Atomistic structure and energetics of GdN clusters in Gd-doped GaN

We present a transmission electron microscopy (TEM) and density-functional theory (DFT) study of the structure, formation and energetics of nanoscale clusters of GdN in Gd-doped GaN, a well-known magnetic semiconductor. The atomic configuration of the clusters was determined by comparing displacement maps from high-resolution TEM images to those predicted by atomistic models. We find that the GdN clusters are coherently embedded in the GaN lattice, and have a bilayer platelet shape whose internal crystal structure is slightly distorted rocksalt. The optimum width of the platelet clusters was explored using DFT in conjunction with a Frenkel-Kontorova (FK) model for describing the energetics of embedding. The results predict a platelet width that is reasonably consistent with the size obtained from TEM images. The FK results indicate that the observed platelet size is a compromise between the gain in cohesive energy from forming large GdN clusters and the penalty from interfacial strain energy due to lattice mismatch between the GdN cluster and GaN host.