The structure, energy, and electronic states of vacancies in Ge nanocrystals

TL;DR

This study uses density functional theory to analyze vacancies in germanium nanocrystals, revealing how surface effects influence vacancy formation energy and electronic states, with implications for defect behavior in nanostructures.

Contribution

It provides detailed insights into vacancy properties in Ge nanocrystals, highlighting the dominant role of surface relaxations over self-purification effects.

Findings

Surface relaxations significantly lower vacancy formation energy.

Vacancies behave bulk-like beyond 0.7 nm from the surface.

No evidence of self-purification effect in nanocrystals.

Abstract

The atomic structure, energy of formation, and electronic states of vacancies in H-passivated Ge nanocrystals are studied by density functional theory (DFT) methods. The competition between quantum self-purification and the free surface relaxations is investigated. The free surfaces of crystals smaller than 2 nm distort the Jahn-Teller relaxation and enhance the reconstruction bonds. This increases the energy splitting of the quantum states and reduces the energy of formation to as low as 1 eV per defect in the smallest nanocrystals. In crystals larger than 2 nm the observed symmetry of the Jahn-Teller distortion matches the symmetry expected for bulk Ge crystals. Near the nanocrystal's surface the vacancy is found to have an energy of formation no larger than 0.5 to 1.4 eV per defect, but a vacancy more than 0.7 nm inside the surface has an energy of formation that is the same as in bulk Ge. No evidence of the self-purification effect is observed; the dominant effect is the free surface relaxations, which allow for the enhanced reconstruction. From the evidence in this paper, it is 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 is within 0.7 nm of the surface.