Abstract
We have performed simulations of dispersion relations for surface acoustic waves in two-dimensional phononic crystal by the finite elements method (FEM) and by the plane wave method (PWM). Considered medium is a thin nickel layer on a silicon single crystal (001) surface. The nickel film is decorated with cylindrical holes of the depth equal to the nickel film thickness arranged in a square lattice. We have obtained full bandgaps for the surface waves propagating in the medium of particular range of filling factor and layer thickness. The width of the bandgap had reached over 500[MHz] for the sample of the lattice constant 500[nm] and is sufficient for experimental design.
Highlights
Properties of elastic waves are interesting in periodic media, characterized by periodic spatial distribution of density and elasticity coefficients
Elastic waves propagate in the form of Bloch waves so that the vector of deformation is periodic in the reciprocal lattice, uk = uk+G, so all inequivalent excitations are found in the first Brillouin zone
At the borders of the first Brillouin zone the energy bandgaps appear, i.e. there are the ranges of frequencies to which no wave vector corresponds in the dispersion relation, so no waves of such frequencies propagate in the medium
Summary
Properties of elastic waves are interesting in periodic media, characterized by periodic spatial distribution of density and elasticity coefficients. At the borders of the first Brillouin zone the energy bandgaps appear, i.e. there are the ranges of frequencies to which no wave vector corresponds in the dispersion relation, so no waves of such frequencies propagate in the medium. This property has been well-known in the band theory of electron waves but it holds true for all other waves in solid state. The periodic media in which elastic waves are studied in the aspect of the search for acoustic bandgaps are known as phononic crystals Both bulk and surface waves are studied for over a decade, mainly in order to establish the full bandgap. The phononic crystals of a lattice constant of an order of hundred nanometers can simultaneously be photonic crystals, which fosters the hope of getting interesting acousto - optical effects
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