The atomic structure, energy of formation, and electronic states of vacancies in H-passivated Ge nanocrystals were studied by density-functional theory methods. The competition between quantum self-purification and the free surface relaxations was investigated. The free surfaces of crystals smaller than 2nm distorted the Jahn-Teller relaxation and enhanced the reconstruction bonds. This increased the energy splitting of the quantum states and reduced the energy of formation to as low as 1eV per defect in the smallest nanocrystals. In crystals larger than 2nm the observed symmetry of the Jahn-Teller distortion matches the symmetry expected for bulk Ge crystals. Near the nanocrystal surface the vacancy was found to have an energy of formation no larger than 0.5–1.4eV per defect, but a vacancy more than 0.7nm inside the surface has an energy of formation that was the same as in bulk Ge. No evidence of the self-purification effect was observed; the dominant effect was the free surface relaxations, which allowed for the enhanced reconstruction. From the evidence in this paper, it was predicted that for moderate sized Ge nanocrystals a vacancy inside the crystal will behave bulk-like and not interact strongly with the surface, except when it was within 0.7nm of the surface.

Structure, Energy, and Electronic States of Vacancies in Ge Nanocrystals. K.Bayus, O.Paz, S.P.Beckman: Physical Review B, 2010, 82[15], 155409