Structural properties of Silicon-Germanium and Germanium-Silicon Core-Shell Nanowires

TL;DR

This study uses ab initio DFT calculations to analyze the detailed atomic structure and strain distribution in Si/Ge and Ge/Si core-shell nanowires, revealing limitations of Vegard's law and highlighting strain effects at interfaces.

Contribution

It provides a detailed atomistic analysis of strain and structural properties in core-shell nanowires, emphasizing the need for ab initio methods over empirical laws.

Findings

Vegard's law can lead to up to 1% error in lattice constant predictions.

Si core or shell always expands regardless of composition.

Strain patterns are highly sensitive to location, composition, and bond direction.

Abstract

Core-shell nanowires made of Si and Ge can be grown experimentally with excellent control for different sizes of both core and shell. We have studied the structural properties of Si/Ge and Ge/Si core-shell nanowires aligned along the $[110]$ direction, with diameters up to 10.2~nm and varying core to shell ratios, using linear scaling Density Functional Theory (DFT). We show that Vegard's law, which is often used to predict the axial lattice constant, can lead to an error of up to 1\%, underlining the need for a detailed \emph{ab initio} atomistic treatment of the nanowire structure. We analyse the character of the intrinsic strain distribution and show that, regardless of the composition or bond direction, the Si core or shell always expands. In contrast, the strain patterns in the Ge shell or core are highly sensitive to the location, composition and bond direction. The highest strains are found at heterojunction interfaces and the surfaces of the nanowires. This detailed understanding of the atomistic structure and strain paves the way for studies of the electronic properties of core-shell nanowires and investigations of doping and structure defects.