Plasmon dispersion in silicon obtained by analytic continuation of the random-phase-approximation dielectric matrix

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Abstract
The plasmon dispersion in silicon has been determined along the Δ and Λ axis of the first Brillouin zone, taking local-field effects fully into account. The empirical pseudopotential method has been used to obtain the electron band structure. A very effective method of analytic continuation is employed to obtain the singular integrals involved in the calculation of the random-phase-approximation polarization matrix. Using the analytic continuation of the dielectric matrix across its branch cut, we investigate the plasmon energies and lifetimes. It is shown that the experimental observability of the theoretically obtained plasmon band gap at the L point is questionable due to an unexpectedly large lifetime of plasmons in the second band as compared with those in the first band. The obtained plasmon energies are typically 10% larger than the reported experimental values. The calculated plasmon energies display a stronger dispersion than the experimental values. Moreover, the experimentally observed anisotropy in the dispersion along the Δ and Λ axis is not reproduced by our calculations.