thick freestanding specimens with surface measurement areas varying between 1×2 and 5×15 μm². The effective mechanical properties were quite invariant with respect to the fabrication facility: the Poisson’s ratio of polycrystalline silicon from the Multi-user MEMS Processes (MUMPs) and from Sandia’s Ultra planar four layer Multilevel MEMS Technology (SUMMiT-IV) was 0.22±0.02, while the elastic moduli for MUMPs and SUMMiT-IV polysilicon were 164±7 and 155±6 GPa, respectively. The AFM/DIC method was used to determine the size of the material domain whose mechanical behavior could be described by the isotropic constants. For SUMMiT polysilicon with columnar grains and 650 nm average grain size, it was found that a 10×10-μm² specimen area, on average containing 15×15 columnar grains, was a representative volume element. However, the axial displacement fields in 4×4 or 2×2 μm² areas could be highly inhomogeneous and the effective behavior of these specimen domains could deviate significantly from that described by isotropy. As a consequence, the isotropic material constants are applicable to MEMS components comprised of 15×15 or more grains, corresponding to specimen areas equal to 10×10 μm² for SUMMiT and 5×5 μm² for MUMPs, and do not provide an accurate description of the mechanics of smaller MEMS components.