Systematic inclusion of the effect of an arbitrary surface profile on the dispersion of surface plasmons

The classical Boltzmann equation approach is developed to systematically include the effect of surface diffuseness in the random phase approximation (RPA) surface plasmon dispersion relation. This is achieved by the introduction of an arbitrary surface potential energy barrier into the distribution function. The resulting Fourier-transformed, linearized equation is solved by a perturbative-iterative scheme based on an expansion of the response function beyond the usual step-function form. The surface plasmon dispersion curves obtained lend support to the more recent experimental results which indicate an almost flat to slightly increasing small wavenumber behaviour. Noticeable dipping of the curves only occurs for broad surface regions, suggestive of surface contamination.