Molecular Dynamics Simulation of Elastic Properties of Silicon Nanocantilevers

Abstract

The molecular dynamics simulation of nanoscale cantilevers made of pure crystalline silicon with different lattice conditions is presented. Young's moduli for various sized specimen is obtained by simulating clamped-free cantilever beam vibrations and static tensile responses. Young's modulus decreases monotonically as the thickness of the specimen decreases. Although significant discrepancies exist between the simulated and experimentally determined Young's modulus, incorporating a minute amount of voids in the specimen during simulation offers a partial account of this discrepancy. The dependence of the Young's modulus on dimensional scaling is then applied to estimate thermal fluctuations of the cantilever under various temperatures, sizes, and lattice conditions and shows excellent agreement with the theoretical estimate based on the equipartition theorem. Finally, the applicability of the nanocantilevers as molecular mass sensors is demonstrated by simulating the change in the first flexural mode frequency as the number of silicon molecules placed at the tip of the cantilever is varied. The results show good agreement with the theoretical predictions of the Euler-Bernoulli beam vibration model.