Mechanical behavior of a pm-sized single crystal silicon structure with sharp notches

摘要

The mechanical behavior of μm-sized single crystal silicon structures is investigated in this paper. A new apparatus for microsample tensile testing is used to determine the mechanical properties of single crystal silicon microbars. Force and elongation are measured independently with high accuracy. Elastic constants as well as critical loads are determined. Failure of the sample occurs at the extremities of the microbar at a sharp notch. The stress field in the notch tip vicinity is therefore analyzed to characterize the load capacity of the structure. For this purpose, finite element computations are combined with approximate analytic solutions based on the Stroh formalism. Both the case of plane stress and two-dimensional displacements are considered. Comparison with the FEM solution shows that the plane stress assumption is better, leading to the determination of the critical stress intensity factor Fcr for this case. Because F_cr is dependent on the geometry, a new scalar failure criterion--i.e. a critical radius R_cr--is introduced and derived from the calculated stress field at the notch. It is based on a comparison of stored elastic energy and surface energy at the critical location. Because it is a scalar criterion, it can be applied to single crystal microstructures with notches of arbitrarv notch angle. For the case considered, experiments yield Rcr = 0.8 nm. The proposed criterion can be considered as a step towards the definition of a design rule for sharp notches in single crystal structures, which is required for the optimized design of micromechanical devic