Planar force-constant models and internal strain parameter of Ge and Si

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Abstract
The phonon-dispersion relations of Ge and Si along [100] and [111] are accurately fitted with planar force-constant models, including a generalization that treats electronic as well as ionic degrees of freedom. Expressions for the internal strain parameter ζ as a function of the planar force constants for longitudinal phonons propagating along [111] and for transverse phonons along either [100] or [111] are derived. It is shown that these expressions lead to inconsistent values of ζ if the electronic degrees of freedom are omitted. Their inclusion restores consistency and leads to values of ζ equal to 0.577±0.027 for Ge and 0.564±0.030 for Si.