Theory of melting in the group-IV semiconductors

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Abstract
We have calculated the melting curves of germanium and silicon. A model of the group-IV semiconductors was used for which the solid consists of interacting systems of ions, conduction electrons, and covalent bond charges. The liquid state of these elements is metallic, and the model used to describe it consists of interacting systems of ions and conduction electrons. Variational calculations were performed to obtain Gibbs free energies for the solid and liquid states. Three adjustable parameters were necessary to describe the interactions between the various components of the models which are yet insufficiently understood for ab initio treatment. Excellent agreement with experiment was obtained for calculations of the melting curves up to 46 kbar for Ge and 21 kbar for Si. The physical origin of the negative-slope melting curve lies in the relatively open diamond-crystal structure and the covalent bonding which stabilizes this structure. The diamond structure is sufficiently openly packed that the liquid finds it energetically favorable to be more dense than the solid in these materials.