  High-entropy alloys (HEAs), which have been intensely studied due to their
excellent mechanical properties, generally refer to alloys with multiple
equimolar or nearly equimolar elements. According to this definition, Si-Ge-Sn
alloys with equal or comparable concentrations of the three Group IV elements
belong to the category of HEAs. As a result, the equimolar elements of Si-Ge-Sn
alloys likely cause their atomic structures to exhibit the same core effects of
metallic HEAs such as lattice distortion. Here we apply density functional
theory (DFT) calculations to show that the SiGeSn HEA indeed exhibits a large
local distortion effect. Unlike metallic HEAs, our Monte Carlo and DFT
calculations show that the SiGeSn HEA exhibits no chemical short-range order
due to the similar electronegativity of the constituent elements, thereby
increasing the configurational entropy of the SiGeSn HEA. Hybrid density
functional calculations show that the SiGeSn HEA remains semiconducting with a
band gap of 0.38 eV, promising for economical and compatible mid-infrared
optoelectronics applications. We then study the energetics of neutral single
Si, Ge, and Sn vacancies and (expectedly) find wide distributions of vacancy
formation energies, similar to those found in metallic HEAs. However, we also
find anomalously small lower bounds (e.g., 0.04 eV for a Si vacancy) in the
energy distributions, which arise from the bond reformation near the vacancy.
Such small vacancy formation energies and their associated bond reformations
retain the semiconducting behavior of the SiGeSn HEA, which may be a signature
feature of a semiconducting HEA that differentiates from metallic HEAs.
