Phonon spectra of diamond, Si, Ge, andα−Sn: Calculations with real-space interatomic force constants

Abstract

The phonon spectra of diamond, Si, Ge, and $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Sn}$ are systematically investigated by using real-space interatomic force constants (IFC's) up to the 25th shell. The calculations are performed employing density functional perturbation theory, a pseudopotential plane-wave approach, and the local density approximation for the exchange-correlation potential. Moreover, analytical expressions are derived for the phonon frequencies at some high-symmetry points, in terms of the IFC's up to second nearest neighbors. Compared to those of Si, Ge, and $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Sn}$, the IFC's of diamond are found to be larger in magnitude and those of the first and second shells show significantly different relative strengths. The reasons behind the peculiar features of the phonon spectra of diamond are identified. Contrary to a common belief, the flatness of some transverse acoustical phonon branches (of Si, Ge, and $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Sn}$) appears only after including IFC's up to the eighth shell. The calculated phonon spectra are in good agreement with the available experimental data, for the four considered systems.