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 direction, with diameters up to 10.2 nm and varying core to shell ratios, using linear scaling density functional theory. 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 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.
Highlights
Scaling down the size of the current generation of electronic devices has led to an increased interest in semiconductor nanostructures, such as nanowires and nanotubes [1,2,3,4,5]
We have studied the structural properties of Si/ Ge and Ge/Si core–shell nanowires aligned along the [1 1 0] direction, with diameters up to 10.2 nm and varying core to shell ratios, using linear scaling density functional theory
It is interesting to note that the core of the NW does not have the same radial freedom as the shell, which can expand into the vacuum, nor the strains induced by reconstruction; as we will see for these nanowires and the present method, the anisotropy is largely associated with germanium, while silicon is much more uniformly strained. (We note that silicon does have a larger Young’s modulus than germanium [53], but it is unlikely that the cause is anything this simple.)
Summary
Scaling down the size of the current generation of electronic devices has led to an increased interest in semiconductor nanostructures, such as nanowires and nanotubes [1,2,3,4,5]. We use linear scaling density functional theory (DFT) to study the structural and strain properties of Si/Ge and Ge/Si core–shell nanowires, as a function of nanowire composition and diameter, from ∼5 nm to ∼10 nm. We use linear scaling DFT to explore the applicability of Vegard’s law estimates to Si/Ge core–shell nanowires, even though these heterostructures do not fall within the area where the law was first derived This analysis is needed for core–shell nanowires, due to highly inhomogeneous and anistropic strain distribution generated as a result of non-statistical distribution of Si and. We explore the accuracy of Vegard’s law in determining the axial lattice constant, and investigate the intrinsic strain patterns of the core–shell nanowires, how these change with core to shell ratio, core–shell composition and diameter
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