  GeSn on Si has attracted much research interest due to its tunable direct
bandgap for mid-infrared applications. Recently, short-range order (SRO) in
GeSn alloys has been theoretically predicted, which profoundly impacts the band
structure. However, characterizing SRO in GeSn is challenging. Guided by
physics-informed Poisson statistical analyses of Kth-nearest neighbors (KNN) in
atom probe tomography, a new approach is demonstrated here for 3D nanoscale SRO
mapping and semi-quantitative strain mapping in GeSn. For GeSn with ~14 at.%
Sn, the SRO parameters of Sn-Sn 1NN in 10x10x10 nm$^{3}$ nanocubes can deviate
from that of the random alloys by $\pm$15%. The relatively large fluctuation of
the SRO parameters contributes to band-edge softening observed optically. Sn-Sn
1NN also tends to be more favored towards the surface, less favored under
strain relaxation or tensile strain, while almost independent of local Sn
composition. An algorithm based on least square fit of atomic positions further
verifies this Poisson-KNN statistical method. Compared to existing macroscopic
spectroscopy or electron microscopy techniques, this new APT statistical
analysis uniquely offers 3D SRO mapping at nanoscale resolution in a relatively
large volume with millions of atoms. It can also be extended to investigate SRO
in other alloy systems.
