Enhancing the electronic and optical properties of germanium nanoclusters through alkali metal doping: a case study on Na 2

In the present study, we have examined the key insight into structural, electronic, and optical properties of Na 2 doped germanium nano-cluster using density functional theory. Analysis of binding energy (BE) indicates enhanced thermodynamical stability increases with cluster size, where Ge 5 Na 2 and Ge 10 Na 2 exhibiting highest BE. Second order energy suggest that cluster with n = 2, 5, 6, and 9 are most stable while thpse with n = 3, 4, and 7 shows lower stability. Embedding energy (EE) shows decreases curve with cluster size indicating large clusters are more favourable for Na encapsulation. Large HOMO–LUMO gap ranges from 1.4 to 3.2 eV illustrate semiconductor nature of clusters. Further investigation of hyperpolarizability suggesting non-linear optical (NLO) activity for Ge n Na 2 (n = 1–4), while lower NLO features shown in high symmetry clusters with n = 5 and 6. These results imply that Ge n Na 2 clusters have potential uses in optoelectronic and semiconductor devices.