Structural and electronic properties ofα-tin nanocrystals from first principles

Abstract

The $\ensuremath{\alpha}$ phase of tin is a zero-gap semiconductor with an inverted band structure with respect to other group-IV elements like Ge. The ${\ensuremath{\Gamma}}_{6c}$ states lie energetically below the ${\ensuremath{\Gamma}}_{8v}$ 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 $\ensuremath{\alpha}$-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 $\ensuremath{\Delta}$SCF method.