Structural and electronic properties of α-tin nanocrystals from first principles

The alpha phase of tin is a zero-gap semiconductor with an inverted band structure with respect to other group-IV elements like Ge. The Gamma(6c) states lie energetically below the Gamma(8 nu) levels. How these unique electronic properties transform in nanostructures with spatial confinement has not been studied. We apply density-functional theory within the local density approximation to investigate the energetic, structural, and electronic properties of bulk alpha-Sn and its nanocrystals (NCs) up to a size of 363 Sn atoms. For NCs with larger diameters up to 14 nm the tight-binding method is applied for the electronic states. Spin-orbit coupling is taken into account. The clusters are modeled in such a way that the T-d symmetry of the bulk system is conserved. Their surfaces are passivated with hydrogen. We show that the spatial confinement causes not only a decrease of the fundamental gap for increased NC size but also a topological transition where the ordering of s- and p-like highest-occupied molecular orbital and lowest-unoccupied molecular orbital states is interchanged. The influence of quasiparticle and excitonic effects on the lowest pair excitation energies is investigated within approximations based on the hybrid exchange-correlation functional by J. Heyd, G. E. Scuseria, and M. Ernzerhof [J. Chem. Phys. 118, 8207 (2003)] (HSE) and the Delta SCF method.