We present a theoretical framework allowing to properly address the nature ofsurface-like eigenmodes in a hypersonic surface phononic crystal, a compositestructure made of periodic metal stripes of nanometer size and periodicity of 1micron, deposited over a semi-infinite silicon substrate. In surface-basedphononic crystals there is no distinction between the eigenmodes of theperiodically nanostructured overlayer and the surface acoustic modes of thesemi-infinite substrate, the solution of the elastic equation being apseudo-surface acoustic wave partially localized on the nanostructures andradiating energy into the bulk. This problem is particularly severe in thehypersonic frequency range, where semi-infinite substrate's surface acousticmodes strongly couple to the periodic overlayer, thus preventing anyperturbative approach. We solve the problem introducing a surface-likenesscoefficient as a tool allowing to find pseudo-surface acoustic waves and tocalculate their line shapes. Having accessed the pseudo-surface modes of thecomposite structure, the same theoretical frame allows reporting on the gapopening in the now well-defined pseudo-SAW frequency spectrum. We show how thefilling fraction, mass loading and geometric factors affect both the frequencygap, and how the mechanical energy is scattered out of the surface waveguidingmodes.
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