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 mm thick freestanding specimens with surface measurement areas varying between 1 Â 2 and 5 Â 15 mm 2 . 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 T 0.02, while the elastic moduli for MUMPs and SUMMiT-IV polysilicon were 164 T 7 and 155 T 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 Â 10-mm 2 specimen area, on average containing 15 Â 15 columnar grains, was a representative volume element. However, the axial displacement fields in 4 Â 4 or 2 Â 2 mm 2 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 Â 15 or more grains, corresponding to specimen areas equal to 10 Â 10 mm 2 for SUMMiT and 5 Â 5 mm 2 for MUMPs, and do not provide an accurate description of the mechanics of smaller MEMS components.

Fracture Behavior of Nanoscale Notched Silicon Beams Investigated by the Theory of Critical Distances

“…In situ observation of mechanical behavior has DOI: 10.1002/adts.201700006 advanced as well. [10][11][12][13] Sumigawa et al [10] published a review of a series of experimental studies at small scales. The authors concluded that the "stress," whose concept is based on continuum mechanics, is still applicable to the fracture phenomenon as the governing parameter while the size approaches the atomic scale.…”

Microscale Experiments at Elevated Temperatures Evaluated with Digital Image Correlation

“…The second approach was easier to implement but it was possible only at high optical magnifications. The effectiveness of the two patterns was found to be equivalent in terms of strain resolution, which, as computed from the axial displacement field using the approach in [26], was ∼0.01%.…”

On-Chip Mechanical Characterization using an Electro-thermo-mechanical Actuator

“…In recently published papers [20][21][22][23] experimental values of polysilicon Young's modulus have been reported in the range 100-173 GPa (see e.g. [22], Table 1); various Authors remark that Young's modulus and fracture strength are …”