Non-substitutional Sn Defects in Ge_1−x Sn _x Alloys for Opto- and Nanoelectronics

Abstract

Important technological applications are envisaged for Ge_1−x Sn _x alloys. They provide a route to obtain direct-gap group IV materials, tuneable by concentration. Therefore, these alloys are ideal candidates for optoelectronic devices, highly compatible with Si integrated circuits. Contrary to other binary alloys with group IV elements, homogeneous Ge_1−x Sn _x alloys, as required for device applications, have proven difficult to form above a certain temperature-dependent critical Sn concentration. Through a detailed ab-initio local defect study, and the proposal of a statistical model for the formation of these alloys, we predicted that a new type of Sn defect (β-Sn), consisting of a single Sn atom in the centre of a Ge divacancy, might be formed. The environment of this defect relaxes towards a cubic octahedral configuration, facilitating the nucleation of white tin and its segregation, as found in amorphous samples. We confirmed that Sn would enter substitutionally in the Ge lattice, but above a temperature-dependent critical concentration, non-substitutional β-Sn defects should be formed, consistent with experimental observations.

In this paper we introduce a two-site substitutional equivalent for the non-substitutional β-Sn defect in Ge, as needed in order to be able to include β-Sn in electronic structure calculations with effective-field electronic models for disorder, like the Virtual Crystal Approximation (VCA). The equivalent substitutional model is derived in order to take into account the different symmetries in the immediate environment of the substitutional α and non-substitutional β defect sites and their effect on the electronic structure.