Theoretical study of two expanded phases of crystalline germanium: clathrate-I and clathrate-II

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Abstract
We study two expanded phases of Ge crystals, type-I (Ge46) and type-II (Ge136) clathrates, using an ab initio density functional planewave pseudopotential method. The equation of state, electronic structure and vibrational modes have been determined. These expanded Ge phases are shown to be only slightly higher in energy than the diamond phase (0.05 eV/atom), and considerably lower in energy than the compressed -tin phase by about 0.14 eV/atom. The electronic band-gaps of Ge clathrates are about 1.21 eV (type-I) and 0.75 eV (type-II) wider that band-gaps in the diamond phase. We have determined lattice vibrational modes and the frequencies of the Raman and infrared modes. The results of Ge clathrates are compared and contrasted with those of Si clathrates, where experiments are more numerous.