Statistical Studies on Random Configurations of Silicon Germanium Carbon Alloys Using Density Functional Theory

SiGeC, a random alloy, is studied by means of density
functional
theory for different Si:Ge ratios across the whole composition range
and small C concentrations of 1.6 and 3.2% in Si-rich alloys. The
random occupation of lattice sites in SiGeC results in statistical
variations of material properties, which we investigate using ≈20,000
random configurations. This is an alternative approach to methods
such as the virtual crystal approximation or the special quasi-random
structure method because the presented approach allows access to statistical
fluctuations. These fluctuations can be seen in the formation energy
of the SiGe alloy, and the fluctuations increase with increasing C
content. In addition, we can associate those fluctuations to structural
features. Stability analysis based on the Gibbs energy shows that
an elevated temperature is required to stabilize the random alloy
via entropic contributions. The solubility of C is rather small (<1%
at room temperature, up to 1.5% at 500 K), depends on the Ge content,
and increases with rising temperature. We also study the band gap
considering methodological as well as structural implications: Their
quantitative values are strongly affected by finite-size effects due
to periodic boundary conditions in the simulation, leading to larger
band gap variations than potentially observable. Despite this issue,
we can conclude qualitative trends such as rising band gap variations
with increasing C content.