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Local Phonon Density of States in an Elastic Substrate

Michael R. Geller
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Abstract

The local, eigenfunction-weighted acoustic phonon density of states (DOS) tensor is calculated for a model substrate consisting of a semi-infinite isotropic elastic continuum with a stress-free surface. On the surface, the local DOS is proportional to the square of the frequency, as for the three-dimensional Debye model, but with a constant of proportionality that is considerably enhanced compared to the Debye value, a consequence of the Rayleigh surface modes. The local DOS tensor at the surface is also anisotropic, as expected. Inside the substrate the local DOS is both spatially anisotropic and non-quadratic in frequency. However, at large depths, the local DOS approaches the isotropic Debye value. The results are applied to a Si substrate.

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Michael R. Geller. 2004-06-03. Local Phonon Density of States in an Elastic Substrate. https://doi.org/10.1103/physrevb.70.205421

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