Non-substitutional single-atom defects in the Ge_(1-x)Sn_x alloy

TL;DR

This study investigates the formation and properties of non-substitutional single-atom defects in GeSn alloys, revealing their role in alloy formation limits and electronic behavior through ab-initio calculations and statistical modeling.

Contribution

It introduces a new type of defect ($eta$-Sn in a divacancy) in GeSn alloys and develops a model explaining alloy formation limits based on defect concentration.

Findings

$eta$ defect relaxes to a cubic octahedral environment

Critical concentration for alloy formation matches experimental data

Lower temperatures increase the critical concentration

Abstract

Ge_(1-x)Sn_x alloys have proved difficult to form at large x, contrary to what happens with other group IV semiconductor combinations. However, at low x they are typical examples of well-behaved substitutional compounds, which is desirable for harnessing the electronic properties of narrow band semiconductors. In this paper, we propose the appearance of another kind of single-site defect ($\beta-Sn$), consisting of a single Sn atom in the center of a Ge divacancy, that may account for these facts. Accordingly, we examine the electronic and structural properties of these alloys by performing extensive numerical ab-initio calculations around local defects. The results show that the environment of the $\beta$ defect relaxes towards a cubic octahedral configuration, facilitating the nucleation of metallic white tin and its segregation, as found in amorphous samples. Using the information stemming from these local defect calculations, we built a simple statistical model to investigate at which concentration these $\beta$ defects can be formed in thermal equilibrium. These results agree remarkably well with experimental findings, concerning the critical concentration above which the homogeneous alloys cannot be formed at room temperature. Our model also predicts the observed fact that at lower temperature the critical concentration increases. We also performed single site effective-field calculations of the electronic structure, which further support our hypothesis.