Effect of surface stress on the stiffness of microanocantilevers: Nanowire elastic modulus measured by nano-scale tensile and vibrational techniques

摘要

Surface stress induced stiffness change of microanocantilevers is reviewed and rigorously examined in this work. The self-equilibrium strain field of microanocantilevers carrying an inherent surface stress on substrate is derived by resorting to the generalized Young-Laplace equation. It is found that the mechanism responsible for the observed stiffness change of microano cantilevers originating from surface stress cannot be attributed to the development of in-plane stress near the clamp. Based on the analysis, two loading modes used in the mechanical test experiments performed on nanowire (NW) are theoretically investigated in detail: tension and electrically-induced-vibration. Lattice distortions arising from surface stress, coupled with that induced by residual strain, are shown to play a significant role in the elastic modulus measurement of NWs using an electric-field-induced vibrational mode, but have no influences on the tensile testing mode. The analytical results are validated by comparisons with molecular dynamic simulations and experimental measurements. The present results are useful in interpreting differences in observed size-dependent elasticity of NWs and developing the nano- and micro-mechanical testing techniques.