Bandgap calculation of in-plane waves in nanoscale phononic crystals taking account of surface/interface effects

• The DtN-map method is extended to research the in-plane waves in nanoscale PNCs.
• We generalize a surface parameter to characterize the surface/interface effects.
• The surface/interface effects have significant influences on the band structures.

In the present paper, the band structures of in-plane waves propagating in two-dimensional nanoscale phononic crystals composed of voids/inclusions in an elastic solid in square and triangular lattices are calculated by the method based on the Dirichlet-to-Neumann map. The surface/interface effects are taken into account due to the high surface-to-volume ratio by applying the Young–Laplace equilibrium equation at the surface/interface. Three systems at nanoscale are calculated in details: vacuum holes in an aluminum matrix in square and triangular lattices, aluminum cylinders in tungsten matrix in a square lattice, and tungsten cylinders in aluminum in a square lattice. The results show that the surface/interface effects are significant when the dimensions of the phononic crystals approach the nanometer scale.

The band structures of the PNC of a square lattice of vacuum cylindrical holes in aluminum matrix without (black) and with (red) the surface effect.Figure optionsDownload as PowerPoint slide